ConocoPhillips Company Debt Securities fully and unconditionally guaranteed by ConocoPhillips UNDERWRITING AGREEMENT

Exhibit 1.1

ConocoPhillips Company

Debt Securities

fully and unconditionally guaranteed by ConocoPhillips

UNDERWRITING AGREEMENT

1. Introductory. ConocoPhillips, a Delaware corporation (the “Company”), and ConocoPhillips Company, a Delaware corporation and a wholly owned subsidiary of ConocoPhillips (the “Issuer”), propose that the Issuer will issue and sell from time to time certain of its unsecured debt securities fully and unconditionally guaranteed by the Company registered under the registration statement referred to in Section 2(a) (such securities, including the guarantee relating thereto by the Company (the “Guarantee”), being hereinafter called the “Registered Securities”). The Registered Securities will be issued under an indenture, dated as of the Closing Date (as defined below) (the “Indenture”), among the Issuer, the Company and The Bank of New York Trust Company, N.A., as trustee (the “Trustee”), in one or more series, which series may vary as to interest rates, maturities, redemption provisions, selling prices and other terms, with all such terms for any particular series of the Registered Securities being determined at the time of sale. Particular series of the Registered Securities will be sold pursuant to a Terms Agreement referred to in Section 3, for resale in accordance with terms of offering determined at the time of sale.

The Registered Securities involved in any such offering are hereinafter referred to as the “Offered Securities”. The firm or firms which agree to purchase the Offered Securities, as set forth in a Terms Agreement referred to in Section 3 hereof, are hereinafter referred to as the “Underwriters” of such securities, and the representative or representatives of the Underwriters, if any, specified in a Terms Agreement referred to in Section 3 are hereinafter referred to as the “Representatives”; provided, however, that if the Terms Agreement does not specify any representative of the Underwriters, the term “Representatives”, as used in this Agreement (other than in Sections 2(b), 2(c), 2(f) and 6 and the second sentence of Section 3), shall mean the Underwriters.

2. Representations and Warranties of the Issuer and the Company. The Company, as of the date of each Terms Agreement referred to in Section 3, represents and warrants to, and agrees with, each Underwriter that:

(a) The Issuer and the Company meet the requirements for use of Form S-3 under the Act and have prepared and filed with the Securities and Exchange Commission (the “Commission”) an automatic shelf registration statement, as defined in Rule 405, on Form S-3 (Nos. 333-179626, 333-179626-03), relating to certain securities of the Company, which registration statement became effective upon filing, and have prepared and filed with the Commission a post-effective amendment to such registration statement dated December 4, 2012, including a prospectus (hereinafter referred to as the “Base Prospectus”), relating to the Registered Securities. Such registration statement, as amended at the time of any Terms Agreement referred to in Section 3 entered into in connection with a

specific offering of the Offered Securities (each such date and time as specified in such Terms Agreement hereinafter referred to as the “Execution Time”) and including any documents incorporated by reference therein, including exhibits (other than any Form T-1) and financial statements and any prospectus supplement relating to the Offered Securities that is filed with the Commission pursuant to Rule 424(b) (“Rule 424(b)”) under the Securities Act of 1933 (the “Act”) and deemed part of such registration statement pursuant to Rule 430B under the Act, is hereinafter referred to as the “Registration Statement.” The Base Prospectus, as supplemented as contemplated by Section 3 to reflect the terms of the Offered Securities and the terms of offering thereof, as first filed with the Commission pursuant to and in accordance with Rule 424(b), including all material incorporated by reference therein, is hereinafter referred to as the “Final Prospectus.” Any preliminary prospectus supplement to the Base Prospectus which describes the Offered Securities and the offering thereof and is used prior to filing of the Final Prospectus, together with the Base Prospectus, is hereinafter referred to as the “Preliminary Final Prospectus.” “Free Writing Prospectus” shall mean a free writing prospectus, as defined in Rule 405 under the Act. “Issuer Free Writing Prospectus” shall mean an issuer free writing prospectus, as defined in Rule 433(h) under the Act. “Disclosure Package” shall mean, with respect to any specific offering of the Offered Securities, (i) the Base Prospectus, as amended and supplemented to the Execution Time, (ii) the Preliminary Final Prospectus, if any, used most recently prior to the Execution Time, (iii) the Issuer Free Writing Prospectuses, if any, identified in Schedule B to the Terms Agreement, (iv) the final term sheet prepared and filed pursuant to Section 4(c) hereto, if any, and (v) any other Free Writing Prospectus that the parties hereto shall hereafter expressly agree in writing to treat as part of the Disclosure Package. No document has been or will be prepared or distributed in reliance on Rule 434 under the Act.

(b) On the effective date of the registration statement relating to the Registered Securities, such registration statement conformed in all material respects to the requirements of the Act, the Trust Indenture Act of 1939 (“Trust Indenture Act”) and the rules and regulations of the Commission (“Rules and Regulations”) and did not include any untrue statement of a material fact or omit to state any material fact required to be stated therein or necessary to make the statements therein not misleading, and at the Execution Time and at the Closing Date, the Registration Statement and the Final Prospectus will conform in all material respects to the requirements of the Act, the Trust Indenture Act and the Rules and Regulations, and neither of such documents will include any untrue statement of a material fact or omit to state any material fact required to be stated therein or necessary to make the statements therein not misleading, except that the foregoing does not apply to statements in or omissions from any of such documents based upon written information furnished to the Company by any Underwriter through the Representatives, if any, specifically for use therein.

2

(c) At the Execution Time, the Disclosure Package will not contain any untrue statement of a material fact or omit to state any material fact necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading, except that the foregoing does not apply to statements in or omissions from any of such documents based upon written information furnished to the Company by any Underwriter through the Representatives, if any, specifically for use therein.

(d) (i) At the time of filing the Registration Statement, (ii) at the time of the most recent amendment thereto for the purposes of complying with Section 10(a)(3) of the Act (whether such amendment was by post-effective amendment, incorporated report filed pursuant to Sections 13 or 15(d) of the Exchange Act or form of prospectus), (iii) at the time either the Issuer or the Company or any person acting on its behalf (within the meaning, for this clause only, of Rule 163(c)) made any offer relating to the Offered Securities in reliance on the exemption in Rule 163, and (iv) at the Execution Time (with such date being used as the determination date for purposes of this clause (iv)), each of the Company and the Issuer was or is (as the case may be) a “well-known seasoned issuer” as defined in Rule 405. The Company agrees to pay the fees required by the Commission relating to the Offered Securities within the time required by Rule 456(b)(1) without regard to the proviso therein and otherwise in accordance with Rules 456(b) and 457(r).

(e) (i) At the earliest time after the filing of the Registration Statement that the Issuer or the Company or another offering participant made a bona fide offer (within the meaning of Rule 164(h)(2)) of any Offered Securities and (ii) as of the Execution Time (with such date being used as the determination date for purposes of this clause (ii)), neither the Issuer nor the Company was or is an Ineligible Issuer (as defined in Rule 405), without taking account of any determination by the Commission pursuant to Rule 405 that it is not necessary that the Issuer be considered an Ineligible Issuer or that it is not necessary that the Company be considered an Ineligible Issuer.

(f) Each Issuer Free Writing Prospectus, if any, and the final term sheet prepared and filed pursuant to Section 4(c) hereto do not include any information that conflicts with the information contained in the Registration Statement, including any document incorporated by reference therein and any prospectus supplement deemed to be a part thereof that has not been superseded or modified, except that the foregoing does not apply to statements in or omissions from any of such documents based upon written information furnished to the Company by any Underwriter through the Representatives, if any, specifically for use therein.

(g) The execution, delivery and performance by the Issuer and the Company of the Indenture, the Offered Securities and the Terms Agreement (including the provisions of this Agreement), as applicable, the issuance and sale of the Offered Securities by the Issuer and the Company, as applicable, and compliance by the Issuer and the Company with the terms and provisions thereof will not result in a breach or violation of any of the terms and provisions of, or constitute a default under, the Delaware General Corporation Law, the laws of the

3

State of Texas or the federal laws of the United States that could reasonably be expected to have a material adverse effect on the condition (financial or otherwise), business, properties or results of operations of the Company and its subsidiaries taken as a whole (a “Material Adverse Effect”), or any agreement or instrument to which the Issuer or the Company is a party or by which the Issuer or the Company is bound or to which any of the properties of the Issuer or the Company is subject that could reasonably be expected to have a Material Adverse Effect, or the certificate of incorporation or by-laws of the Issuer or the Company.

(h) Neither the Issuer nor the Company is (i) in violation of its certificate of incorporation or by-laws, (ii) in default under any agreement or instrument to which the Issuer or the Company is a party or by which the Issuer or the Company is bound or to which any of the properties of the Issuer or the Company is subject, or (iii) in violation of any law, ordinance, governmental rule or regulation or court decree to which it may be subject, which default or violation in the case of clause (ii) or (iii) could reasonably be expected to have a Material Adverse Effect.

(i) The Company has prepared, and Ernst & Young LLP has audited, the consolidated balance sheets of the Company as of December 31, 2011 and 2010 and the consolidated statements of income, comprehensive income, changes in equity, and cash flows for each of the three years in the period ended December 31, 2011 (the “Audited Financial Statements”), which are included in the Company’s Current Report on Form 8-K dated December 3, 2012 and incorporated by reference in the Registration Statement, the Disclosure Package and the Final Prospectus. The consolidated financial statements of the Company and its consolidated subsidiaries, together with the related notes thereto, including the Audited Financial Statements, included or incorporated by reference in the Registration Statement, the Disclosure Package and the Final Prospectus, present fairly the financial position of the Company and its consolidated subsidiaries as of the dates shown and their results of operations and cash flows for the periods shown, and such financial statements comply in all material respects as to form with the accounting requirements of the Act and have been prepared in conformity with generally accepted accounting principles in the United States (“GAAP”) applied on a consistent basis throughout the periods involved, except as otherwise noted therein or as may be expressly stated in the related notes thereto. No other financial statements are required to be included in the Registration Statement. The interactive data in eXtensible Business Reporting Language furnished with the Exchange Act filings incorporated by reference in the Registration Statement, the Disclosure Package and the Final Prospectus fairly presents the information called for in all material respects and has been prepared in accordance with the Commission’s rules and guidelines applicable thereto. All non-GAAP financial information included in the Registration Statement, if any, complies with the requirements of Item 10 of Regulation S-K under the Act. The selected financial data set forth in Exhibit 99.1 to the Company’s Current Report on Form 8-K filed December 3, 2012 (the “Selected Financial Data”) fairly present the information included therein and have been compiled on a basis consistent with that of the Audited Financial Statements. The Selected Financial

4

Data for the years ended December 31, 2007 and December 31, 2008 were derived from the Company’s financial statements, and such financial statements were prepared on a basis consistent with that of the Audited Financial Statements. The information under the heading “Ratio of Earnings to Fixed Charges” in the Disclosure Package and the Final Prospectus has been prepared in accordance with the requirements of the Act, has been derived, where applicable, from the financial statements included or incorporated by reference in the Disclosure Package and the Final Prospectus, including the Audited Financial Statements, and fairly presents the information included therein.

3. Purchase and Offering of Offered Securities. The obligation of the Underwriters to purchase the Offered Securities will be evidenced by an agreement or exchange of other written communications (“Terms Agreement”) at the time the Issuer determines to sell the Offered Securities. The Terms Agreement will incorporate by reference the provisions of this Agreement, except as otherwise provided therein, and will specify the firm or firms which will be Underwriters, the names of any Representatives, the principal amount of the Offered Securities to be purchased by each Underwriter, the commission or fee to be paid to the Underwriters and the terms of the Offered Securities not already specified in the Indenture, including, but not limited to, interest rate, maturity, any redemption provisions and any sinking fund requirements. The Terms Agreement will also specify the time and date of delivery and payment (such time and date, or such other time not later than seven full business days thereafter as the Representatives and the Issuer agree as the time for payment and delivery, being herein and in the Terms Agreement referred to as the “Closing Date”), the place of delivery and payment and any details of the terms of offering that should be reflected in the prospectus supplement relating to the offering of the Offered Securities. For purposes of Rule 15c6-1 under the Securities Exchange Act of 1934 (the “Exchange Act”) the Closing Date (if later than the otherwise applicable settlement date) shall be the date for payment of funds and delivery of securities for all the Offered Securities sold pursuant to the offering. The obligations of the Underwriters to purchase the Offered Securities will be several and not joint. It is understood that the Underwriters propose to offer the Offered Securities for sale as set forth in the Final Prospectus.

If the Terms Agreement specifies “Book-Entry Only” settlement or otherwise states that the provisions of this paragraph shall apply, the Issuer will deliver against payment of the cash purchase price the Offered Securities in the form of one or more permanent global securities in definitive form (the “Global Securities”) deposited with the Trustee as custodian for The Depository Trust Company (“DTC”) and registered in the name of Cede & Co., as nominee for DTC. Interests in any permanent global securities will be held only in book-entry form through DTC, except in the limited circumstances described in the Final Prospectus. Payment for the Offered Securities shall be made by the Underwriters in Federal (same day) funds by official check or checks or wire transfer to an account previously designated by the Company at a bank acceptable to the Representatives, in each case drawn to the order of the Issuer at the place of payment specified in the Terms Agreement on the Closing Date, against delivery to the Trustee as custodian for DTC of the Global Securities representing all of the Offered Securities.

5

4. Certain Agreements of the Issuer and the Company. The Issuer and the Company, jointly and severally, agree with the several Underwriters that the Company will furnish to counsel for the Underwriters one signed copy of the registration statement relating to the Registered Securities, including all exhibits, in the form it became effective and of all amendments thereto and that, in connection with each offering of Offered Securities:

(a) The Company will cause the Final Prospectus to be filed with the Commission pursuant to and in accordance with Rule 424(b)(2) (or, if applicable and if consented to by the Representatives, subparagraph (5)) not later than the second business day following the execution and delivery of the Terms Agreement.

(b) During any time when a prospectus relating to the Offered Securities is required to be delivered under the Act in connection with sales by any Underwriter or dealer (including in circumstances where such requirement may be satisfied pursuant to Rule 172), the Company will advise the Representatives promptly of any proposal to amend or supplement the Registration Statement or the Final Prospectus and will afford the Representatives a reasonable opportunity to comment on any such proposed amendment or supplement; and the Company will also advise the Representatives promptly of the filing of any such amendment or supplement and of the institution by the Commission of any stop order proceedings or any notice from the Commission objecting to its use in respect of the Registration Statement or of any part thereof and will use its best efforts to prevent the issuance of any such stop order and to obtain as soon as possible its lifting, if issued.

(c) The Company will prepare a final term sheet, containing solely a description of the Offered Securities, in a form approved by the Representatives, and will cause such term sheet to be filed pursuant to Rule 433(d) under the Act within the time required by such Rule.

(d) If there occurs an event or development as a result of which the Disclosure Package would include an untrue statement of a material fact or would omit to state a material fact necessary in order to make the statements therein, in the light of the circumstances then prevailing, not misleading, the Company will promptly notify the Representatives, so that any use of the Disclosure Package may cease until it is amended or supplemented, and will promptly prepare and cause to be filed with the Commission, at its own expense, an amendment or supplement that will correct such statement or omission or an amendment that will effect such compliance.

(e) If, at any time when a prospectus relating to the Offered Securities is required to be delivered under the Act in connection with sales by any Underwriter or dealer (including in circumstances where such requirement may be satisfied pursuant to Rule 172), any event occurs as a result of which the Final Prospectus as then amended or supplemented would include an untrue statement

6

of a material fact or omit to state any material fact necessary to make the statements therein, in the light of the circumstances under which they were made, not misleading, or if it is necessary at any time to amend the Final Prospectus to comply with the Act, the Company promptly will notify the Representatives of such event and will promptly prepare and cause to be filed with the Commission, at its own expense, an amendment or supplement that will correct such statement or omission or an amendment that will effect such compliance. The terms “supplement” and “amendment” as used in this Agreement include, without limitation, all documents filed by the Issuer and the Company with the Commission subsequent to the date of the Final Prospectus that are deemed to be incorporated by reference in the Final Prospectus. Neither the Representatives’ consent to, nor the Underwriters’ delivery of, any such amendment or supplement shall constitute a waiver of any of the conditions set forth in Section 5 hereof.

(f) As soon as practicable, but not later than 16 months, after the date of each Terms Agreement, the Company will make generally available to security holders of the Issuer an earnings statement of the Company covering a period of at least 12 months beginning after the latest of (i) the effective date of the registration statement relating to the Registered Securities, (ii) the effective date of the most recent post-effective amendment to the Registration Statement to become effective prior to the date of such Terms Agreement and (iii) the date of the Company’s most recent Annual Report on Form 10-K filed with the Commission prior to the date of such Terms Agreement, which will satisfy the provisions of Section 11(a) of the Act.

(g) The Company will furnish to the Representatives copies of the Registration Statement, including all exhibits, and during any time when a prospectus relating to the Offered Securities is required to be delivered under the Act in connection with sales by any Underwriter or dealer (including in circumstances where such requirement may be satisfied pursuant to Rule 172), the Base Prospectus, any related Preliminary Final Prospectus, the Final Prospectus and each Issuer Free Writing Prospectus and all amendments and supplements to such documents, in each case as soon as available and in such quantities as the Representatives reasonably request.

(h) The Company will use its reasonable best efforts to arrange for the qualification of the Offered Securities for sale and the determination of their eligibility for investment under the laws of such jurisdictions as the Representatives designate and will continue such qualifications in effect so long as required for the distribution; provided, however, that neither the Company nor the Issuer will be required in connection therewith to register or qualify as a foreign corporation where it is not now so qualified or to execute a general consent to service of process in any jurisdiction or subject itself to taxation in any jurisdiction where it is not now so subject. The Company will promptly advise the Representatives of the receipt by it or the Issuer of any notification with respect to the suspension of the qualification of the Offered Securities for offer and sale in any such jurisdiction or the initiation or threatening of any proceeding for such purpose.

7

(i) During the period of five years after the date of any Terms Agreement, the Company will furnish or make available to the Representatives and, upon request, to each of the other Underwriters, if any, as soon as practicable after the end of each fiscal year, a copy of the Company’s annual report to stockholders for such year; and the Company will furnish or make available to the Representatives (i) as soon as available, a copy of each report (other than a report on Form 11-K) and any definitive proxy statement of the Company filed with the Commission under the Exchange Act or mailed to stockholders, and (ii) from time to time, such other information concerning the Company or the Issuer as the Representatives may reasonably request in connection with the offering of the Offered Securities.

(j) The Company will pay all expenses incident to the performance of the obligations of the Issuer and the Company under the Terms Agreement (including the provisions of this Agreement), for any filing fees or other expenses (including reasonable fees and disbursements of counsel) in connection with qualification of the Registered Securities for sale and determination of their eligibility for investment under the laws of such jurisdictions as the Representatives may designate in accordance with Section 4(h) and the printing of memoranda relating thereto, for any fees charged by investment rating agencies for the rating of the Offered Securities, for any applicable filing fee incident to, and the reasonable fees and disbursements of counsel for the Underwriters in connection with, the review by the Financial Industry Regulatory Authority, Inc. of the Registered Securities, for any travel expenses of the Issuer’s or the Company’s officers and employees and any other expenses of the Issuer or the Company in connection with attending or hosting meetings with prospective purchasers of Registered Securities and for expenses incurred in preparing, printing and distributing the Final Prospectus, any preliminary prospectuses, any preliminary prospectus supplements or any other amendments or supplements to the Final Prospectus to the Underwriters.

(k) Each of the Issuer and the Company agrees that, unless the Company has obtained or will obtain, as the case may be, the prior written consent of the Representatives, and each Underwriter, severally and not jointly, agrees with the Issuer and the Company that, unless it has obtained or will obtain, as the case may be, the prior written consent of the Company, it has not made and will not make any offer relating to the Offered Securities that would constitute an Issuer Free Writing Prospectus or that would otherwise constitute a “free writing prospectus” (as defined in Rule 405) required to be filed by the Issuer with the Commission or retained by the Issuer under Rule 433, other than the final term sheet prepared and filed pursuant to Section 4(c) hereto; provided that the prior written consent of the parties hereto shall be deemed to have been given in respect of the Free Writing Prospectuses, if any, included in Schedule B to the applicable Terms Agreement. Any such free writing prospectus consented to by the Representatives or the

8

Company is hereinafter referred to as a “Permitted Free Writing Prospectus.” Each of the Issuer and the Company agrees that (x) it has treated and will treat, as the case may be, each Permitted Free Writing Prospectus as an Issuer Free Writing Prospectus and (y) it has complied and will comply, as the case may be, with the requirements of Rules 164 and 433 applicable to any Permitted Free Writing Prospectus, including in respect of timely filing with the Commission, legending and record keeping.

(l) Each of the Issuer and the Company consents to the use by any Underwriter of a free writing prospectus that (a) is not an Issuer Free Writing Prospectus, and (b) contains only (i) information describing the preliminary terms of the Offered Securities or their offering, (ii) information required or permitted by Rule 134 under the Act that is not “issuer information” as defined in Rule 433 or (iii) information that describes the final terms of the Offered Securities or their offering and that is included in the final term sheet prepared and filed pursuant to Section 4(c) hereto.

(m) The Company will not, and will cause the Issuer not to, offer, sell, contract to sell, pledge or otherwise dispose of, directly or indirectly, or file with the Commission a registration statement under the Act relating to United States dollar-denominated debt securities issued or guaranteed by the Issuer or the Company and having a maturity of more than one year from the date of issue, or publicly disclose the intention to make any such offer, sale, pledge, disposition or filing, without the prior written consent of the Representatives for a period beginning at the time of execution of the Terms Agreement and ending the number of days after the Closing Date specified under “Blackout” in the Terms Agreement.

5. Conditions of the Obligations of the Underwriters. The obligations of the several Underwriters to purchase and pay for the Offered Securities will be subject to the accuracy of the representations and warranties on the part of the Issuer and the Company herein, to the accuracy of the statements of Issuer and Company officers made pursuant to the provisions hereof, to the performance by each of the Issuer and the Company of their respective obligations hereunder and to the following additional conditions precedent:

(a) Immediately after the Final Prospectus is filed with the Commission, the Representatives, on behalf of the Underwriters, shall have received a letter, dated as of the Execution Date, of Ernst & Young LLP confirming that they are independent registered public accountants within the meaning of the Act and the applicable published Rules and Regulations thereunder and stating to the effect that:

(i) in their opinion the financial statements and any schedules audited by them and included or incorporated by reference in the Base Prospectus, Preliminary Final Prospectus, Final Prospectus and the Disclosure Package comply as to form in all material respects with the applicable accounting requirements of the Act and the related published Rules and Regulations;

9

(ii) they have performed the procedures specified by the Public Company Accounting Oversight Board for a review of interim financial information as described in Statement of Auditing Standards No. 100, Interim Financial Information, on any unaudited financial statements included in the Registration Statement;

(iii) on the basis of the review referred to in clause (ii) above, a reading of the latest available interim financial statements of the Company, inquiries of officials of the Company who have responsibility for financial and accounting matters and other specified procedures, nothing came to their attention that caused them to believe that:

(A) the unaudited financial statements, if any, included in the Disclosure Package or the Final Prospectus do not comply as to form in all material respects with the applicable accounting requirements of the Act and the related published Rules and Regulations or any material modifications should be made to such unaudited financial statements for them to be in conformity with generally accepted accounting principles;

(B) if any unaudited “capsule” information is contained in the Disclosure Package or the Final Prospectus, the unaudited consolidated total revenues, net income and net income per share amounts or other amounts constituting such “capsule” information and described in such letter do not agree with the corresponding amounts set forth in the unaudited consolidated financial statements or were not determined on a basis substantially consistent with that of the corresponding amounts in the audited statements of income;

(C) at the date of the latest available consolidated balance sheet of the Company read by such accountants, there was any change in the capital stock, any increase in total debt, any decrease in consolidated net current assets (working capital) or any decrease in stockholders’ equity, as compared with amounts shown on the latest consolidated balance sheet included in the Disclosure Package or the Final Prospectus;

(D) At a subsequent specified date not more than three business days prior to the date of such letter, there was any change greater than 1% in the capital stock, or any increase greater than 1% in total debt, as compared with the latest available consolidated balance sheet; or

10

(E) for the period from the closing date of the latest income statement included in the Disclosure Package or the Final Prospectus to the closing date of the latest available income statement read by such accountants there were any decreases, as compared with the corresponding period of the previous year and with the period of corresponding length ended the date of the latest income statement included in the Disclosure Package or the Final Prospectus, in consolidated total revenues or net income;

except in all cases set forth in clauses (C), (D) and (E) above for changes, increases or decreases which the Disclosure Package and the Final Prospectus discloses have occurred or may occur or which are described in such letter;

(iv) they have compared specified dollar amounts (or percentages derived from such dollar amounts) and other financial information contained in the Registration Statement, the Final Prospectus and the Disclosure Package (in each case to the extent that such dollar amounts, percentages and other financial information are derived from the general accounting records of the Company and its subsidiaries subject to the internal controls of the Company’s accounting system or are derived directly from such records by analysis or computation) with the results obtained from inquiries, a reading of such general accounting records and other procedures specified in such letter and have found such dollar amounts, percentages and other financial information to be in agreement with such results, except as otherwise specified in such letter; and

(v) they have read any pro forma financial information which is included in the Disclosure Package or the Final Prospectus and performed the additional procedures suggested by Example D of Statement of Auditing Standards No. 72.

All financial statements and schedules included in material incorporated by reference into the Disclosure Package or the Final Prospectus shall be deemed included in the Disclosure Package or the Final Prospectus for purposes of this subsection.

(b) The Final Prospectus shall have been filed with the Commission in accordance with the Rules and Regulations and Section 4(a) of this Agreement. The final term sheet contemplated by Section 4(c) hereto, and any other material required to be filed by the Company pursuant to Rule 433(d) under the Act, shall have been filed with the Commission within the applicable time periods prescribed for such filings by Rule 433. No stop order suspending the effectiveness of the Registration Statement or of any part thereof or any notice from the Commission objecting to its use shall have been issued and no proceedings for that purpose shall have been instituted or, to the knowledge of the Company or any Underwriter, shall be contemplated by the Commission.

11

(c) Subsequent to the execution of the Terms Agreement, there shall not have occurred (i) any change, or any development or event involving a prospective change, in the condition (financial or other), business, properties or results of operations of the Company and its subsidiaries taken as one enterprise which, in the judgment of a majority in interest of the Underwriters including any Representatives, is material and adverse and makes it impractical or inadvisable to proceed with completion of the public offering or the sale of and payment for the Offered Securities; (ii) any downgrading in the rating of any debt securities of the Issuer or the Company by any “nationally recognized statistical rating organization” (as defined in Section 3(a)(62) of the Exchange Act), or any public announcement that any such organization has under surveillance or review its rating of any debt securities of the Company (other than an announcement with positive implications of a possible upgrading, and no implication of a possible downgrading, of such rating); (iii) any material suspension or material limitation of trading in securities generally on the New York Stock Exchange, or any setting of minimum prices for trading on such exchange or any suspension of trading of any securities of the Company on any exchange or in the over-the-counter market; (iv) any banking moratorium declared by U.S. Federal or New York authorities; or (v) any outbreak or escalation of major hostilities in which the United States is involved, any declaration of war by Congress or any other substantial national or international calamity or emergency if, in the judgment of a majority in interest of the Underwriters including any Representatives, the effect of any such outbreak, escalation, declaration, calamity or emergency makes it impractical or inadvisable to proceed with completion of the public offering or the sale of and payment for the Offered Securities.

(d) The Representatives, on behalf of the Underwriters, shall have received an opinion, dated the Closing Date, of Bracewell & Giuliani LLP, counsel for the Company, to the effect that:

(i) the Company has been duly incorporated and is an existing corporation in good standing under the laws of the State of Delaware, with corporate power and authority to own its properties and conduct its business as described in the Final Prospectus;

(ii) the Indenture has been duly authorized, executed and delivered by the Issuer and has been duly qualified under the Trust Indenture Act; the Offered Securities have been duly authorized, executed, issued and delivered by the Issuer; the Indenture and the Offered Securities are, and when authenticated and delivered by the Trustee pursuant to the terms of the Indenture and paid for by the Underwriters in accordance with the Terms Agreement (including this Agreement incorporated by reference in the Terms Agreement) will be, valid and legally binding obligations of the Issuer, enforceable against the Issuer in accordance with their terms; the Indenture and the Guarantee has been duly authorized, executed and delivered by the Company and is a valid and legally binding obligation of the Company, enforceable against the Company in accordance with its

12

terms, except in each case to the extent such enforceability may be limited by applicable bankruptcy, insolvency, fraudulent conveyance or transfer, reorganization, moratorium and similar laws of general applicability relating to or affecting creditors’ rights and to general principles of equity (whether considered in a proceeding in equity or at law); and the Offered Securities conform in all material respects to the description thereof contained in the Disclosure Package and the Final Prospectus;

(iii) no consent, approval, authorization or order of, or filing with, any governmental agency or body or any court is required under the Delaware General Corporation Law, the laws of the State of Texas or the federal laws of the United States for the consummation of the transactions contemplated by the Terms Agreement (including the provisions of this Agreement) in connection with the issuance or sale of the Offered Securities by the Issuer, or with the issuance or sale of the Guarantee by the Company, except such as have been obtained and made under the Act and the Trust Indenture Act and such as may be required under state securities laws;

(iv) the execution, delivery and performance by the Issuer and the Company of the Indenture and the Offered Securities and by the Issuer and the Company of the Terms Agreement (including the provisions of this Agreement) and the issuance and sale of the Offered Securities by the Issuer and of the Guarantee by the Company, and compliance by the Issuer and the Company with the terms and provisions thereof will not result in a breach or violation of any of the terms and provisions of, or constitute a default under, the Delaware General Corporation Law, the laws of the State of Texas or the federal laws of the United States; and the Issuer has all necessary corporate power and authority to authorize, issue and sell the Offered Securities and the Company has all necessary corporate power and authority to authorize and issue the Guarantee as contemplated by the Terms Agreement (including the provisions of this Agreement);

(v) the Registration Statement has become effective under the Act, the Final Prospectus was filed with the Commission pursuant to the subparagraph of Rule 424(b) specified in such opinion on the date specified therein and the final term sheet contemplated by Section 4(c) hereto has been filed with the Commission within the applicable time period prescribed therefor by Rule 433, and, to the knowledge of such counsel, no stop order suspending the effectiveness of the Registration Statement or any part thereof or any notice from the Commission objecting to its use has been issued and no proceedings for that purpose have been instituted or are pending or threatened under the Act, and the Registration Statement, as of its latest effective date, the Registration Statement and the Final Prospectus, as of the Execution Time, (in each case, other than the financial statements and schedules, the notes thereto

13

and the auditor’s reports thereon, management’s report on internal control over financial reporting, if any, and the other financial, reserve engineering, numerical, statistical and accounting data included or incorporated by reference therein, or omitted therefrom, as to which such counsel need not comment), appear on their face to comply as to form in all material respects with the requirements of the Act, the Trust Indenture Act and the Rules and Regulations; and

(vi) the Terms Agreement (including the provisions of this Agreement) has been duly authorized, executed and delivered by the Issuer and the Company.

(e) The Representatives, on behalf of the Underwriters, shall have received an opinion, dated the Closing Date, of Christopher A. Lause, Esq., Managing Counsel for the Company, to the effect that:

(i) the Company is duly qualified to do business as a foreign corporation in good standing in all jurisdictions in which its ownership or lease of property or the conduct of its business requires such qualification, except to the extent that the failure to be so qualified or be in good standing would not have a material adverse effect on the Company and its subsidiaries, taken as whole;

(ii) the Issuer has been duly incorporated, is validly existing as a corporation in good standing under the laws of the jurisdiction of its incorporation, has the corporate power and authority to own its property and to conduct its business as described in the Final Prospectus and is duly qualified to transact business and is in good standing in each jurisdiction in which the conduct of its business or its ownership or leasing of property requires such qualification, except to the extent that the failure to be so qualified or be in good standing would not have a material adverse effect on the Company and its subsidiaries, taken as a whole; all of the issued shares of capital stock of the Issuer have been duly and validly authorized and issued, are fully paid and non-assessable; except as set forth in the Final Prospectus, all of the issued shares of capital stock of the Issuer, where applicable, are owned directly or indirectly by the Company, free and clear of all liens, encumbrances, equities or claims;

(iii) the execution, delivery and performance by the Issuer and the Company, as applicable, of the Indenture and the Terms Agreement (including the provisions of this Agreement) and the issuance and sale of the Offered Securities by the Issuer and the Company, as applicable, and compliance by the Issuer and the Company, as applicable, with the terms and provisions thereof will not result in a breach or violation of any of the terms and provisions of, or constitute a default under, any agreement or instrument to which the Company or the Issuer is a party or by which the Company or the Issuer is bound or to which any of the properties of the Company or the Issuer is subject that is material to the Company and its subsidiaries, taken as a whole, or the charter or by-laws of the Company;

14

(iv) the descriptions in the Registration Statement and the Final Prospectus of statutes, legal and governmental proceedings and contracts and other documents are accurate in all material respects and fairly present the information required to be shown; and

(v) such counsel does not know of any legal or governmental proceedings pending or threatened to which the Company or any of its subsidiaries is a party or to which any of the properties of the Company or any of its subsidiaries is subject that, in such counsel’s judgment, are required to be described in the Registration Statement or the Final Prospectus and are not so described or of any statutes, regulations, contracts or other documents that are required to be described in the Registration Statement or the Final Prospectus or to be filed as exhibits to the Registration Statement that are not described or filed as required.

Such counsel shall also state that such counsel has participated in conferences with officers and other representatives of the Company, representatives of the independent registered public accounting firm of the Company, representatives of the Underwriters and counsel to the Underwriters at which the contents of the Registration Statement, the Final Prospectus and the Disclosure Package were discussed and, although such counsel did not independently verify such information and is not passing upon and does not assume any responsibility for the accuracy, completeness or fairness of the statements contained in the Registration Statement, the Final Prospectus and the Disclosure Package, on the basis of the foregoing no facts came to such counsel’s attention that led such counsel to believe that the Registration Statement (other than the financial statements and schedules, the notes thereto and the auditor’s reports thereon, management’s report on internal control over financial reporting, if any, the other financial, reserve engineering, numerical, statistical and accounting data included or incorporated by reference therein, or omitted therefrom, and the exhibits thereto, as to which such counsel need not comment) as of its effective date contained an untrue statement of a material fact or omitted to state a material fact required to be stated therein or necessary in order to make the statements therein not misleading, or that the Final Prospectus (other than the financial statements and schedules, the notes thereto and the auditors’ report thereon, management’s report on internal control over financial reporting, if any, and the other financial, reserve engineering, numerical, statistical and accounting data included or incorporated by reference therein, or omitted therefrom, as to which such counsel need not comment) as of its date or as of the Closing Date included an untrue statement of a material fact or omitted to state a material fact necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading, or that the Disclosure Package (other than the financial statements and schedules, the notes thereto and the auditors’ report thereon, management’s report on internal control over financial

15

reporting, if any, and the other financial, reserve engineering, numerical, statistical and accounting data included or incorporated by reference therein, or omitted therefrom, as to which such counsel need not comment) as of the Execution Time included an untrue statement of a material fact or omitted to state a material fact necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading.

(f) The Representatives, on behalf of the Underwriters, shall have received from Cravath, Swaine & Moore LLP, counsel for the Underwriters, such opinion or opinions, dated the Closing Date, with respect to the incorporation of the Issuer and the Company, the validity of the Offered Securities, the Registration Statement, the Final Prospectus, the Disclosure Package and other related matters as the Representatives may require, and the Company shall have furnished to such counsel such documents as they request for the purpose of enabling them to pass upon such matters.

(g) The Representatives, on behalf of the Underwriters, shall have received a certificate, dated the Closing Date, of the President or any Vice President and a principal financial or accounting officer of the Company in which such officers, to the best of their knowledge after reasonable investigation, shall state that the representations and warranties of the Issuer and the Company in this Agreement are true and correct, that each of the Issuer and the Company has complied with all agreements and satisfied all conditions on its part to be performed or satisfied hereunder at or prior to the Closing Date, that no stop order suspending the effectiveness of the Registration Statement or of any part thereof or any notice from the Commission objecting to its use has been issued and no proceedings for that purpose have been instituted or are contemplated by the Commission and that, subsequent to the date of the most recent financial statements in the Final Prospectus, there has been no material adverse change, nor any development or event involving a prospective material adverse change, in the condition (financial or other), business, properties or results of operations of the Company and its subsidiaries taken as a whole except as set forth in or contemplated by the Disclosure Package and the Final Prospectus or as described in such certificate.

(h) The Representatives, on behalf of the Underwriters, shall have received a letter, dated the Closing Date, of Ernst & Young LLP which meets the requirements of subsection (a) of this Section, except that the specified date referred to in such subsection will be a date not more than three days prior to the Closing Date for the purposes of this subsection.

(i) Such other conditions precedent, if any, as may be specified in the Terms Agreement.

The Company will furnish the Representatives with such conformed copies of such opinions, certificates, letters and documents as the Representatives reasonably request. The Representatives may in their sole discretion waive on behalf of the Underwriters compliance with any conditions to the obligations of the Underwriters under this Agreement and the Terms Agreement.

16

6. Indemnification and Contribution. (a) The Company will indemnify and hold harmless each Underwriter, its partners, directors and officers and each person, if any, who controls such Underwriter within the meaning of Section 15 of the Act, against any losses, claims, damages or liabilities, joint or several, to which such Underwriter may become subject, under the Act or otherwise, insofar as such losses, claims, damages or liabilities (or actions in respect thereof) arise out of or are based upon any untrue statement or alleged untrue statement of any material fact contained in the Registration Statement, the Base Prospectus, any Preliminary Final Prospectus, the Final Prospectus, any Issuer Free Writing Prospectus or the information contained in the final term sheet required to be prepared and filed pursuant to Section 4(c) hereto, or any amendment or supplement thereto, or arise out of or are based upon the omission or alleged omission to state therein a material fact required to be stated therein or necessary to make the statements therein not misleading, and will reimburse each Underwriter for any legal or other expenses reasonably incurred by such Underwriter in connection with investigating or defending any such loss, claim, damage, liability or action as such expenses are incurred; provided, however, that the Company will not be liable in any such case to the extent that any such loss, claim, damage or liability arises out of or is based upon an untrue statement or alleged untrue statement in or omission or alleged omission from any of such documents in reliance upon and in conformity with written information furnished to the Company by any Underwriter through the Representatives, if any, specifically for use therein, it being understood and agreed that the only such information furnished by any Underwriter consists of the information described as such in the Terms Agreement.

(b) Each Underwriter will severally and not jointly indemnify and hold harmless the Issuer and the Company, their respective directors and officers and each person, if any, who controls the Issuer or the Company within the meaning of Section 15 of the Act, against any losses, claims, damages or liabilities to which the Issuer or the Company may become subject, under the Act or otherwise, insofar as such losses, claims, damages or liabilities (or actions in respect thereof) arise out of or are based upon any untrue statement or alleged untrue statement of any material fact contained in the Registration Statement, the Base Prospectus, any Preliminary Final Prospectus, the Final Prospectus, any Issuer Free Writing Prospectus or the information contained in the final term sheet required to be prepared and filed pursuant to Section 4(c) hereto, or any amendment or supplement thereto, or arise out of or are based upon the omission or the alleged omission to state therein a material fact required to be stated therein or necessary to make the statements therein not misleading, in each case to the extent, but only to the extent, that such untrue statement or alleged untrue statement or omission or alleged omission was made in reliance upon and in conformity with written information furnished to the Company by such Underwriter through the Representatives, if any, specifically for use therein, and will reimburse any legal or other expenses reasonably incurred by the Issuer or the Company in connection with investigating or defending any such loss, claim, damage, liability or action as such expenses are incurred, it being understood and agreed that the only such information furnished by any Underwriter consists of the information described as such in the Terms Agreement.

17

(c) Promptly after receipt by an indemnified party under this Section of notice of the commencement of any action, such indemnified party will, if a claim in respect thereof is to be made against the indemnifying party under subsection (a) or (b) above, notify the indemnifying party of the commencement thereof; but the omission so to notify the indemnifying party will not relieve it from any liability which it may have to any indemnified party otherwise than under subsection (a) or (b) above. In case any such action is brought against any indemnified party and it notifies the indemnifying party of the commencement thereof, the indemnifying party will be entitled to participate therein and, to the extent that it may wish, jointly with any other indemnifying party similarly notified, to assume the defense thereof, with counsel satisfactory to such indemnified party (who shall not, except with the consent of the indemnified party, be counsel to the indemnifying party), and after notice from the indemnifying party to such indemnified party of its election so to assume the defense thereof, the indemnifying party will not be liable to such indemnified party under this Section for any legal or other expenses subsequently incurred by such indemnified party in connection with the defense thereof other than reasonable costs of investigation. No indemnifying party shall, without the prior written consent of the indemnified party, effect any settlement of any pending or threatened action in respect of which any indemnified party is or could have been a party and indemnity could have been sought hereunder by such indemnified party unless such settlement (i) includes an unconditional release of such indemnified party from all liability on any claims that are the subject matter of such action and (ii) does not include a statement as to, or an admission of fault, culpability or a failure to act by or on behalf of an indemnified party.

(d) If the indemnification provided for in this Section is unavailable or insufficient to hold harmless an indemnified party under subsection (a) or (b) above, then each indemnifying party shall contribute to the amount paid or payable by such indemnified party as a result of the losses, claims, damages or liabilities referred to in subsection (a) or (b) above (i) in such proportion as is appropriate to reflect the relative benefits received by the Issuer and the Company on the one hand and the Underwriters on the other from the offering of the Offered Securities or (ii) if the allocation provided by clause (i) above is not permitted by applicable law, in such proportion as is appropriate to reflect not only the relative benefits referred to in clause (i) above but also the relative fault of the Issuer and the Company on the one hand and the Underwriters on the other in connection with the statements or omissions which resulted in such losses, claims, damages or liabilities as well as any other relevant equitable considerations. The relative benefits received by the Issuer and the Company on the one hand and the Underwriters on the other shall be deemed to be in the same proportion as the total net proceeds from the offering (before deducting expenses) received by the Issuer bear to the total underwriting fees paid to (including any underwriting discounts and commissions received by) the Underwriters. The

18

relative fault shall be determined by reference to, among other things, whether the untrue or alleged untrue statement of a material fact or the omission or alleged omission to state a material fact relates to information supplied by the Company or the Underwriters and the parties’ relative intent, knowledge, access to information and opportunity to correct or prevent such untrue statement or omission. The amount paid by an indemnified party as a result of the losses, claims, damages or liabilities referred to in the first sentence of this subsection (d) shall be deemed to include any legal or other expenses reasonably incurred by such indemnified party in connection with investigating or defending any action or claim which is the subject of this subsection (d). Notwithstanding the provisions of this subsection (d), no Underwriter shall be required to contribute any amount in excess of the amount by which the total price at which the Offered Securities underwritten by it and distributed to the public were offered to the public exceeds the amount of any damages which such Underwriter has otherwise been required to pay by reason of such untrue or alleged untrue statement or omission or alleged omission. No person guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of the Act) shall be entitled to contribution from any person who was not guilty of such fraudulent misrepresentation. The Underwriters’ obligations in this subsection (d) to contribute are several in proportion to their respective underwriting obligations and not joint.

(e) The obligations of the Issuer and the Company under this Section shall be in addition to any liability which the Issuer and the Company may otherwise have and shall extend, upon the same terms and conditions, to the partners, directors, officers and each person, if any, who controls any Underwriter within the meaning of the Act; and the obligations of the Underwriters under this Section shall be in addition to any liability which the respective Underwriters may otherwise have and shall extend, upon the same terms and conditions, to each director of the Issuer or the Company, to each officer of the Issuer or the Company who has signed the Registration Statement and to each person, if any, who controls the Issuer or the Company within the meaning of the Act.

7. Default of Underwriters. If any Underwriter or Underwriters default in their obligations to purchase Offered Securities under the Terms Agreement and the aggregate principal amount of Offered Securities that such defaulting Underwriter or Underwriters agreed but failed to purchase does not exceed 10% of the total principal amount of Offered Securities, the Representatives may make arrangements satisfactory to the Company for the purchase of such Offered Securities by other persons, including any of the Underwriters, but if no such arrangements are made by the Closing Date, the non-defaulting Underwriters shall be obligated severally, in proportion to their respective commitments under the Terms Agreement (including the provisions of this Agreement), to purchase the Offered Securities that such defaulting Underwriters agreed but failed to purchase. If any Underwriter or Underwriters so default and the aggregate principal amount of Offered Securities with respect to which such default or defaults occur exceeds 10% of the total principal amount of Offered Securities and arrangements satisfactory to the Representatives and the Company for the purchase of such Offered Securities by other persons are not made within 36 hours after such default, the Terms Agreement will

19

terminate without liability on the part of any non-defaulting Underwriter, the Issuer or the Company, except as provided in Section 8. As used in this Agreement, the term “Underwriter” includes any person substituted for an Underwriter under this Section. Nothing herein will relieve a defaulting Underwriter from liability for its default.

8. Survival of Certain Representations and Obligations. The respective indemnities, agreements, representations, warranties and other statements of the Issuer or the Company or their respective officers and of the several Underwriters set forth in or made pursuant to the Terms Agreement (including the provisions of this Agreement) will remain in full force and effect, regardless of any investigation, or statement as to the results thereof, made by or on behalf of any Underwriter, the Issuer or the Company or any of their respective representatives, officers or directors or any controlling person, and will survive delivery of and payment for the Offered Securities. If the Terms Agreement is terminated pursuant to Section 7 or if for any reason the purchase of the Offered Securities by the Underwriters is not consummated, the Company shall remain responsible for the expenses to be paid or reimbursed by it pursuant to Section 4 and the respective obligations of the Company and the Underwriters pursuant to Section 6 shall remain in effect. If the purchase of the Offered Securities by the Underwriters is not consummated for any reason other than solely because of the termination of the Terms Agreement pursuant to Section 7 or the occurrence of any event specified in clause (iii), (iv) or (v) of Section 5(c), the Company will reimburse the Underwriters for all out-of-pocket expenses (including fees and disbursements of counsel) reasonably incurred by them in connection with the offering of the Offered Securities.

9. No Fiduciary Duty. The Company hereby acknowledges that (a) the purchase and sale of any Offered Securities pursuant to this Agreement and the applicable Terms Agreement is an arm’s-length commercial transaction between the Issuer and the Company, on the one hand, and the Underwriters and any affiliate through which it may be acting, on the other, (b) the Underwriters are acting as principal and not as an agent or fiduciary of the Issuer or the Company and (c) the engagement by the Issuer and the Company of the Underwriters in connection with any offering and the process leading up to the offering of any Offered Securities is as independent contractors and not in any other capacity. Furthermore, the Company agrees that it is solely responsible for making its own judgments in connection with any offering (irrespective of whether any of the Underwriters has advised or is currently advising the Issuer or the Company on related or other matters). The Company agrees that it will not claim that the Underwriters have rendered advisory services of any nature or respect, or owe an agency, fiduciary or similar duty to the Issuer or the Company, in connection with such offering or the process leading thereto.

10. Notices. All communications hereunder will be in writing and, if sent to the Underwriters, will be mailed, delivered or telegraphed and confirmed to them at their address furnished to the Company in writing for the purpose of communications hereunder or, if sent to the Issuer or the Company, will be mailed, delivered or telegraphed and confirmed to it at ConocoPhillips, 600 North Dairy Ashford, Houston, Texas 77079, Attention: Chief Financial Officer.

20

11. Successors. The Terms Agreement (including the provisions of this Agreement) will inure to the benefit of and be binding upon the Issuer, the Company and such Underwriters as are identified in the Terms Agreement and their respective successors and the officers and directors and controlling persons referred to in Section 6, and no other person will have any right or obligation hereunder.

12. Representation of Underwriters. Any Representatives will act for the several Underwriters in connection with the financing described in the Terms Agreement, and any action under such Terms Agreement (including the provisions of this Agreement) taken by the Representatives will be binding upon all the Underwriters.

13. Counterparts. The Terms Agreement may be executed in any number of counterparts, each of which shall be deemed to be an original, but all such counterparts shall together constitute one and the same Agreement.

14. Applicable Law. This Agreement and the Terms Agreement shall be governed by, and construed in accordance with, the laws of the State of New York, without regard to principles of conflicts of laws.

Each of the Issuer and the Company hereby submits to the non-exclusive jurisdiction of the Federal and state courts in the Borough of Manhattan in The City of New York in any suit or proceeding arising out of or relating to the Terms Agreement (including the provisions of this Agreement) or the transactions contemplated thereby.

21

ConocoPhillips Company (“Issuer”)

Debt Securities

fully and unconditionally guaranteed by ConocoPhillips (“Company”)

TERMS AGREEMENT

December 4, 2012

To: The Representatives of the Underwriters identified herein

Ladies & Gentlemen:

The Issuer agrees to sell to the several Underwriters named in Schedule A hereto for their respective accounts, on and subject to the terms and conditions of the Underwriting Agreement to be filed by the Company in its Current Report on Form 8-K dated December 4, 2012 (“Underwriting Agreement”), the following securities (“Offered Securities”) on the following terms:

Optional Redemption: The Issuer may redeem the notes of a series, in whole or in part, at any time and from time to time, according to the price formulas set forth in the Final Prospectus.

Sinking Fund: None.

Listing: None.

Purchase Price: 99.421% of principal amount of the 2017 Notes and 99.452% of principal amount of the 2022 Notes plus, in each case, accrued interest, if any, from December 7, 2012.

Underwriters’ Fee: 0.35% of principal amount of the 2017 Notes and 0.45% of principal amount of the 2022 Notes.

Expected Reoffering Price: 99.771% of principal amount of the 2017 Notes and 99.902% of principal amount of the 2022 Notes, in each case subject to change by the Representatives.

Closing: 10 A.M., New York City time, on December 7, 2012, at the offices of Cravath, Swaine & Moore LLP, 825 Eighth Avenue, New York, New York 10019 in Federal (same day) funds.

Settlement and Trading: Book-Entry Only via DTC.

Blackout: Until 14 days after the Closing Date.

Names and Addresses of Representatives:

RBS Securities Inc.

600 Washington Blvd.

Stamford, CT 06901

Merrill Lynch, Pierce, Fenner & Smith Incorporated

One Bryant Park

New York, NY 10036

Barclays Capital Inc.

745 Seventh Avenue

New York City, NY 10019

J.P. Morgan Securities LLC

383 Madison Avenue

New York, NY 10179

Additional Condition Precedent Pursuant to Section 5(i) of the Underwriting Agreement: The Representatives, on behalf of the Underwriters, shall have received a certificate of the chief financial officer of the Company as to certain financial information included or incorporated by reference in the Registration Statement, the Disclosure Package and the Final Prospectus.

Execution Time: 4:25 p.m., New York City time, on the date hereof.

The respective principal amounts of the Offered Securities to be purchased by each of the Underwriters are set forth opposite their names in Schedule A hereto.

The provisions of the Underwriting Agreement are incorporated herein by reference. Capitalized terms used but not defined herein shall have the respective meanings given such terms in the Underwriting Agreement.

2

For purposes of Section 6 of the Underwriting Agreement, the only information furnished to the Company by the Representatives on behalf of any Underwriter for use in the Final Prospectus and the final term sheet prepared and filed pursuant to Section 4(c) of the Underwriting Agreement consists of the following information in the Prospectus furnished on behalf of each Underwriter: The third, fourth, fifth, seventh, eighth and ninth paragraphs and the second sentence in the sixth paragraph under the caption “Underwriting” in the prospectus supplement.

European Economic Area

In relation to each Member State of the European Economic Area which has implemented the Prospectus Directive (each, a “Relevant Member State”), each Underwriter has represented and agreed that with effect from and including the date on which the Prospectus Directive is implemented in that Relevant Member State (the “Relevant Implementation Date”) it has not made and will not make an offer of Notes which are the subject of the offering contemplated by this Prospectus to the public in that Relevant Member State other than:

provided that no such offer of Notes shall require ConocoPhillips or CPCo or any underwriter to publish a prospectus pursuant to Article 3 of the Prospectus Directive.

For the purposes of this provision, the expression an “offer of Notes to the public” in relation to any Notes in any Relevant Member State means the communication in any form and by any means of sufficient information on the terms of the offer and the Notes to be offered so as to enable an investor to decide to purchase or subscribe the Notes, as the same may be varied in that Member State by any measure implementing the Prospectus Directive in that Member State and the expression “Prospectus Directive” means Directive 2003/71/EC (and amendments thereto, including the 2010 PD Amending Directive, to the extent implemented in the Relevant Member State), and includes any relevant implementing measure in the Relevant Member State and the expression “2010 PD Amending Directive” means Directive 2010/73/EU.

United Kingdom

Each Underwriter has represented and agreed that

3

4

If the foregoing is in accordance with your understanding of our agreement, kindly sign and return to the Company one of the counterparts hereof, whereupon it will become a binding agreement among the Issuer, the Company and the several Underwriters in accordance with its terms.

Very truly yours,

ConocoPhillips

By /s/ Frances M. Vallejo                                    

     Name: Frances M. Vallejo

     Title: Vice President and Treasurer

ConocoPhillips Company

By /s/ Frances M. Vallejo                                    

     Name: Frances M. Vallejo

     Title: Vice President and Treasurer

5

The foregoing Terms Agreement is hereby confirmed and accepted as of the date first above written.

RBS Securities Inc.

Merrill Lynch, Pierce, Fenner & Smith Incorporated

Barclays Capital Inc.

J.P. Morgan Securities LLC

Acting on behalf of themselves and as

the Representatives of the several Underwriters.

By RBS Securities Inc.

By /s/ Mark Frenzel                                    

    Name: Mark Frenzel

    Title: Director

By Merrill Lynch, Pierce, Fenner & Smith Incorporated

By /s/ Keith Harman                                    

    Name: Keith Harman

    Title: Managing Director

By Barclays Capital Inc.

By /s/ Gregory J. Hall                                    

    Name: Gregory J. Hall

    Title: Managing Director

By J.P. Morgan Securities LLC

By /s/ Maria Sramek                                    

    Name: Maria Sramek

    Title: Executive Director

6

SCHEDULE A

SCHEDULE B

Schedule of Free Writing Prospectuses included in the Disclosure Package