SOUTHWEST AIRLINES CO. Debt Securities UNDERWRITING AGREEMENT

EX-1.1

SOUTHWEST AIRLINES CO.

Debt Securities

UNDERWRITING AGREEMENT

September 14, 2004

CITIGROUP GLOBAL MARKETS INC.

SUNTRUST CAPITAL MARKETS, INC.

BARCLAYS CAPITAL INC.

BNP PARIBAS SECURITIES CORP.

DEUTSCHE BANK SECURITIES INC.

UBS SECURITIES LLC

c/o CITIGROUP GLOBAL MARKETS INC.

388 Greenwich Street
New York, New York 10013

Ladies and Gentlemen:

Southwest Airlines Co., a Texas corporation (the “Company”), proposes to issue and sell to the underwriters named in Schedule II hereto $350,000,000 aggregate principal amount of its debt securities (the “Securities”) with the interest rate and date of maturity set forth on Schedule I hereto on the terms and conditions stated herein. The Securities will be issued under an indenture dated as of September 17, 2004 (the “Indenture”) between the Company and Wells Fargo Bank, N.A., as Trustee. As used herein, unless the context otherwise requires, the term “Underwriters” shall mean the firms named as Underwriters in Schedule II, and the term “you” shall mean Citigroup Global Markets Inc. Terms not otherwise defined herein shall have the meanings specified in the Indenture. For purposes hereof, the term “Operative Agreements” shall mean, collectively, this Agreement, the Indenture and the Securities.

The Company has filed with the Securities and Exchange Commission (the “Commission”) a registration statement on Form S-3 (No. 333-100861) for the registration of debt securities, including the Securities, under the Securities Act of 1933, as amended (the “1933 Act”), and the offering thereof from time to time in accordance with Rule 415 of the rules and regulations of the Commission under the 1933 Act (the “1933 Act Regulations”). Such registration statement has been declared effective by the Commission and the Indenture has been qualified under the Trust Indenture Act of 1939, as amended (the “1939 Act”). The Company has, pursuant to Rule 424 under the 1933 Act, filed with, or transmitted for filing to, or shall within the required period of time hereafter file with or transmit for filing to, the Commission a prospectus supplement (the “Prospectus Supplement”) specifically relating to the Securities. The term “Registration Statement” means the above-referenced registration statement in the form in which it became effective, including the exhibits thereto and the documents incorporated by reference therein, as amended to the date hereof. The term “Basic Prospectus” means the prospectus relating to the debt securities included in the Registration Statement. The term “Prospectus” means the Basic Prospectus as supplemented by the Prospectus Supplement, except that if any revised prospectus and/or prospectus supplement shall be provided to you by the Company for use in connection with the offering of the Securities which is not required to be filed by the Company pursuant to Rule 424(b) of the 1933 Act Regulations, the term “Prospectus” shall refer to such revised prospectus, if any, together with any such revised prospectus supplement from and after the time it is first provided to you for such use. As used herein, the terms “Basic Prospectus” and “Prospectus” shall include in each case the documents, if any, incorporated by reference therein. The terms “supplement” and “amendment” or “amend” as used herein shall include all documents deemed to be incorporated by reference in the Prospectus that have been filed subsequent to the date of the Prospectus Supplement by the Company with the Commission pursuant to the Securities Exchange Act of 1934, as amended (the “1934 Act”).

1. Representations and Warranties. (a) The Company represents and warrants to, and agrees with each Underwriter that:

(i) The Company has been duly incorporated and is validly existing as a corporation in good standing under the laws of the State of Texas and has the corporate power and authority to own, lease and operate its properties and to conduct its business as described in the Prospectus; the Company is duly qualified as a foreign corporation to transact business and is in good standing in each jurisdiction in which such qualification is required, whether by reason of the ownership or leasing of property or the conduct of business, except where those failures to so qualify in the aggregate would not have a material adverse effect on the business, properties, financial condition, results of operations or prospects of the Company and its consolidated subsidiaries taken as a whole (a “Material Adverse Effect”).

(ii) The Company meets the requirements for the use of Form S-3 under the 1933 Act Regulations, and the Registration Statement has become effective under the 1933 Act. At the time the Registration Statement became effective, the Registration Statement complied, and as of the date hereof does comply, in all material respects with the requirements of the 1933 Act and the 1933 Act Regulations and the 1939 Act and the rules and regulations of the Commission promulgated thereunder. The Registration Statement, at the time it became effective (and if an amendment to the Registration Statement has been filed by the Company with the Commission subsequent to the effectiveness of the Registration Statement, then at the time of the most recent such filing) did not contain 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 the Prospectus, as of the date hereof, does not, and at all times subsequent hereto up to the Closing Date 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; provided, however, that the representations and warranties in this subsection shall not apply to statements in or omissions from the Registration Statement or Prospectus made in reliance upon and in conformity with information furnished to the Company in writing by an Underwriter expressly for use in the Registration Statement or Prospectus or to that part of the Registration Statement which constitutes the Trustee’s Statement of Eligibility and Qualification under the 1939 Act (Form T-1). No stop order suspending the effectiveness of the Registration Statement has been issued, and, to the Company’s knowledge, no proceedings for that purpose have been initiated or threatened by the Commission.

(iii) The documents incorporated by reference in the Prospectus, at the time they were or hereafter are filed with the Commission, complied and will comply in all material respects with the requirements of the 1934 Act and the rules and regulations promulgated thereunder (the “1934 Act Regulations”), and, when read together and with the other information in the Prospectus, at the time the Registration Statement and any amendments thereto became effective and as of the date hereof did not and will not contain any untrue statement of a material fact or omit to state any material fact required to be stated therein or necessary in order to make the statements therein, in the light of the circumstances under which they were or are made, not misleading.

(iv) The consolidated financial statements of the Company included or incorporated by reference in the Prospectus and the Registration Statement present fairly in all material respects the consolidated financial position of the Company as of the dates indicated and the results of operations, changes in stockholders’ equity and cash flows of the Company, for the respective period covered thereby, all in conformity with generally accepted accounting principles applied, except as stated therein, on a consistent basis throughout the entire period involved; and the financial schedules included or incorporated by reference in the Registration Statement meet the requirements of the 1933 Act Regulations or the 1934 Act Regulations, as applicable, and fairly present the information required to be shown therein. The selected consolidated financial data incorporated by reference in the Prospectus present fairly the information shown therein and have been compiled on a basis consistent with that of the audited consolidated financial statements incorporated by reference in the Registration Statement and the Prospectus.

(v) Except as stated in or contemplated by the Prospectus, subsequent to the respective dates as of which information is given in the Registration Statement and the Prospectus, there has not been any material adverse change in the financial condition or results of operations of the Company and its subsidiaries, considered as one enterprise.

(vi) The Company is a “citizen of the United States” within the meaning of Section 40102(a)(15)(C) of Title 49, U.S.C. and is a holder of an “air carrier operating certificate” issued by the Secretary of Transportation pursuant to Chapter 447 of Title 49, U.S.C. for aircraft capable of carrying 10 or more individuals or 6,000 pounds or more of cargo.

(vii) This Agreement has been duly authorized, executed and delivered by the Company.

(viii) The Indenture has been duly authorized by the Company, and when duly executed and delivered by the Company and the Trustee, it will be a valid and binding agreement of, the Company, enforceable against the Company in accordance with its terms, except as enforcement thereof may be limited by bankruptcy, insolvency (including, without limitation, all laws relating to fraudulent transfers), reorganization, moratorium or other similar laws now or hereafter in effect relating to creditors’ rights generally and except as enforcement thereof is subject to general principles of equity (regardless of whether enforcement is considered in a proceeding in equity or at law).

(ix) The Securities have been duly authorized by the Company and when duly authenticated by the Trustee and executed and delivered in the manner provided for in the Indenture and sold and paid for as provided in this Agreement, the Securities will be legally and validly executed, issued and delivered and will be a valid and binding obligation of the Company entitled to the benefits of the Indenture.

(x) No authorization, approval, consent, order or license of or filing with or notice to any government, governmental instrumentality or court, domestic or foreign, is required on behalf of the Company for (i) the valid authorization, issuance, sale and delivery of the Securities, (ii) the valid authorization, execution, delivery and performance by the Company of the Operative Agreements, or (iii) the consummation by the Company of the transactions contemplated by the Operative Agreements, except such as are required under the 1933 Act, the 1934 Act, the 1939 Act and the securities or blue sky or similar laws of the various states and of foreign jurisdictions.

(xi) Except as disclosed in the Prospectus, there is no action, suit or proceeding before or by any governmental agency or body or court, domestic or foreign, now pending or, to the knowledge of the Company, threatened against the Company or any of its subsidiaries or any of their respective properties that individually (or in the aggregate in the case of any class of related lawsuits), could reasonably be expected to result in a Material Adverse Effect or that could reasonably be expected to materially and adversely affect the consummation of the transactions contemplated by this Agreement or the other Operative Agreements.

(xii) Except as disclosed in the Prospectus, no union contract dispute respecting the employees of the Company or any subsidiary exists or, to the knowledge of the Company, is imminent that, in either case, could reasonably be expected to have a Material Adverse Effect.

(xiii) Each of the Company and its subsidiaries has all necessary consents, authorizations, approvals, orders, certificates and permits of and from, and has made all declarations and filings with, all federal, state, local and other governmental authorities, all self-regulatory organizations and all courts and other tribunals, and is in compliance with all statutes and regulations as required, to own, lease, license and use its properties and assets and to conduct its business in the manner described in the Prospectus, except to the extent that the failure to so obtain, declare, file or comply would not have a Material Adverse Effect.

(xiv) Except as disclosed in the Prospectus, (x) to the knowledge of the Company, neither the Company nor any of its subsidiaries is in violation of any statute, rule, regulation, decision or order of any governmental agency or body or any court, domestic or foreign, relating to the use, disposal or release of hazardous or toxic substances (collectively, “environmental laws”), owns or operates any real property contaminated with any substance that is subject to any environmental laws, or is subject to any claim relating to any environmental laws, which violation, contamination, liability or claim individually or in the aggregate is reasonably expected to have a Material Adverse Effect, and (y) the Company is not aware of any pending investigation which might lead to such a claim that is reasonably expected to have a Material Adverse Effect.

(xv) Except as disclosed in the Prospectus, neither the Company nor any of its subsidiaries is in violation of its charter or by-laws or in default (nor has any event occurred which with notice or lapse of time or both would constitute a default or acceleration) in the performance of any obligation, agreement or condition contained in any indenture, mortgage, loan agreement, bond, debenture, note agreement or other evidence of indebtedness, lease, contract or other agreement or instrument to which the Company or any of its subsidiaries is a party or by which any of them or their respective properties is bound or affected and none of the Company or any of its subsidiaries is in violation of any judgment, ruling, decree, order, franchise, license or permit or any statute, rule or regulation applicable to the business or properties of any of the Company or any of its subsidiaries, except for such violations or defaults which do not have a Material Adverse Effect.

(xvi) The Company carries, or is covered by, insurance in such amounts and covering such risks as is customary for major U.S. airlines operating similar flight equipment over similar routes.

(xvii) The accountants that examined and issued an auditors’ report with respect to the consolidated financial statements of the Company and the financial statement schedules, if any, included or incorporated by reference in the Registration Statement are independent public accountants within the meaning of the 1933 Act.

(xviii) The Company is not an “investment company”, or an entity “controlled” by an “investment company”, within the meaning of the Investment Company Act of 1940, as amended (the “Investment Company Act”) required to register under the Investment Company Act; and after giving effect to the offering and sale of the Securities and the application of the proceeds thereof as described in the Prospectus, the Company will not be an “investment company”, or an entity “controlled” by an “investment company”, as defined in the Investment Company Act, required to register under the Investment Company Act.

(xix) This Agreement and the other Operative Agreements will, upon execution and delivery thereof, conform in all material respects to the descriptions thereof contained in the Prospectus.

(b) Any certificate signed by any officer of the Company and delivered to you or to counsel for the Underwriters in connection with an offering of the Securities shall be deemed a representation and warranty by the Company to each Underwriter participating in such offering as to the matters covered thereby on the date of such certificate unless subsequently amended or supplemented subsequent thereto. None of the foregoing applies to statements in or omissions from any of the aforementioned documents based upon written information furnished to the Company by any Underwriter specifically for use therein.

2. Purchase and Sale. Subject to the terms and conditions and in reliance upon the representations and warranties set forth herein, the Company agrees to cause the Trustee to sell to each Underwriter, and each Underwriter agrees, severally and not jointly, to purchase from the Trustee, at a purchase price of 98.739% of the principal amount thereof, the aggregate principal amounts of such Securities set forth opposite the name of such Underwriter in Schedule II hereto, together with interest thereon, if any, from September 17, 2004, if closing occurs thereafter.

3. Delivery and Payment. Payment of the purchase price for any Securities to be purchased by the Underwriters shall be made at the offices of the Company, 2702 Love Field Drive, Dallas, Texas 75235, or at such other place as shall be agreed upon by you and the Company, at 9:00 A.M., New York time, on the third business day (unless postponed in accordance with the provisions of Section 10) following the date hereof or at such other date, time or location as otherwise shall be agreed upon by you and the Company (such time and date being referred to as the “Closing Date”). Unless otherwise specified, delivery of the Securities shall be made to The Depository Trust Company for your account against payment by you to the Company of the purchase price thereof by wire transfer of Federal funds or other immediately available funds. Such Securities shall be registered in the name of Cede & Co. or in such other names, and in such denominations, as you may request in writing at least two business days prior to the Closing Date. The Company agrees to have the Securities available for inspection by you at its offices in Dallas, Texas, not later than 5:00 P.M. on the business day prior to the Closing Date.

(b) It is understood that each Underwriter has authorized you, on its behalf and for its account, to accept delivery of, receipt for, and make payment of the purchase price for, the Securities that it has agreed to purchase. You, individually and not as a representative, may (but shall not be obligated to) make payment of the purchase price for the Securities to be purchased by any Underwriter whose check or checks shall not have been received by the Closing Date.

4. Offering by Underwriters. It is understood that the several Underwriters propose to offer the Securities for sale to the public as set forth in the Prospectus.

5. Agreements. The Company covenants with each Underwriter that:

(a) Immediately following the execution of this Agreement, the Company will prepare a Prospectus Supplement setting forth the principal amount of the Securities covered thereby, the terms of the Securities not otherwise specified in the Basic Prospectus, the names of the Underwriters participating in the offering and the principal amount of the Securities which each severally has agreed to purchase, the names of the Underwriters acting as manager or co-managers in connection with the offering, the price at which the Securities are to be purchased by the Underwriters from the Company, the initial public offering price, the selling concession and reallowance, if any, and such other information as you and the Company deem appropriate in connection with the offering of the Securities. The Company will promptly transmit copies of the Prospectus to the Commission for filing pursuant to Rule 424 of the 1933 Act Regulations and will furnish to the Underwriters named therein as many copies of the Prospectus as you shall reasonably request.

(b) The Company will notify you immediately (i) of the effectiveness of any amendment to the Registration Statement, (ii) of the transmittal to the Commission for filing of any supplement to the Prospectus or any document to be filed pursuant to the 1934 Act that will be incorporated by reference in the Prospectus, (iii) of the receipt of any comments from the Commission with respect to the Registration Statement, the Prospectus or the Prospectus Supplement, (iv) of any request by the Commission for any amendment to the Registration Statement or any amendment or supplement to the Prospectus or for additional information, and (v) of the issuance by the Commission of any stop order suspending the effectiveness of the Registration Statement or the initiation of any proceedings for that purpose. The Company will use its best efforts to prevent the issuance of any stop order and, if any stop order is issued, to obtain the lifting thereof as soon as possible.

(c) For so long as a Prospectus is required to be delivered in connection with the Securities, the Company will give you notice of its intention to file or prepare any amendment to the Registration Statement or any amendment or supplement to the Prospectus, whether by the filing of documents pursuant to the 1934 Act, the 1933 Act or otherwise (except for its Current Report on Form 8-K relating to this Agreement and the form of the Securities), and will furnish you with copies of any such amendment or supplement or other documents proposed to be filed or prepared a reasonable time in advance of such proposed filing or preparation, as the case may be.

(d) The Company will deliver to you as many signed and conformed copies of the Registration Statement (as originally filed) and of each amendment thereto (including exhibits filed therewith or incorporated by reference therein and documents incorporated by reference in the Prospectus) as you may reasonably request. The Company will furnish to you as many copies of the Prospectus (as amended or supplemented) as you shall reasonably request, so long as you are required to deliver a Prospectus in connection with sales or solicitations of offers to purchase the Securities.

(e) If at any time when the Prospectus is required by the 1933 Act to be delivered in connection with sales of the Securities any event shall occur or condition exist as a result of which it is necessary to further amend or supplement the Prospectus in order that the Prospectus will not include an untrue statement of a material fact or omit to state any material fact necessary in order to make the statements therein not misleading in the light of the circumstances existing at the time it is delivered to a purchaser, or if it shall be necessary at any such time to amend or supplement the Registration Statement or the Prospectus in order to comply with the requirements of the 1933 Act or the 1933 Act Regulations, the Company will promptly prepare and file with the Commission such amendment or supplement, whether by filing documents pursuant to the 1934 Act, the 1933 Act, or otherwise, as may be necessary to correct such untrue statement or omission or to make the Registration Statement and Prospectus comply with such requirements.

(f) With respect to the sale of the Securities, the Company will make generally available to its security holders earning statements (in form complying with the provisions of Rule 158 under the 1933 Act), which will satisfy the requirements of Section 11(a) of the 1933 Act.

(g) The Company will endeavor, in cooperation with you, to qualify the Securities for offering and sale under the applicable securities laws of such states and other jurisdictions of the United States as the Underwriters may designate, and will maintain such qualifications in effect for so long as may be required for the distribution of the Securities; provided, however, that the Company shall not be obligated to file any general consent to service of process or to qualify as a foreign corporation or to subject itself to taxation as doing business in any jurisdiction in which it is not otherwise required to be so qualified. The Company will file such statements and reports as may be required by the laws of each jurisdiction in which the Securities have been qualified as provided above.

(h) Between the date of this Agreement and the Closing Date, the Company shall not, without your prior written consent, offer, sell, or enter into any agreement to sell (as public debt securities registered under the 1933 Act (other than the Securities) or as debt securities which may be resold in a transaction exempt from the registration requirements of the 1933 Act in reliance on Rule 144A thereunder and which are marketed through the use of a disclosure document containing substantially the same information as a prospectus for similar debt securities registered under the 1933 Act), any debt securities similar to the Securities, equipment notes, pass through certificates, equipment trust certificates or equipment purchase certificates secured by aircraft owned or leased by the Company (or rights relating thereto).

6. Conditions to the Obligations of Underwriters. The several obligations of the Underwriters to purchase the Securities pursuant to this Agreement will be subject at all times to the accuracy of the representations and warranties on the part of the Company herein, to the accuracy of the statements of the Company’s officers made in any certificate furnished pursuant to the provisions hereof, to the performance and observance by the Company of all covenants and agreements contained herein, on its part to be performed and observed and to the following additional conditions precedent:

(a) At the Closing Date, (i) the Prospectus, and any supplement thereto, shall have been filed within the time period required by Rule 424(b); and (ii) no stop order suspending the effectiveness of the Registration Statement shall have been issued under the 1933 Act or proceedings therefor initiated or threatened by the Commission.

(b) At the Closing Date, you shall have received the following opinions:

(1) The opinion of the General Counsel of the Company, dated the Closing Date, in form and substance reasonably satisfactory to you and substantially to the effect set forth in Exhibit A hereto.

(2) The opinion of Vinson & Elkins L.L.P., counsel to the Underwriters, with respect to such matters as you may reasonably request.

(c) Subsequent to the execution and delivery of this Agreement, there shall not have occurred 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 considered as one enterprise that, in your judgment, is material and adverse and that makes it, in your judgment, impracticable or inadvisable to proceed with the completion of the public offering of the Securities on the terms and in the manner contemplated by the Prospectus.

(d) You shall have received a certificate of the Vice Chairman of the Board and Chief Executive Officer, the President or the Senior Vice President and Chief Financial Officer of the Company and the Treasurer or the Secretary of the Company, dated as of the Closing Date to the effect that:

(1) the representations and warranties of the Company in this

Agreement are true and correct in all material respects on and as of the Closing Date with the same effect as if made at the Closing Date and the Company has complied with all the agreements and satisfied all the conditions on its part to be performed or satisfied at or prior to the Closing Date;

(2) no stop order suspending the effectiveness of the Registration Statement has been issued and no proceedings for that purpose have been instituted or, to the Company’s knowledge, threatened; and

(3) since the respective dates as of which information is given in the Registration Statement and the Prospectus, there has been no material adverse change, or any development involving a prospective material adverse change, in or affecting particularly the business or properties of the Company or its subsidiaries, considered as one enterprise.

(e) The Underwriters shall have received on each of the date of this Agreement and the Closing Date, a letter dated the date hereof or the Closing Date, as the case may be, in form and substance satisfactory to the Underwriters, from the Company’s independent public accountants, containing statements and information of the type ordinarily included in accountants’ “comfort letters” to underwriters with respect to the financial statements and certain other financial or statistical data and certain financial information contained in or incorporated by reference into the Registration Statement and the Prospectus.

(f) Subsequent to the execution and delivery of this Agreement and prior to the Closing Date, (i) there shall not have been any downgrading in the rating accorded any of the Company’s securities by any “nationally recognized statistical rating organization”, as such term is defined for purposes of Rule 436(g)(2) under the 1933 Act, or (ii) any public announcement that any such organization has under surveillance or review, in each case for possible change, its ratings of any such securities (other than an announcement with positive implications of a possible upgrading, and no implication of a possible downgrading, of such rating).

(g) On the Closing Date, the Securities shall be rated (x) not lower than “A” by Standard & Poor’s Ratings Services, and (y) not lower than “Baa1” by Moody’s Investors Service, Inc.

(h) At the Closing Date, counsel for the Underwriters shall have been furnished with such documents and opinions as such counsel may reasonably require for the purpose of enabling such counsel to pass upon the issuance and sale of Securities as herein contemplated and related proceedings, or in order to evidence the accuracy and completeness of any of the representations and warranties, or the fulfillment of any of the conditions, herein contained.

If any of the conditions specified in this Section 6 shall not have been fulfilled in all material respects when and as provided in this Agreement, or if any of the opinions and certificates mentioned above or elsewhere in this Agreement shall not be in all material respects reasonably satisfactory in form and substance to you and counsel for the Underwriters, this Agreement and all obligations of the Underwriters hereunder may be cancelled by you at any time at or prior to the Closing Date, and such termination shall be without liability of any party to any other party except as provided in Section 7 hereof. Notice of any such cancellation shall be given to the Company in writing or by telephone or facsimile confirmed in writing. Notwithstanding any such termination, the

provisions of Sections 8 and 11 shall remain in effect.

7. Payment of Expenses. The Company will pay all expenses incident to the performance of its obligations under this Agreement, including:

(i) the printing and filing of the Registration Statement and all amendments thereto, and the Prospectus and any amendments or supplements thereto;

(ii) the preparation, printing, issuance and delivery of the Securities;

(iii) the reasonable fees and disbursements of the Company’s accountants and counsel and of the Trustee and its counsel, and of any issuing and paying agent or transfer agent;

(iv) the qualification of the Securities under securities laws in accordance with the provisions of Section 5(g), including filing fees and the reasonable fees and disbursements of counsel to the Underwriters in connection therewith and in connection with the preparation of any Blue Sky Survey;

(v) the printing and delivery to the Underwriters in quantities as hereinabove stated of copies of the Registration Statement and any amendments thereto, and of the Prospectus and any amendments or supplements thereto, and the delivery by the Underwriters of the Prospectus and any amendments or supplements thereto in connection with solicitations or confirmations of sales of the Securities;

(vi) the preparation and delivery to the Underwriters of copies of the Operative Agreements;

(vii) any fees charged by rating agencies for the rating of the Securities; and

(viii) the fees and expenses, if any, incurred with respect to any filing with the National Association of Securities Dealers, Inc.

If this Agreement is terminated by you in accordance with the provisions of Section 6 hereof, the Company shall reimburse the Underwriters for all of their out-of-pocket expenses, including the reasonable fees and disbursements of Vinson & Elkins L.L.P., counsel for the Underwriters, or, in any other case, including any termination pursuant to Section 9 or 10 hereof, the Underwriters will pay all of their own expenses, including their fees of counsel, transfer taxes on resale of any of the Securities and any advertising expenses connected with any offers they may make.

8. Indemnification and Contribution; Default of Underwriters.

(a) The Company agrees to indemnify and hold harmless each Underwriter, and each person, if any, who controls such Underwriter within the meaning of either Section 15 of the 1933 Act or Section 20 of the 1934 Act from and against any and all losses, claims, damages and liabilities (including, without limitation, any legal or other expenses reasonably incurred by any Underwriter or any such controlling person in connection with defending or investigating any such action or claim) caused by any untrue statement or alleged untrue statement of a material fact contained in the Registration Statement or any amendment thereof or the Prospectus (as amended or supplemented if the Company shall have furnished any amendments or supplements thereto), or caused by any omission or alleged omission to state therein a material fact required to be stated therein or necessary to make the statements therein not misleading, except insofar as such losses, claims, damages or liabilities are caused by any such untrue statement or omission or alleged untrue statement or omission based upon and in conformity with information relating to any Underwriter furnished to the Company in writing by such Underwriter (“Underwriter Information”).

(b) Each Underwriter agrees, severally and not jointly, to indemnify and hold harmless the Company, its directors, each of the officers who signed the Registration Statement and each person, if any, who controls the Company, within the meaning of either Section 15 of the 1933 Act or Section 20 of the 1934 Act, to the same extent as the foregoing indemnity from the Company to such Underwriter but only with reference to the Underwriter Information provided by such Underwriter.

(c) In case any proceeding (including any governmental investigation) shall be instituted involving any person in respect of which indemnity may be sought pursuant to either paragraph (a) or (b) above, such person (the “indemnified party”) shall promptly notify the person against whom such indemnity may be sought (the “indemnifying party”) in writing. The indemnifying party, upon request of the indemnified party, shall, and the indemnifying party may elect to, retain counsel reasonably satisfactory to the indemnified party to represent the indemnified party and any others the indemnifying party may designate in such proceeding and the indemnifying party shall pay the fees and disbursements of such counsel related to such proceeding. In any such proceeding, any indemnified party shall have the right to retain its own counsel, but the fees and expenses of such counsel shall be at the expense of such indemnified party unless (i) the indemnifying party and the indemnified party shall have mutually agreed to the retention of such counsel, (ii) the named parties to any such proceeding (including any impleaded parties) include both the indemnifying party and the indemnified party and representation of both parties by the same counsel would be inappropriate due to actual or potential differing interests between them, or (iii) the indemnifying party shall have failed to retain counsel as required by the prior sentence to represent the indemnified party within a reasonable amount of time. It is understood that the indemnifying party shall not, in connection with any proceeding or related proceedings in the same jurisdiction, be liable for the fees and expenses of more than one separate firm (in addition to any local counsel) for all such indemnified parties and that all such fees and expenses shall be reimbursed as they are incurred. The firm chosen to represent the indemnified parties shall be designated in writing by you in the case of parties indemnified pursuant to paragraph (a) above and by the Company in the case of parties indemnified pursuant to paragraph (b) above. The indemnifying party shall not be liable for any settlement of any proceeding effected without its written consent, but if settled with such consent or if there be a final judgment for the plaintiff, the indemnifying party agrees to indemnify the indemnified party from and against any loss or liability by reason of such settlement or judgment. Notwithstanding the foregoing sentence, if at any time an indemnified party shall have requested in writing an indemnifying party to reimburse the indemnified party for fees and expenses of counsel as contemplated by the second and third sentences of this paragraph, the indemnifying party agrees that it shall be liable for any settlement of any proceeding effected without its written consent if (i) such settlement is entered into more than 90 days after receipt by such indemnifying party of the aforesaid request and (ii) such indemnifying party shall not have reimbursed the indemnified party in accordance with such request prior to the date of such settlement, unless such fees and expenses are being disputed in good faith. The indemnifying party at any time may, subject to the last sentence of this Section 8(c), settle or compromise any proceeding described in this paragraph at the expense of the indemnifying party. No indemnifying party shall, without the prior written consent of the indemnified party, effect any settlement of any pending or threatened proceeding 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 claims that are the subject matter of such proceeding 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) To the extent the indemnification provided for in paragraph (a) or (b) of this Section 8 is required to be made but is unavailable to an indemnified party or insufficient in respect of any losses, claims, damages or liabilities, then the applicable indemnifying party under such paragraph, in lieu of indemnifying such indemnified party thereunder, shall contribute to the amount paid or payable by such indemnified party as a result of such losses, claims, damages or liabilities (i) in such proportion as is appropriate to reflect the relative benefits received by the Company, on the one hand, and the Underwriters, on the other hand, from the offering of such 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 Company on the one hand and the Underwriters on the other hand in connection with the statements or omissions that resulted in such losses, claims, damages or liabilities, as well as any other relevant equitable considerations. The relative benefits received by the Company on the one hand and the Underwriters on the other hand in connection with the offering of such Securities shall be deemed to be in the same respective proportions as the proceeds from the offering of such Securities received by the Company (before deducting expenses) less total underwriting discounts and commissions paid to the Underwriters by the Company, and the total underwriting discounts and commissions paid to the Underwriters by the Company, in each case as set forth on the cover of the Prospectus, bear to the aggregate public offering price of such Securities. The relative fault of the Company on the one hand and of the Underwriters on the other hand 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 information supplied by the Underwriters, and the parties’ relative intent, knowledge, access to information and opportunity to correct or prevent such statement or omission. The Underwriters’ respective obligations to contribute pursuant to this Section 8 are several in proportion to the respective principal amount of Securities they have purchased hereunder, and not joint.

(e) The Company and the Underwriters agree that it would not be just or equitable if contribution pursuant to this Section 8 were determined by pro rata allocation (even if the Underwriters were treated as one entity for such purpose) or by any other method of allocation that does not take account of the equitable considerations referred to in paragraph (d) above. The amount paid or payable by an indemnified party as a result of the losses, claims, damages and liabilities referred to in paragraph (d) above shall be deemed to include, subject to the limitations set forth above, any legal or other expenses reasonably incurred by such indemnified party in connection with investigating or defending any such action or claim. Notwithstanding the provisions of this Section 8, no Underwriter shall be required to contribute any amount in excess of the amount by which the total price at which the Securities underwritten by it and distributed to the public were offered to the public exceeds the amount of any damages that 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 1933 Act) shall be entitled to contribution from any person who was not guilty of such fraudulent misrepresentation.

9. Default by an Underwriter. If any Underwriter or Underwriters default in their obligations to purchase Securities hereunder and the aggregate principal amount of the Securities that such defaulting Underwriter or Underwriters agreed but failed to purchase does not exceed 10% of the total principal amount of the Securities, you may make arrangements satisfactory to the Company for the purchase of such 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 hereunder, to purchase the Securities that such defaulting Underwriter or Underwriters agreed but failed to purchase. If any Underwriter or Underwriters so default and the aggregate principal amount of the Securities with respect to which such default or defaults occurs exceeds 10% of the total principal amount of the Securities and arrangements satisfactory to you and the Company for purchase of such Securities by other persons are not made within 36 hours after such default, this Agreement will terminate without liability on the part of any non-defaulting Underwriter or the Company, except as provided in Section 7 and 8 hereof. 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.

10. Termination. This Agreement shall be subject to termination, in the absolute discretion of the Underwriters, immediately upon notice to the Company, at any time if after the execution and delivery of this Agreement and prior to the Closing Date (i) trading generally shall have been suspended or materially limited on or by, as the case may be, any of the New York Stock Exchange or the National Association of Securities Dealers, Inc., (ii) trading of any securities of the Company shall have been suspended on any exchange or in any over-the-counter market, (iii) a general moratorium on commercial banking activities in New York shall have been declared by either Federal or New York State authorities, (iv) any outbreak or escalation of hostilities shall have occurred in which the United States is involved, any declaration of war by Congress or any substantial national or international calamity or emergency shall occur and the effect of which is such as to make it, in your judgment, impracticable or inadvisable to proceed with the offering or delivery of the Securities on the terms and in the manner contemplated in the Prospectus or (v) there shall have occurred such a material adverse change in general economic, political or financial conditions (or the effect of international conditions on the financial markets in the United States shall be such) as to make it, in your judgment, impracticable or inadvisable to proceed with the offering or delivery of the Securities on the terms and in the manner contemplated in the Prospectus. In the event of any such termination of this Agreement, the provisions of Section 7 hereof, the indemnity and contribution agreements set forth in Section 8 hereof, and the provisions of Sections 11 through 15 hereof shall remain in effect.

11. Representations and Indemnities to Survive. The respective indemnities, agreements, representations, warranties and other statements of the Company or its officers and of the Underwriters set forth in or made pursuant to this Agreement will remain in full force and effect, regardless of any termination of this Agreement, any investigation, or statement as to the results thereof, made by or on behalf of any Underwriter, the Company or any of their respective representatives, officers or directors or any controlling person and will survive delivery of and payment for the Securities. If for any reason the purchase of the 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 7 and the respective obligations of the Company and the Underwriters pursuant to Section 8 shall remain in effect. If the purchase of the Securities by the Underwriters is not consummated for any reason other than solely because of the occurrence of the termination of this Agreement pursuant to Section 9 or 10, the Company will reimburse the Underwriters for all out-of-pocket expenses (including reasonable fees and disbursements of counsel) reasonably incurred by them in connection with the offering of such Securities and comply with its other obligations under Section 7.

12. Notices. All notices and other communications hereunder shall be in writing and shall be deemed to have been duly given if mailed, delivered by Federal Express service or transmitted by any standard form of telecommunication. Notices to the Underwriters shall be directed to them at the address indicated on page 1 hereof. Notices to the Company shall be directed to it at Southwest Airlines Co., 2702 Love Field Drive, Dallas, Texas ###-###-####, Attention of the Senior Vice President – Finance and Chief Financial Officer, with a copy thereof directed to the General Counsel.

13. Successors. This Agreement shall inure to the benefit of and be binding upon you and the Company and any Underwriter who becomes a party hereto and their respective successors. Nothing expressed or mentioned in this Agreement is

intended or shall be construed to give any firm or corporation, other than the parties hereto and their respective successors and the controlling persons and officers and directors referred to in Section 8 and their heirs and legal representatives, any legal or equitable right, remedy or claim under or in respect of this Agreement or any provision herein contained. This Agreement and all conditions and provisions hereof are intended to be for the sole and exclusive benefit of the parties hereto, their respective successors and said controlling persons and officers and directors and their heirs and legal representatives, and for the benefit of no other person, firm or corporation. No purchaser of Securities from any Underwriter shall be deemed to be a successor by reason merely of such purchase.

14. APPLICABLE LAW. THIS 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 LAW.

15. Counterparts. This Agreement may be executed in one or more counterparts and when a counterpart has been executed by each party, all such counterparts taken together shall constitute one and the same agreement. A party may submit its signed counterpart of this Agreement by facsimile and such counterpart so

received by facsimile shall for all purposes constitute an original.

[signature pages follow]

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If the foregoing is in accordance with your understanding of our agreement, please sign and return to the Company a counterpart hereof, whereupon this instrument along with all counterparts will become a binding agreement between each Underwriter and the Company in accordance with its terms.

Very truly yours,

SOUTHWEST AIRLINES CO.

By: /s/ Laura Wright   

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1808050.3

CONFIRMED AND ACCEPTED, as of
the date first above written:

CITIGROUP GLOBAL MARKETS INC.

SUNTRUST CAPITAL MARKETS, INC.

BARCLAYS CAPITAL INC.

BNP PARIBAS SECURITIES CORP.

DEUTSCHE BANK SECURITIES INC.

UBS SECURITIES LLC

By: CITIGROUP GLOBAL MARKETS INC.

By:    /s/ Jeffrey J. Singer   

Title: Director

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1808050.3

SCHEDULE I

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SCHEDULE II

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Exhibit A

CITIGROUP GLOBAL MARKETS INC.

SUNTRUST CAPITAL MARKETS, INC.

BARCLAYS CAPITAL INC.

BNP PARIBAS SECURITIES CORP.

DEUTSCHE BANK SECURITIES INC.

UBS SECURITIES LLC

c/o CITIGROUP GLOBAL MARKETS INC.

388 Greenwich Street
New York, New York 10013

Ladies and Gentlemen:

I am the Vice President – General Counsel of Southwest Airlines Co., a Texas corporation (“Southwest”). In such capacity, I and persons on my legal staff have acted as counsel to Southwest in connection with the transactions contemplated by the Underwriting Agreement dated September 14, 2004 among Citigroup Global Markets Inc., SunTrust Capital Markets, Inc., Barclays Capital Inc., BNP Paribas Securities Corp., Deutsche Bank Securities Inc. and UBS Securities LLC (collectively, the “Underwriters”) and Southwest (the “Underwriting Agreement”). Capitalized terms used but not defined herein shall have the meanings ascribed to them in the Underwriting Agreement. This opinion is furnished pursuant to Section 6(b)(1) of the Underwriting Agreement.

In arriving at the opinions expressed below, I or members of my legal staff have reviewed the following documents, each of which is dated as of the date hereof, except where otherwise indicated above or below:

(a) an executed copy of the Underwriting Agreement,

The Indenture, the Notes and the Underwriting Agreement are referred to herein collectively as the “Transaction Documents”.

In addition, I or members of my legal staff have reviewed the originals or copies certified or otherwise identified to my or their satisfaction of all such corporate records of Southwest and such other instruments and other certificates of public officials, officers and representatives of Southwest and such other persons, and I or members of my legal staff have made such investigations of law, as I deemed appropriate as a basis for the opinions expressed below.

In arriving at the opinions expressed below, I and members of my legal staff have assumed the authenticity of all documents submitted to us as originals and the conformity to the originals of all documents submitted to us as copies. In addition, I and members of my legal staff have assumed and have not verified the accuracy as to factual matters of each document I or they have reviewed including, without limitation, the accuracy of the representations and warranties of Southwest in the Underwriting Agreement. As used herein, the phrase “to my knowledge” shall mean to my actual knowledge after reasonable investigation, including inquiry of members of my legal staff, but shall not be interpreted to impute to me knowledge of others.

Based on the foregoing, and subject to the further assumptions, qualifications and limitations set forth below, it is my opinion that:

1. Southwest has been duly incorporated and is an existing corporation in good standing under the laws of the State of Texas, with corporate power to own, lease and operate its properties and conduct its business as described in the Prospectus; Southwest is duly qualified to do business as a foreign corporation in good standing in all other jurisdictions in the United States in which its ownership or lease of property or the conduct of its business requires such qualification, except where the failure to be so qualified would not have a material adverse effect on the business or consolidated financial condition of Southwest.

2. To my knowledge, except as disclosed in the Prospectus, there is no action, suit or proceeding before or by any governmental agency or body or court, domestic or foreign, now pending against Southwest or any of the Subsidiaries or any of their respective properties that will have a material adverse effect on the business or consolidated financial condition of Southwest and the Subsidiaries taken as a whole or the ability of Southwest to perform its obligations under any of the Transaction Documents.

3. Southwest is a “citizen of the United States” within the meaning of Section 40102(a)(15) of Title 49 of the United States Code, as amended, holding an air carrier operating certificate issued by the Secretary of Transportation pursuant to Chapter 447 of Title 49 of the United States Code, as amended, for aircraft capable of carrying 10 or more individuals or 6,000 pounds or more of cargo.

4. The execution, delivery and performance by Southwest of the Transaction Documents, and the consummation by Southwest of the transactions contemplated by such documents, will not result in any violation of the provisions of the articles of incorporation or by-laws of Southwest or, to my knowledge, any applicable law, administrative regulation or any administrative or court decree, nor does any such action, to my knowledge, constitute a breach of, or default under, or (except as contemplated therein) result in the creation or imposition of any lien, charge or encumbrance upon any assets of Southwest or any of the Subsidiaries pursuant to, any material contract, indenture, mortgage, loan agreement, note, lease or other instrument to which Southwest is a party or by which it is bound or to which any of the assets of Southwest is subject.

5. The execution and delivery by Southwest of the Indenture, the Notes and the Underwriting Agreement have been duly authorized by all necessary corporate action of Southwest, and each of the Indenture, the global security representing the Notes and the Underwriting Agreement has been duly executed and delivered by Southwest. Each of the Indenture and the Notes is a valid and binding obligation of Southwest enforceable against Southwest in accordance with its terms.

6. The Indenture and the Notes conform in all material respects to the descriptions thereof in the Prospectus and the Prospectus Supplement;

7. The Indenture is qualified under the 1939 Act.

8. The issuance and sale of the Notes to the Underwriters pursuant to the Underwriting Agreement, the valid authorization, execution and delivery of the Transaction Documents by Southwest and the performance by Southwest of its obligations under the Transaction Documents do not require Southwest to obtain or effect any consent, approval, authorization, registration or qualification of or with any governmental agency or body of the United States or the State of Texas, except such as may be required under federal or state securities or blue sky laws.

9. To my knowledge, except as disclosed in the Prospectus, there is no event of default under any material agreement or instrument under which indebtedness of Southwest is outstanding or by which it is bound or any of its properties is subject.

10. To my knowledge, there are no legal or governmental proceedings pending or threatened against the Company or any Subsidiary which are required to be disclosed in the Registration Statement, other than those disclosed therein or those which individually (or in the aggregate in the case of any class of related lawsuits) could not reasonably be expected to have a Material Adverse Effect.

11. The Registration Statement has become effective under the Securities Act and, to my knowledge, (i) no stop order suspending the effectiveness of the Registration Statement has been issued and (ii) no proceedings for that purpose have been instituted or threatened by the Commission.

12. Without independent check or verification of the statements contained therein, the Registration Statement and the Base Prospectus (other than the financial statements, financial statement schedules and other financial or statistical data included therein, or omitted there from, other matters referred to in the Prospectus or the Prospectus Supplement under the captions “Experts” and the Statement of Eligibility on Form T-1, as to which I am not expressing an opinion), in each case excluding the documents incorporated or deemed incorporated by reference therein, as of their respective effective or issue dates, appear on their face to have been appropriately responsive in all material respects to the requirements of the Securities Act.

13. Each document filed pursuant to the Securities Exchange Act of 1934, as amended, and the rules and regulations there under (the “Exchange Act”), and incorporated or deemed incorporated by reference in the Registration Statement or the Prospectus (other than the exhibits thereto, the financial statements, financial statement schedules and other financial or statistical data included therein, or incorporated or deemed incorporated therein by reference, or omitted there from, and other matters referred to in the Base Prospectus or the Prospectus Supplement under the captions “Experts”, as to which I am not expressing an opinion), when so filed with the Commission, appeared on its face to have been appropriately responsive in all material respects to the requirements of the Exchange Act.

I have examined the Registration Statement, the Base Prospectus and the Prospectus Supplement. The limitations inherent in the independent verification of factual matters and in the role of General Counsel are such, however, that I cannot and do not assume any responsibility for the accuracy, completeness or fairness of the statements made therein have made no independent check or verification thereof. In the course of the preparation of the Registration Statement and the Prospectus, I have participated in conferences with certain officers and employees of Southwest and with representatives of the Underwriters. My examination of the Registration Statement and the Prospectus and my participation in the above-mentioned conferences did not disclose to me any information which has led me to believe that the Registration Statement (other than the exhibits thereto, the financial statements, financial statement schedules and other financial or statistical data included therein, or incorporated or deemed incorporated by reference therein, or omitted there from, and other matters referred to in the Base Prospectus or the Prospectus Supplement under the caption “Experts”, as to which I express no belief), as of its effective date, contained any untrue statement of a material fact or omitted to state any material fact required to be stated therein or necessary in order to make the statements therein not misleading, or that the Prospectus (other than the financial statements, financial statement schedules and other financial or statistical data included therein, or incorporated or deemed incorporated by reference therein, or omitted therefrom, and other matters referred to in the Base Prospectus or the Prospectus Supplement under the caption “Experts”, as to which I express no belief), as of September 14, 2004 contained, or as of the date hereof contains, any untrue statement of a material fact or, as of September 14, 2004 omitted, or as of the date hereof omits, to state a material fact necessary in order to make the statements therein, in the light of the circumstances in which they were made, not misleading.

Insofar as the foregoing opinions relate to the valid existence and good standing of Southwest, they are based solely on a certificate of existence and of good standing received from the Secretary of State of the State of Texas and the Comptroller of Public Accounts of the State of Texas. Insofar as the foregoing opinions relate to qualification to do business of Southwest and the Subsidiaries, they are based solely on certificates of foreign qualification received from the applicable Secretary of State’s office.

The opinions in the last sentence of paragraph 5 above are subject to (i) bankruptcy, insolvency, fraudulent transfer, fraudulent conveyance or other similar laws affecting the rights or remedies of creditors generally, (ii) general principles of equity including, without limitation, laches and estoppel as equitable defenses and concepts of materiality, reasonableness, good faith and fair dealing (regardless of whether enforceability is considered or applied in a proceeding in equity or at law) and considerations of impracticability or impossibility of performance, and defenses based upon unconscionability of otherwise enforceable obligations in the context of the factual circumstances under which enforcement thereof is sought and (iii) the qualification that the remedy of specific performance and injunctive and other forms of equitable relief may be subject to equitable defenses and to the discretion of the court before which any proceeding therefore may be brought.

The foregoing opinions are limited to the federal law of the United States of America and the law of the State of Texas, in each case as in effect on the date hereof, except that I express no opinion with respect to (i) the laws, regulations or ordinances of any county, town or municipality or governmental subdivision or agency thereof, (ii) (x) state securities or blue sky laws and (y) except as set forth in paragraphs 7, 11, 12 and 13 above, federal securities laws, including without limitation the Securities Act, the Exchange Act, the Trust Indenture Act of 1939, as amended, and the Investment Company Act of 1940, as amended, (iii) any federal or state tax, antitrust or fraudulent transfer or conveyance laws, and (iv) the Employee Retirement Income Security Act of 1974, as amended. In addition, my opinions are based upon a review of those laws, statutes, rules and regulations which, in my experience, are normally applicable to transactions of the type contemplated by the Transaction Documents.

The opinions set forth above may be relied upon by Wells Fargo Bank, N.A., as Trustee under the Indenture, as fully as if this opinion letter had been addressed to it. Otherwise, such opinions are solely for the benefit of you and your counsel and may not be relied upon in any manner by any other persons without my written permission. This opinion letter speaks only as of the date hereof and I disclaim any obligation to advise you of changes of law or fact that occur after the date hereof.

Very truly yours,

Deborah Ackerman
Vice President – General Counsel

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1808050.3

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