SECOND AMENDMENT TO CREDIT AGREEMENT

Exhibit 4.1(b)

SECOND AMENDMENT TO CREDIT AGREEMENT

THIS SECOND AMENDMENT TO CREDIT AGREEMENT (this “Amendment”) dated as of the 18th day of June, 2008, by and among CABOT OIL & GAS CORPORATION (“Borrower”), BANK OF AMERICA, N.A., successor to Fleet National Bank, as Administrative Agent, and the Banks party hereto.

WITNESSETH:

WHEREAS, Borrower, Administrative Agent and Banks named therein entered into that certain Credit Agreement dated as of October 28, 2002, amended by that certain First Amendment to Credit Agreement dated December 10, 2008 (as amended, the “Original Agreement”) for the purposes and consideration therein expressed; and

WHEREAS, Borrower, Administrative Agent and Banks desire to amend the Original Agreement for the purposes described herein;

NOW, THEREFORE, in consideration of the premises and the mutual covenants and agreements contained herein and in the Original Agreement, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto do hereby agree as follows:

ARTICLE I. — Definitions and References

§ 1.1. Terms Defined in the Original Agreement. Unless the context otherwise requires or unless otherwise expressly defined herein, the terms defined in the Original Agreement shall have the same meanings whenever used in this Amendment.

§ 1.2. Other Defined Terms. Unless the context otherwise requires, the following terms when used in this Amendment shall have the meanings assigned to them in this § 1.2.

“Amendment” means this Second Amendment to Credit Agreement.

“Credit Agreement” means the Original Agreement as amended hereby.

ARTICLE II. — Amendments

§ 2.1. Material Subsidiary. The reference to “any Subsidiary of Borrower” in the introductory clause of the definition of “Material Subsidiary” set forth in Section 1.01 of the Original Agreement is hereby amended to refer instead to “any Subsidiary of Borrower that is organized under the laws of any political subdivision of the United States”.

§ 2.2. Subsidiary Guaranties. The last sentence of Section 5.08 of the Original Agreement is hereby deleted in its entirety.

§ 2.3. Subsidiary Debt. Clause (i) of Section 5.15 of the Original Agreement is hereby amended in its entirety to read as follows:

(i) (A) guaranties of the Indebtedness, (B) guaranties of Debt of Borrower incurred in compliance with Section 5.10(a) by Subsidiary Guarantors, and (C) Debt owing to the Borrower or a Wholly-Owned Subsidiary

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§ 2.4. Release and Termination of Cody Texas Subsidiary Guaranty. Administrative Agent and Lenders hereby release Cody Texas, L.P. from all obligations and liabilities under that certain Subsidiary Guaranty dated October 28, 2002 (the “Guaranty”) by Cody Texas, L.P. in favor of Administrative Agent for the benefit of the Banks, and do hereby RELEASE and TERMINATE such Guaranty.

ARTICLE III. — Conditions of Effectiveness

§ 3.1. Effective Date. This Amendment shall become effective as of the date first written above, when and only when

(a) Administrative Agent shall have received, at Administrative Agent’s office a counterpart of this Amendment executed and delivered by Borrower and all Banks;

(b) Administrative Agent shall have received, for the account of Administrative Agent and Banks, all amendment fees payable to Administrative Agent or any Bank;

(c) Administrative Agent shall have additionally received all of the following documents, each document (unless otherwise indicated) being dated the date of receipt thereof by Administrative Agent, duly authorized, executed and delivered, and in form and substance satisfactory to Administrative Agent:

(i) Supporting Documents. Such supporting documents as Administrative Agent may reasonably request.

ARTICLE IV. — Representations and Warranties

§ 4.1. Representations and Warranties of Borrower. In order to induce Administrative Agent and Banks to enter into this Amendment, Borrower represents and warrants to Administrative Agent and each Bank that:

(a) the representations and warranties of the Borrower contained in the Credit Agreement (except the representations and warranties covering historical information in Sections 4.04(a) and (b) and the first sentence of Section 4.05, and except to the extent the representations and warranties would cover price and other economic assumptions furnished by the Required Banks under Section 5.09(d)) are be true and correct on and as of the date hereof;

(b) no Default has occurred and is continuing;

(c) the execution, delivery and performance by the Borrower of this Amendment and each other Financing Document to which it is a party, and by each Subsidiary Guarantor of the Financing Documents to which it is a party, are within the Borrower’s and each Subsidiary Guarantor’s corporate powers, have been duly authorized by all necessary corporate action, require no action by or in respect of, or filing with, any governmental body, agency or official and do not contravene, or constitute a default under, any provision of applicable law or

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regulation or of the certificate of incorporation or by-laws of the Borrower or any Subsidiary Guarantor or of any agreement or instrument evidencing or governing Debt of the Borrower or any Subsidiary or any other agreement, instrument, judgment, injunction, order or decree binding upon the Borrower or any Subsidiary or result in the creation or imposition of any Lien on any asset of the Borrower or any Subsidiary Guarantor pursuant to any such agreement, instrument, judgment, injunction, order or decree;

(d) this Amendment constitutes a valid and binding agreement of the Borrower and each of the other Financing Documents, when executed and delivered in accordance with the Credit Agreement, constitute valid and binding obligations of the Borrower and each Subsidiary Guarantor, to the extent a party thereto, in each case enforceable in accordance with its terms, except as the same may be limited by bankruptcy, insolvency or similar laws affecting creditors’ rights generally and by general principles of equity.

ARTICLE V. — Miscellaneous

§ 5.1. Ratification of Agreements. The Original Agreement, as hereby amended, is hereby ratified and confirmed in all respects. The Financing Documents, as they may be amended or affected by this Amendment, are hereby ratified and confirmed in all respects by Borrower. Any reference to the Credit Agreement in any Financing Document shall be deemed to refer to this Amendment also. The execution, delivery and effectiveness of this Amendment shall not, except as expressly provided herein, operate as a waiver of any right, power or remedy of Administrative Agent or any Bank under the Credit Agreement or any other Financing Document nor constitute a waiver of any provision of the Credit Agreement or any other Financing Document.

§ 5.2. Survival of Agreements. All representations, warranties, covenants and agreements of Borrower shall survive the execution and delivery of this Amendment and the performance hereof, including without limitation the making or granting of each Loan, and shall further survive until all of the Indebtedness is paid in full. All statements and agreements of Borrower or any Subsidiary Guarantor contained in any certificate or instrument delivered by Borrower or any Subsidiary Guarantor hereunder or under the Credit Agreement to Administrative Agent or any Bank shall be deemed to constitute representations and warranties by, or agreements and covenants of, Borrower under this Amendment and under the Credit Agreement.

§ 5.3. Financing Document. This Amendment is a Financing Document, and all provisions in the Credit Agreement pertaining to Financing Documents apply hereto.

§ 5.4. GOVERNING LAW. THIS AMENDMENT SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK AND ANY APPLICABLE LAWS OF THE UNITED STATES OF AMERICA IN ALL RESPECTS, INCLUDING CONSTRUCTION, VALIDITY AND PERFORMANCE.

§ 5.5. Counterparts. This Amendment may be separately executed in counterparts and by the different parties hereto in separate counterparts, each of which when so executed shall be deemed to constitute one and the same Amendment. Delivery of an executed signature page by facsimile transmission shall be effective as delivery of a manual executed counterpart.

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IN WITNESS WHEREOF, this Amendment is executed as of the date first above written.

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