<PAGE>

                                                                   EXHIBIT 10.18
                                                                   -------------

--------------------------------------------------------------------------------


                     SECOND AMENDMENT TO CREDIT AGREEMENT



                                    BETWEEN



                          CONTANGO OIL & GAS COMPANY



                                      AND



                              GUARANTY BANK, FSB
                                   AS LENDER



                       Effective as of February 13, 2002


                      __________________________________

            REDUCING REVOLVING LINE OF CREDIT OF UP TO $50,000,000
                      ___________________________________



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<PAGE>

                               TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                            PAGE
                                                                            ----
<S>                                                                         <C>
ARTICLE I   DEFINITIONS...................................................    1
   1.01     Terms Defined Above...........................................    1
   1.02     Terms Defined in Agreement....................................    1
   1.03     References....................................................    1
   1.04     Articles and Sections.........................................    1
   1.05     Number and Gender.............................................    2
ARTICLE II  AMENDMENTS....................................................    2
   2.01     Amendment of Section 2.6(a)...................................    2
ARTICLE III CONDITIONS....................................................    2
   3.01     Receipt of Documents..........................................    2
   3.02     Accuracy of Representations and Warranties....................    2
   3.03     Matters Satisfactory to Lender................................    3
ARTICLE IV  REPRESENTATIONS AND WARRANTIES................................    3
ARTICLE V   RATIFICATION..................................................    3
ARTICLE VI  MISCELLANEOUS.................................................    3
   6.01     Scope of Amendment............................................    3
   6.02     Agreement as Amended..........................................    3
   6.03     Parties in Interest...........................................    3
   6.04     Rights of Third Parties.......................................    3
   6.05     ENTIRE AGREEMENT..............................................    3
   6.06     GOVERNING LAW.................................................    4
   6.07     JURISDICTION AND VENUE........................................    4
</TABLE>
<PAGE>

                     SECOND AMENDMENT TO CREDIT AGREEMENT
                     ------------------------------------

     This SECOND AMENDMENT TO CREDIT AGREEMENT (this "Second Amendment") is made
                                                      ----------------
and entered into effective as of February 13, 2002, between CONTANGO OIL & GAS
COMPANY, a Delaware corporation, (the "Borrower"), and GUARANTY BANK, FSB, a
                                       --------
federal savings bank (the "Lender").
                           ------

                              W I T N E S S E T H
                              - - - - - - - - - -

     WHEREAS, the above named parties did execute and exchange counterparts of
that certain Credit Agreement dated June 29, 2001, as further amended by First
Amendment to Credit Agreement dated January 8, 2002 (the "Agreement"), to which
                                                          ---------
reference is here made for all purposes;

     WHEREAS, the parties subject to and bound by the Agreement are desirous of
amending the Agreement in the particulars hereinafter set forth;

     NOW, THEREFORE, in consideration of the mutual covenants and agreements of
the parties to the Agreement, as set forth therein, and the mutual covenants and
agreements of the parties hereto, as set forth in this Second Amendment, the
parties hereto agree as follows:

                                   ARTICLE I
                                  DEFINITIONS

       1.01  Terms Defined Above.  As used herein, each of the terms
             -------------------
"Agreement," "Borrower," "Second Amendment," and "Lender" shall have the meaning
 ---------    --------    ----------------        ------
assigned to such term hereinabove.

       1.02  Terms Defined in Agreement.  As used herein, each term defined in
             --------------------------
the Agreement shall have the meaning assigned thereto in the Agreement, unless
expressly provided herein to the contrary.

       1.03  References.  References in this Second Amendment to Article or
             ----------
Section numbers shall be to Articles and Sections of this Second Amendment,
unless expressly stated herein to the contrary.  References in this Second
Amendment to "hereby," "herein," hereinafter," hereinabove," "hereinbelow,"
"hereof," and "hereunder" shall be to this Second Amendment in its entirety and
not only to the particular Article or Section in which such reference appears.

       1.04  Articles and Sections.  This Second Amendment, for convenience
             ---------------------
only, has been divided into Articles and Sections and it is understood that the
rights, powers, privileges, duties, and other legal relations of the parties
hereto shall be determined from this Second Amendment as an entirety and without
regard to such division into Articles and Sections and without regard to
headings prefixed to such Articles and Sections.

                                       1
<PAGE>

       1.05  Number and Gender.  Whenever the context requires, reference herein
             -----------------
made to the single number shall be understood to include the plural and likewise
the plural shall be understood to include the singular.  Words denoting sex
shall be construed to include the masculine, feminine, and neuter, when such
construction is appropriate, and specific enumeration shall not exclude the
general, but shall be construed as cumulative.  Definitions of terms defined in
the singular and plural shall be equally applicable to the plural or singular,
as the case may be.

                                  ARTICLE II
                                  AMENDMENTS
                                  ----------

     The Borrower and the Lender hereby amend the Agreement in the following
particulars:

     2.01 Amendment of Section 2.6(a).  Section 2.6(a) of the Agreement is
          ---------------------------
amended to read as follows:

     "2.6  Borrowing Base Determination.  (a) The Borrowing Base as of February
           ----------------------------
     1, 2002, is acknowledged by the Borrower and the Lender to be
     $20,000.000.00. Commencing on March 1, 2002, and continuing thereafter on
     the first day of each calendar month through the next Borrowing Base review
     the amount of the Borrowing Base shall be reduced by $350,000.00."

                                  ARTICLE III
                                  CONDITIONS
                                  ----------

     The obligation of the Lender to amend the Agreement as provided herein is
subject to the fulfillment of the following conditions precedent:

     3.01  Receipt of Documents.  The Lender shall have received, reviewed, and
           --------------------
approved the following documents and other items, appropriately executed when
necessary and in form and substance satisfactory to the Lender:

     (a)   multiple counterparts of this Second Amendment, as requested by the
           Lender;

     (b)   multiple counterparts of the Ratification and Amendment to Mortgage;

     (c)   closing of purchase of certain Oil and Gas Properties from Southern
           Ute Indian Tribe d/b/a Red Willow Production Company;

     (d)   payment of Facility Fee in the amount of $22,500.00;

     (e)   payment of Engineering Fee in the amount of $5,000; and

     (f)   such other agreements, documents, items, instruments, opinions,
           certificates, waivers, consents, and evidence as the Lender may
           reasonably request.

     3.02  Accuracy of Representations and Warranties.  The representations
           ------------------------------------------
and warranties contained in Article IV of the Agreement and this Second
Amendment shall be true and correct.

                                       2
<PAGE>

     3.03  Matters Satisfactory to Lender.  All matters incident to the
           ------------------------------
consummation of the transactions contemplated hereby shall be satisfactory to
the Lender.

                                  ARTICLE IV
                        REPRESENTATIONS AND WARRANTIES
                        ------------------------------

     The Borrower hereby expressly re-makes, in favor of the Lender, all of the
representations and warranties set forth in Article IV of the Agreement, and
represents and warrants that all such representations and warranties remain true
and unbreached.

                                   ARTICLE V
                                 RATIFICATION
                                 ------------

     Each of the parties hereto does hereby adopt, ratify, and confirm the
Agreement and the other Loan Documents, in all things in accordance with the
terms and provisions thereof, as amended by this Second Amendment.

                                  ARTICLE VI
                                 MISCELLANEOUS
                                 -------------

     6.01 Scope of Amendment.  The scope of this Second Amendment is expressly
          ------------------
limited to the matters addressed herein and this Second Amendment shall not
operate as a waiver of any past, present, or future breach, Default, or Event of
Default under the Agreement. except to the extent, if any, that any such breach,
Default, or Event of Default is remedied by the effect of this Second Amendment.

     6.02 Agreement as Amended.  All references to the Agreement in any
          --------------------
document heretofore or hereafter executed in connection with the transactions
contemplated in the Agreement shall be deemed to refer to the Agreement as
amended by this Second Amendment.

     6.03 Parties in Interest.  All provisions of this Second Amendment shall
          -------------------
be binding upon and shall inure to the benefit of the Borrower, the Lender and
their respective successors and assigns.

     6.04 Rights of Third Parties.  All provisions herein are imposed solely
          -----------------------
and exclusively for the benefit of the Lender and the Borrower, and no other
Person shall have standing to require satisfaction of such provisions in
accordance with their terms and any or all of such provisions may be freely
waived in whole or in part by the Lender at any time if in its sole discretion
it deems it advisable to do so.

     6.05 ENTIRE AGREEMENT.  THIS SECOND AMENDMENT CONSTITUTES THE ENTIRE
          ----------------
AGREEMENT BETWEEN THE PARTIES HERETO WITH RESPECT TO THE SUBJECT HEREOF AND
SUPERSEDES ANY PRIOR AGREEMENT, WHETHER WRITTEN OR ORAL, BETWEEN SUCH PARTIES
REGARDING THE SUBJECT HEREOF.  FURTHERMORE IN THIS REGARD, THIS SECOND
AMENDMENT, THE AGREEMENT, THE NOTE, THE SECURITY INSTRUMENTS, AND THE OTHER
WRITTEN DOCUMENTS REFERRED TO IN THE AGREEMENT OR EXECUTED IN CONNECTION WITH OR
AS SECURITY FOR THE NOTE REPRESENT, COLLECTIVELY, THE FINAL AGREEMENT AMONG THE
PARTIES THERETO AND

                                       3
<PAGE>

MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS, OR SUBSEQUENT
ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS AMONG THE
PARTIES.

     6.06 GOVERNING LAW.  THIS SECOND AMENDMENT, THE AGREEMENT AND THE NOTE
          -------------
SHALL BE DEEMED TO BE CONTRACTS MADE UNDER AND SHALL BE CONSTRUED IN ACCORDANCE
WITH AND GOVERNED BY THE LAWS OF THE STATE OF TEXAS.  THE PARTIES ACKNOWLEDGE
AND AGREE THAT THIS AGREEMENT AND THE NOTE AND THE TRANSACTIONS CONTEMPLATED
HEREBY BEAR A NORMAL, REASONABLE, AND SUBSTANTIAL RELATIONSHIP TO THE STATE OF
TEXAS.

     6.07 JURISDICTION AND VENUE.  ALL ACTIONS OR PROCEEDINGS WITH RESPECT
          ----------------------
TO, ARISING DIRECTLY OR INDIRECTLY IN CONNECTION WITH, OUT OF, RELATED TO, OR
FROM THIS SECOND AMENDMENT, THE AGREEMENT OR ANY OTHER LOAN DOCUMENT MAY BE
LITIGATED IN COURTS HAVING SITUS IN HARRIS COUNTY, TEXAS.  EACH OF THE BORROWER
AND THE LENDER HEREBY SUBMITS TO THE JURISDICTION OF ANY LOCAL, STATE, OR
FEDERAL COURT LOCATED IN HARRIS COUNTY, TEXAS, AND HEREBY WAIVES ANY RIGHTS IT
MAY HAVE TO TRANSFER OR CHANGE THE JURISDICTION OR VENUE OF ANY LITIGATION
BROUGHT AGAINST IT BY THE BORROWER OR THE LENDER IN ACCORDANCE WITH THIS
SECTION.

     IN WITNESS WHEREOF, this Second Amendment to Credit Agreement is executed
effective the date first hereinabove written.

                                            BORROWER
                                            --------

                                            CONTANGO OIL & GAS COMPANY



                                            By: /s/ WILLIAM H. GIBBONS
                                                -------------------------
                                                    William H. Gibbons
                                                    Vice President and Treasurer

                                       4
<PAGE>

                                            LENDER
                                            ------

                                            GUARANTY BANK, FSB



                                            By: /s/ RICHARD E. MENCHACA
                                                -------------------------
                                                    Richard E. Menchaca
                                                    Vice President

                                       5