<PAGE>
 
                                                                   EXHIBIT 10.57

            SIXTH AMENDMENT TO CREDIT AGREEMENT AND PROMISSORY NOTE

          THIS SIXTH AMENDMENT TO CREDIT AGREEMENT AND PROMISSORY NOTE (herein
called this "Amendment") is made as of the 22nd day of November, 1996 by and
between Neo Energy, Inc., a Texas corporation ("Borrower"), Aviva Petroleum
Inc., a Texas corporation ("Aviva Petroleum"), Aviva America, Inc., a Delaware
corporation ("Aviva America"), and ING (U.S.) Capital Corporation (formerly
named Internationale Nederlanden (U.S.) Capital Corporation), a Delaware
corporation ("Lender").

                                   RECITALS:

          1.  Borrower, Aviva Petroleum, Aviva America and Internationale
Nederlanden Bank N.V., New York Branch (the "Bank") entered into that certain
Credit Agreement dated as of August 6, 1993.

          2.  Pursuant to such Credit Agreement, Borrower executed and delivered
to Bank that certain Promissory Note dated as of August 6, 1993 made payable to
the order of Bank in the stated principal amount of $25,000,000 (as heretofore
amended, the "Original Note").

          3.  To secure repayment of the Original Note, Aviva America executed
and delivered to Bank that certain Deed of Trust, Open-End Mortgage, Assignment,
Security Agreement and Financing Statement dated August 6, 1993 (as from time to
time modified or restated, the "Mortgage"), which granted Bank a Lien on certain
of Aviva America's oil and gas properties, including without limitation all of
Aviva America's oil and gas properties (the "Subject Properties") described on
Exhibits A and B to that certain Purchase and Sale Agreement dated of even date
herewith by and between Aviva America and BWAB Incorporated (the "Purchase and
Sale Agreement").

          4.  Pursuant to that certain Assignment and Assumption dated as of
September 8, 1993, between Lender and Bank, Bank assigned to Lender all of
Bank's rights, interests and obligations in and to such Credit Agreement, the
Original Note, the Mortgage and the other Loan Documents (as such term is
defined in such Credit Agreement).

          5.  Such Credit Agreement has been amended by (a) that certain First
Amendment to Credit Agreement and Promissory Note dated March 31, 1994; (b) a
letter amendment concerning Permitted Investments dated December 31, 1994; (c) a
letter amendment concerning Consolidated Tangible Net Worth dated March 7, 1995;
(d) that certain Fourth Amendment to Credit Agreement and Promissory Note dated
June 9, 1995; and (e) that certain Fifth Amendment to Credit Agreement and
Promissory Note dated March 29, 1996.  (As so amended, such Credit Agreement is
herein called the "Original Agreement".)
<PAGE>
 
          6.  Aviva America intends to sell the Subject Properties to BWAB
Incorporated on the terms and conditions set forth in the Purchase and Sale
Agreement (the "Sale").

          7.  Borrower and Aviva America have asked Lender (i) to consent to the
Sale and (ii) to release its Liens against the Subject Properties, and Lender
has agreed to do so, provided that the Original Agreement and Original Note are
amended as set forth 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
                          --------------------------

          (S) 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.

          (S) 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 (S) 1.2.

                 "Amendment" means this Sixth Amendment to Credit Agreement and
                  ---------                                                    
          Promissory Note.

                 "Credit Agreement" means the Original Agreement as heretofore
                  ----------------
          amended and as amended hereby.

                 "Note" means the Original Note as heretofore amended and as
                  ----
          amended hereby.


                                  ARTICLE II.

          Amendments to the Original Agreement and the Original Note
          ----------------------------------------------------------

          (S) 2.1.  Mandatory prepayments. Section 2.7 of the Original Agreement
                    ---------------------
is hereby amended by adding a new subsection (c) to read as follows:

                 "(c)  Borrower shall make a $2,800,000 prepayment on the
          principal of the Loan on the date which is the earlier of (i) the date
          on which Borrower receives the proceeds from the Sale or (ii) December
          31, 1996."

                                      -2-
<PAGE>
 
          (S) 2.2.  Regular Payments.  Section 2.8 of the Original Agreement is
                    ----------------                                           
hereby amended in its entirety to read as follows:

                 "Section 2.8  Regular Payments.  Beginning November 29, 1996
                               ----------------
          and continuing on the last Business Day of each calendar month
          thereafter, Borrower will, in addition to paying any interest then due
          on the Loan, repay the principal balance of the Loan in accordance
          with the following schedule:


<TABLE>
<CAPTION>

          Payment Dates                  Monthly Principal Payment
          -------------                  -------------------------
<S>                                      <C>

          November, 1996                         $ 120,000
          December, 1996                                 0
                                      
          January, 1997                          $  25,000
          February, 1997                            25,000
          March, 1997                               25,000
          April, 1997                               25,000
          May, 1997                                 25,000
          June, 1997                                25,000
          July, 1997                                25,000
          August, 1997                             521,000
          September, 1997                          521,000
          October, 1997                            521,000
          November, 1997                           521,000
          December, 1997                           521,000
                                      
          January, 1998                          $ 521,000
          February, 1998                           521,000
          March, 1998                              521,000
          April, 1998                              521,000
          May, 1998                                521,000
          June, 1998                               521,000
          July, 1998                               521,000
          August, 1998                             521,000
          September, 1998                          521,000
          October, 1998                            521,000"
</TABLE>

          (S) 2.3.  Amendments to Original Note. The sixth paragraph of the
                    ---------------------------
Original Note is hereby amended in its entirety to read as follows:

          "On October 31, 1998 the unpaid principal balance of this Note and all
          interest accrued hereon shall be due and payable in full."

                                      -3-
<PAGE>
 
                                 ARTICLE III.

                            Agreements and Consents
                            -----------------------

          (S) 3.1.  Limitations on Investments in Colombian Operations.
                    -------------------------------------------------- 

                 (a) During the Fiscal Year beginning January 1, 1997, the
          aggregate value of all Related Persons' expenditures for and
          investments in the development of Borrower's Colombian properties
          shall not exceed $2,165,000 (calculated on a accrual basis).

                 (b) During the Fiscal Year beginning January 1, 1997, the
          aggregate value of all Related Persons' expenditures for and
          investments in the exploration of Borrower's Colombian properties
          shall not exceed $1,780,000 (calculated on a accrual basis).

          (S) 3.2.  Consent re: Sale of Subject Properties. Lender hereby
                    --------------------------------------
consents to the Sale and agrees to waive any Default or Event of Default arising
therefrom under Section 5.2(e) of the Credit Agreement.

                                  ARTICLE IV.

                        Representations and Warranties
                        ------------------------------

          (S) 4.1.  Representations and Warranties of Borrower. In order to
                    ------------------------------------------
induce Lender to enter into this Amendment, each Obligor represents and warrants
to Lender that:

                 (a) The representations and warranties contained in Section 4.1
          of the Original Agreement are true and correct at and as of the time
          of the effectiveness hereof.

                 (b) Each Obligor is duly authorized to execute and deliver this
          Amendment and Borrower is and will continue to be duly authorized to
          borrow and to perform its obligations under the Credit Agreement. Each
          Obligor has duly taken all corporate action necessary to authorize the
          execution and delivery of this Amendment and to authorize the
          performance of the obligations of Borrower hereunder.

                 (c) The execution and delivery by each Obligor of this
          Amendment, the performance by each Obligor of its obligations
          hereunder and the consummation of the transactions contemplated hereby
          do not and will not conflict with any provision of law, statute, rule
          or regulation or of the articles or certificate, as appropriate, of
          incorporation and bylaws of each Obligor, or of any material
          agreement, judgment, license, order or permit applicable to or binding
          upon each Obligor, or result in the creation of any lien, charge or
          encumbrance upon any

                                      -4-
<PAGE>
 
          assets or properties of any Obligor. Except for those which have been
          duly obtained, no consent, approval, authorization or order of any
          court or governmental authority or third party is required in
          connection with the execution and delivery by each Obligor of this
          Amendment or to consummate the transactions contemplated hereby.

                 (d) When duly executed and delivered, each of this Amendment,
          the Note and the Credit Agreement will be a legal and binding
          instrument and agreement of each Obligor, enforceable in accordance
          with its terms, except as limited by bankruptcy, insolvency and
          similar laws applying to creditors' rights generally and by principles
          of equity applying to creditors' rights generally.

                 (e) The audited annual Consolidated financial statements of
          Aviva Petroleum dated as of December 31, 1995 fairly present its
          Consolidated financial position at such date and its Consolidated
          results of operations and Consolidated cash flows for the period
          ending on such date. Since December 31, 1995, no material adverse
          change has occurred in the financial condition or businesses or in the
          Consolidated financial condition or businesses of the Obligors.

                                  ARTICLE V.

                                 Miscellaneous
                                 -------------

          (S) 5.1.  Effective Date.  This Amendment shall become effective as of
                    --------------
the date first above written when and only when Lender shall have received, at
Lender's office:
 
          (i)   a counterpart of this Amendment executed and delivered by
Borrower; and

          (ii)  verification that the Sale has been consummated.

          (S) 5.2.  Ratification of Agreements. The Original Agreement and the
                    --------------------------
Original Note as hereby amended are hereby ratified and confirmed in all
respects. The Loan Documents, as they may be amended or affected by this
Amendment, are hereby ratified and confirmed in all respects. Any reference to
the Credit Agreement in any Loan Document shall be deemed to refer to this
Amendment also, and any reference in any Loan Document to the Note and any other
document or instrument amended, renewed, extended or otherwise affected by this
Amendment shall also refer to such document as amended hereby. Any reference to
the Note in any other Loan Document shall be deemed to be a reference to the
Original Note as amended by this Amendment. 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 Lender under the Credit
Agreement or any other

                                      -5-
<PAGE>
 
Loan Document nor constitute a waiver of any provision of the Credit Agreement
or any other Loan Document.

          (S) 5.3.  Ratification of Security Documents. Each of the Obligors
                    ----------------------------------
hereby consents to the provisions of this Amendment and the transactions
contemplated herein (including without limitation the amendment to the Original
Note), and hereby ratifies and confirms each Loan Document executed and
delivered by it to and for the benefit of Lender, and each hereby agrees that
its respective obligations and covenants thereunder are unimpaired hereby and
shall remain in full force and effect.

          (S) 5.4.  Survival of Agreements.  All representations, warranties,
                    ----------------------                                   
covenants and agreements of each Obligor herein shall survive the execution and
delivery of this Amendment and the performance hereof, including without
limitation the making or granting of the Loan, and shall further survive until
all of the Obligations are paid in full.  All statements and agreements
contained in any certificate or instrument delivered by any Obligor hereunder or
under the Credit Agreement to Lender shall be deemed to constitute
representations and warranties by, or agreements and covenants of, such Obligor
under this Amendment and under the Credit Agreement.

          (S) 5.5.  Loan Documents.  This Amendment is a Loan Document, and all
                    --------------                                             
provisions in the Credit Agreement pertaining to Loan Documents apply hereto.

          (S) 5.6.   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.

          (S) 5.7.  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.

              [the balance of this page intentionally left blank]


                                      -6-
<PAGE>
 
    IN WITNESS WHEREOF, this Amendment is executed as of the date first above
written.

                              AVIVA PETROLEUM INC.
                              NEO ENERGY, INC.
                              AVIVA AMERICA, INC.



                              By: /s/ James L. Busby
                                 --------------------------------
                                 James L. Busby
                                 Treasurer


                              ING (U.S) CAPITAL CORPORATION



                              By: /s/ Christopher R. Wagner
                                 --------------------------------
                                 Christopher R. Wagner
                                 Vice President


                                      -7-
<PAGE>
 
                             CONSENT AND AGREEMENT
                             ---------------------

     Aviva Operating Company, a Nevada corporation, hereby consents to (i) the
provisions of that certain Sixth Amendment to Credit Agreement and Promissory
Note (the "Amendment") made as of the 22nd day of November, 1996 by and between
Neo Energy, Inc., a Texas corporation, Aviva Petroleum Inc., a Texas
corporation, Aviva America, Inc., a Delaware corporation, and ING (U.S.) Capital
Corporation (formerly named Internationale Nederlanden (U.S.) Capital
Corporation), a Delaware corporation ("Lender") and (ii) the transactions
contemplated in the Amendment (including without limitation the amendment to the
Original Note), and hereby ratifies and confirms the Guaranty (the "Guaranty")
dated as of August 6, 1993 made by it for the benefit of Internationale
Nederlanden Bank N.V., New York Branch (which has since assigned all its rights,
interests, and obligations under the Guaranty to Lender), and agrees that its
obligations and covenants under the Guaranty are unimpaired by the Amendment and
shall remain in full force and effect.


                              AVIVA OPERATING COMPANY



                              By: /s/ James L. Busby
                                 -------------------------------- 
                                  James L. Busby
                                  Treasurer


                                      -8-