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                                                                   EXHIBIT 10.24



                               FIRST AMENDMENT TO
                     AMENDED AND RESTATED CREDIT AGREEMENT


         This First Amendment to Amended and Restated Credit Agreement (this
"Amendment") dated as of December 30, 1997 is among COSTILLA ENERGY, INC., a
Delaware corporation (the "Borrower"), the banks named on the signature pages
hereto (together with their respective successors and assigns in such capacity,
the "Banks"), BANKERS TRUST COMPANY, as agent for the Banks (together with its
successors and assigns in such capacity, the "Agent") and UNION BANK OF
CALIFORNIA, N.A., as co-agent for the Banks (together with its successors and
assigns in such capacity, the "Co-Agent").

                             PRELIMINARY STATEMENT

         A.      The Borrower and the Bank Group have entered into that certain
Amended and Restated Credit Agreement dated as of August 28, 1997 (the "Credit
Agreement").

         B.      The Borrower and the Bank Group desire to amend the Credit
Agreement as set forth herein.

         NOW THEREFORE, in consideration of the foregoing and the mutual
agreements set forth herein, the parties agree as follows:

         Section 1. Definitions. Unless otherwise defined in this Amendment,
each capitalized term used in this Amendment has the meaning assigned to such
term in the Credit Agreement.

         Section 2. Amendments. The Credit Agreement is hereby amended as
follows:

         a.      The second sentence of Section 2.04(a) of the Credit Agreement
    is hereby amended in its entirety to read as follows:

                 "During the period from and after the Effective Date until the
         Borrowing Base is redetermined in accordance with this Section, the
         amount of the Borrowing Base shall be $50,000,000; provided, however,
         that if the Concho Properties are sold, the amount of the Borrowing
         Base shall automatically be reduced to $36,500,000 during the period
         from the date of such sale until the Borrowing Base is redetermined in
         accordance with this Section."

         b.      Section 6.07 of the Credit Agreement is hereby amended in its
    entirety to read as follows:


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                 "Section 6.07. Sales of Properties. The Borrower will not, and
         will not permit any of its Subsidiaries to, sell, transfer, assign,
         farm-out, lease or otherwise transfer or dispose of any Properties
         other than (a) sales of Hydrocarbon production in the ordinary course
         of business and sales of obsolete or worn-out equipment in the
         ordinary course of business, (b) sales or transfers of Properties by
         any of the Borrower's wholly-owned Subsidiaries to the Borrower or any
         such other wholly-owned Subsidiary, (c) the sale of the Concho
         Properties for a purchase price of $17,000,000; provided, that at
         least $13,500,000 of the sales proceeds from the sale of the Concho
         Properties is used to partially repay the Loans, and (d) any other
         sale of Properties sold at fair market value, so long as the aggregate
         Net Proceeds for all such sales made under this subclause (d) during
         the period between each redetermination of the Borrowing Base does not
         exceed $1,000,000."

         c.      The following defined terms are hereby added to Annex A of the
    Credit Agreement in their appropriate alphabetical order:

                 ""Concho Properties" means the Borrower's Oil and Gas
         Properties and other related assets described as the "Assets" in the
         Concho Purchase Agreement.

                 "Concho Purchase Agreement" means that certain Purchase and
         Sale Agreement dated December 17, 1997, by and between the Borrower
         and Concho Resources, Inc., a Delaware corporation."

         Section 3. Ratification. The Borrower hereby ratifies and confirms all
of the Obligations under the Credit Agreement (as amended hereby) and the other
Loan Documents. All references in the Loan Documents to the "Credit Agreement"
shall mean the Credit Agreement as amended hereby and as the same may be
amended, supplemented, restated or otherwise modified and in effect from time
to time in the future.

         Section 4. Effectiveness. The effectiveness of this Amendment is
subject to the condition precedent that the Agent shall have received all of
the following, each in form and substance reasonably satisfactory to the Bank
Group and in such number of counterparts as may be reasonably requested by the
Agent:

         a.      this Amendment executed by the Borrower and each member of the
Bank Group; and

         b.      a fully executed copy of the Concho Purchase Agreement.


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         Section 5. Representations and Warranties. The Borrower hereby
represents and warrants to the Bank Group that (a) the execution, delivery and
performance of this Amendment has been duly authorized by all requisite
corporate action on the part of the Borrower, (b) each of the Credit Agreement
(as amended hereby) and the other Loan Documents to which it is a party
constitutes a valid and legally binding agreement enforceable against the
Borrower in accordance with its terms except, as such enforceability may be
limited by bankruptcy, insolvency, reorganization, moratorium, fraudulent
transfer or other similar laws relating to or affecting the enforcement of
creditors' rights generally and by general principles of equity, (c) the
representations and warranties by the Borrower contained in the Credit
Agreement as amended hereby and in the other Loan Documents are true and
correct on and as of the date hereof in all material respects as though made as
of the date hereof, (d) no Default or Event of Default exists under the Credit
Agreement (as amended hereby) or any of the other Loan Documents.

         Section 6. Choice of Law. This Amendment shall be governed by, and
construed in accordance with, the laws of the State of New York.

         Section 7. Final Agreement. THE CREDIT AGREEMENT (AS AMENDED HEREBY)
AND THE OTHER LOAN DOCUMENTS REPRESENT THE FINAL AGREEMENT BETWEEN THE PARTIES
AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS OR SUBSEQUENT
ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO ORAL AGREEMENTS BETWEEN THE
PARTIES.

         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to
be executed by its officers thereunto duly authorized as of the date first
above written.

                                       COSTILLA ENERGY, INC.
                                                            
                                       
                                       By:     /s/ BOBBY W. PAGE
                                           -----------------------------------
                                       Name:       Bobby W. Page
                                             ---------------------------------
                                       Title:      Senior Vice President
                                              --------------------------------





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                                       BANKERS TRUST COMPANY,
                                          as Agent and Bank
                                       
                                       By:        /s/ RYAN A. ZANIN
                                               --------------------------------
                                       Name:          RYAN A. ZANIN
                                               --------------------------------
                                       Title:         MANAGING DIRECTOR
                                               --------------------------------
                                       
                                       UNION BANK OF CALIFORNIA, N.A.,
                                          as Co-Agent and Bank
                                       
                                       By:        /s/ CARL STUTZMAN
                                               --------------------------------
                                       Name:          CARL STUTZMAN
                                               --------------------------------
                                       Title:         VICE PRESIDENT
                                               --------------------------------
                                       

                                       By:        /s/ RANDALL OSTERBER
                                               --------------------------------
                                       Name:          RANDALL OSTERBER
                                               --------------------------------
                                       Title:         VICE PRESIDENT
                                               --------------------------------
                                           
                                       
                                       DEN NORSKE BANK ASA
                                          as Bank

                                       By:        /s/ MORTEN BJORNSEN
                                               --------------------------------
                                       Name:          MORTEN BJORNSEN
                                               --------------------------------
                                       Title:         SENIOR VICE PRESIDENT
                                               --------------------------------


                                       By:        /s/ J. MORTEN KREUTZ
                                               --------------------------------
                                       Name:          J. MORTEN KREUTZ
                                               --------------------------------
                                       Title:         VICE PRESIDENT
                                               --------------------------------
                                           
                                       THE TORONTO DOMINION BANK
                                          as Bank
                                       
                                       By:        /s/ JORGE A. GARCIA
                                               --------------------------------
                                       Name:          JORGE A. GARCIA
                                               --------------------------------
                                       Title:         MGR. CR. ADMIN.
                                               --------------------------------
                                           



                                      
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                                       WELLS FARGO BANK, N.A. 
                                          as Bank
                                       
                                       By:        /s/ JEFFREY P. ROSE
                                               --------------------------------
                                       Name:          Jeffrey P. Rose
                                               --------------------------------
                                       Title:         Vice President
                                               --------------------------------




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