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                                                                    EXHIBIT 23.1
 
                        CONSENT OF INDEPENDENT AUDITORS
 
The Board of Directors
Costilla Energy, Inc.
 
     We consent to the use of our reports incorporated herein by reference and
to the reference to our firm under the heading "Experts" in the Prospectus.
 
                                            KPMG LLP
 
Midland, Texas
   
February 10, 1999