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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 included herein and to the reference
to our firm under the heading "Experts" in the Prospectus.
 
                                            KPMG PEAT MARWICK LLP
 
Midland, Texas
April, 17, 1998