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                                                                    EXHIBIT 23.1

                        CONSENT OF KPMG PEAT MARWICK LLP


The Board of Directors
Costilla Energy, Inc.

We consent to incorporation by reference in the registration statements on Form
S-8 filed by Costilla Energy, Inc. (No.  333-16513, No. 333-16515, No.
333-16517, No. 333-38747 and No. 333-38751) of our report dated March 6, 1998,
relating to the consolidated balance sheets of Costilla Energy, Inc. and
subsidiaries as of December 31, 1997, 1996 and 1995, and the related
consolidated statements of operations, stockholders' equity, and cash flows for
each of the years in the three-year period ended December 31, 1997, which report
appears in the annual report on Form 10-K of Costilla Energy, Inc. for the year
ended December 31, 1997.




                                                KPMG PEAT MARWICK LLP

Midland, Texas
March 26, 1998