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                                                                    EXHIBIT 24.1

                                POWER OF ATTORNEY

         KNOW ALL MEN BY THESE PRESENTS, the undersigned, being certain of the
Officers and all of the Directors of Costilla Energy, Inc. (the "Company"), a
Delaware Corporation, do hereby constitute and appoint Cadell S. Liedtke,
Michael J. Grella and Bobby W. Page, or any one of them, with full power of
substitution, our true and lawful attorneys and agents, to do any and all acts
and things in our names in the capacities indicated which Cadell S. Liedtke,
Michael J. Grella and Bobby W. Page, or any one of them, may deem necessary or
advisable to enable the Company to comply with the Securities Exchange Act of
1934, as amended, and any rules, regulations and requirements of the Securities
and Exchange Commission in connection with the Company's Annual Report on Form
10-K for the year ended December 31, 1998, including specifically, but not
limited to, the power and authority to sign such Form 10-K, any and all
amendments thereto and any other forms or documents related to such Form 10-K
which are required under federal securities law for us, or any of us, in our
names in the capacities indicated; and we do hereby ratify and confirm all that
Cadell S. Liedtke, Michael J. Grella and Bobby W. Page, or any one of them,
shall do or cause to be done by virtue hereof. This Power of Attorney maybe
signed in any number of counterparts, and each such counterpart shall be
considered an original hereof.

         IN WITNESS WHEREOF, I have hereunto set my hand this 19th day of March,
1999.


                                       /s/ Cadell S. Liedtke
                             --------------------------------------------------
                             CADELL S. LIEDTKE, Chairman of the Board
                             and Director


                                       /s/ Michael J. Grella
                             --------------------------------------------------
                             MICHAEL J. GRELLA, President, Chief
                             Executive Officer and Director


                                       /s/ Henry J. Musselman
                             --------------------------------------------------
                             HENRY G. MUSSELMAN, Executive Vice
                             President, Chief Operating Officer and Director


                                       /s/ Bobby W. Page
                             --------------------------------------------------
                             BOBBY W. PAGE, Senior Vice President,
                             Treasurer, Chief Financial Officer and Secretary


                                       /s/ Jerry J. Langdon
                             --------------------------------------------------
                             JERRY J. LANGDON, Director


                                       /s/ W. D. Kennedy
                             --------------------------------------------------
                             W. D. KENNEDY, Director

                                       /s/ Samuel J. Atkins
                             --------------------------------------------------
                             SAMUEL J. ATKINS, III, Director