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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., a Delaware
Corporation, do hereby constitute and appoint Michael J. Grella and Bobby W.
Page, or either 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 Michael J. Grella and Bobby W. Page, or either of
them, may deem necessary or advisable to enable the Company to comply with the
Securities Act of 1933, as amended, any state securities laws and any rules,
regulations and requirements of the Securities and Exchange Commission in
connection with a Registration Statement or Registration Statements on Form S-4
seeking to register 10 1/4% Notes due 2006 of Costilla Energy, Inc., to be
issued in exchange for certain outstanding 10 1/4% notes of Costilla Energy,
Inc., including specifically, but not limited to, the power and authority to
sign such Registration Statement, any and all amendments (including post-
effective amendments) to such Registration Statement and any other forms or
documents related to such Registration Statement which are required under
federal or state securities laws for us, or any of us, in our names in the
capacities indicated; and we do hereby ratify and confirm all that Michael J.
Grella and Bobby W. Page, or either of them, shall do or cause to be done by
virtue hereof. This Power of Attorney may be 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,
1998.
 
                                                  /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 G. MUSSELMAN
                                            ------------------------------------
                                                     Henry G. Musselman
                                              Executive Vice President, Chief
                                               Operating Officer and Director
 
                                                     /s/ BOBBY PAGE
                                            ------------------------------------
                                                       Bobby W. Page
                                             Senior Vice President, Treasurer,
                                                Chief Financial Officer and
                                                         Secretary
 
                                                    /s/ JERRY LANGDON
                                            ------------------------------------
                                                       Jerry Langdon
                                                          Director
 
                                                    /s/ W.D. KENNEDY
                                            ------------------------------------
                                                        W.D. Kennedy
                                                          Director
 
                                                /s/ SAMUEL J. ATKINS, III
                                            ------------------------------------
                                                   Samuel J. Atkins, III
                                                          Director