<PAGE>   1




                                                                    Exhibit 24.1


                                POWER OF ATTORNEY



KNOW ALL MEN BY THESE PRESENTS, that the undersigned hereby constitutes and
appoints Mikel D. Faulkner, Bruce N. Huff, Larry E. Cummings and Gregory S.
Porter, or any of them (with full power of each of them to act alone), his true
and lawful attorney-in-fact and agent, with full power of substitution, for him
and on his behalf and in his name, place and stead, in any and all capacities,
to sign, execute and file a Registration Statement on Form S-3 under the
Securities Act of 1933, as amended, and any or all amendments (including without
limitation, post-effective amendments and any amendment or amendments increasing
the amount of securities for which registration is being sought), with all
exhibits and any and all documents required to be filed with respect thereto,
with the Securities and Exchange Commission and/or any regulatory authority
relating to the registration of 5,751,073 shares of Common Stock, $0.01 par
value, of Harken Energy Corporation and such additional shares of Common Stock
as the holders of "piggy-back" registration rights may request to be included in
such registration statement, granting unto said attorneys-in-fact and agents,
and each of them, full power and authority to do and perform each and every act
and thing requisite and necessary to be done in and about the premises in order
to effectuate the same, as fully and to all intents and purposes as he himself
might or could do if personally present, hereby ratifying and confirming all
that the said attorneys-in-fact and agents, or any of them, or their substitute
or substitutes, may lawfully do or cause to be done.

IN WITNESS WHEREOF, this Power of Attorney has been signed by the following
persons in the capacities indicated as of the 15th day of May, 1998.


       NAME                            CAPACITIES

       /s/ Mikel D. Faulkner           Chairman of the Board, Director and
       --------------------------      Chief Executive Officer 
       Mikel D. Faulkner               (Principal Executive Officer)
                                       

       /s/ Bruce N. Huff               President and Chief Operating Officer and
       --------------------------      Director 
       Bruce N. Huff                   


       /s/  Richard H. Schroeder       Vice Chairman and Director
       --------------------------
       Richard H. Schroeder



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POWER OF ATTORNEY
May 15, 1998
Page 2




       /s/ Stephen C. Voss             President of Harken International, Ltd. 
       --------------------------      and Director
       Stephen C. Voss                 


       /s/ Gary R. Petersen            Director
       --------------------------
       Gary R. Petersen


       /s/ Michael M. Ameen, Jr.       Director
       --------------------------
       Michael M. Ameen, Jr.


       --------------------------     Director
       Michael R. Eisenson


       /s/ Hobart A. Smith            Director
       --------------------------
       Hobart A. Smith

      /s/ Donald W. Raymond          
      ----------------------------    Director
      Donald W. Raymond


       /s/ Gary B. Wood               Director
       --------------------------
       Gary B. Wood


       /s/ A. Wayne Hennecke          Vice President of Finance and Chief 
       --------------------------     Financial Officer (Principal Accounting 
       A. Wayne Hennecke              Officer and Principal Financial Officer)