<PAGE>   1

                                                                     EXHIBIT 24



                               POWER OF ATTORNEY

         The person whose signature appears below hereby appoints Michael D.
Burke and Lori L. Maddox, or either of them, as attorneys-in-fact with full
power of substitution, to execute in the name and on behalf of the undersigned
in his capacity as a director of EOTT Energy Corp., and to file with the
Securities and Exchange Commission, the Form 10-K Annual Report of EOTT Energy
Partners, L.P. for the year ended December 31, 1998 and any and all amendments
thereto.


                                       /s/ EDWARD O. GAYLORD   
                                       -----------------------------------------
                                       Edward O. Gaylord



<PAGE>   2



                               POWER OF ATTORNEY

         The person whose signature appears below hereby appoints Michael D.
Burke and Lori L. Maddox, or either of them, as attorneys-in-fact with full
power of substitution, to execute in the name and on behalf of the undersigned
in his capacity as a director of EOTT Energy Corp., and to file with the
Securities and Exchange Commission, the Form 10-K Annual Report of EOTT Energy
Partners, L.P. for the year ended December 31, 1998 and any and all amendments
thereto.


                                       /s/ JOHN H. DUNCAN      
                                       -----------------------------------------
                                       John H. Duncan



<PAGE>   3



                               POWER OF ATTORNEY

         The person whose signature appears below hereby appoints Michael D.
Burke and Lori L. Maddox, or either of them, as attorneys-in-fact with full
power of substitution, to execute in the name and on behalf of the undersigned
in his capacity as a director of EOTT Energy Corp., and to file with the
Securities and Exchange Commission, the Form 10-K Annual Report of EOTT Energy
Partners, L.P. for the year ended December 31, 1998 and any and all amendments
thereto.


                                       /s/ KENNETH L. LAY      
                                       -----------------------------------------
                                       Kenneth L. Lay



<PAGE>   4



                               POWER OF ATTORNEY

         The person whose signature appears below hereby appoints Michael D.
Burke and Lori L. Maddox, or either of them, as attorneys-in-fact with full
power of substitution, to execute in the name and on behalf of the undersigned
in his capacity as a director of EOTT Energy Corp., and to file with the
Securities and Exchange Commission, the Form 10-K Annual Report of EOTT Energy
Partners, L.P. for the year ended December 31, 1998 and any and all amendments
thereto.


                                       /s/ DEE S OSBORNE       
                                       -----------------------------------------
                                       Dee S. Osborne



<PAGE>   5



                               POWER OF ATTORNEY

         The person whose signature appears below hereby appoints Michael D.
Burke and Lori L. Maddox, or either of them, as attorneys-in-fact with full
power of substitution, to execute in the name and on behalf of the undersigned
in his capacity as a director of EOTT Energy Corp., and to file with the
Securities and Exchange Commission, the Form 10-K Annual Report of EOTT Energy
Partners, L.P. for the year ended December 31, 1998 and any and all amendments
thereto.


                                       /s/ STANLEY C. HORTON   
                                       -----------------------------------------
                                       Stanley C. Horton



<PAGE>   6



                               POWER OF ATTORNEY

         The person whose signature appears below hereby appoints Michael D.
Burke and Lori L. Maddox, or either of them, as attorneys-in-fact with full
power of substitution, to execute in the name and on behalf of the undersigned
in his capacity as a director of EOTT Energy Corp., and to file with the
Securities and Exchange Commission, the Form 10-K Annual Report of EOTT Energy
Partners, L.P. for the year ended December 31, 1998 and any and all amendments
thereto.


                                       /s/ DANIEL P. WHITTY    
                                       -----------------------------------------
                                       Daniel P. Whitty