<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, 1999 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, 1999 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, 1999 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, 1999 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, 1999 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, 1999 and any and all amendments thereto.


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