<PAGE>   1
                                                                EXHIBIT 24 (CEI)


                 POWER OF ATTORNEY OF DIRECTOR AND/OR OFFICER OF
                 -----------------------------------------------

                   THE CLEVELAND ELECTRIC ILLUMINATING COMPANY
                   -------------------------------------------






         The undersigned, being a director or officer or both (as stated under
his or her signature below) of The Cleveland Electric Illuminating Company, an
Ohio corporation (hereinafter called the "Company"), does hereby constitute and
appoint each of Robert J. Farling, Murray R. Edelman, Fred J. Lange, Jr., Gary
R. Leidich, Terrence G. Linnert, David M. Blank, E. Lyle Pepin, Janis T. Percio,
Ronald J. Studeny, Mary E. O'Reilly and Paul N. Edwards as an attorney of the
undersigned with power to act alone for and in the name, place and stead of the
undersigned, with power of substitution and resubstitution, to sign and file,
including electronic filing, on behalf of the undersigned acting in his or her
capacity as such director or officer the Company's Form 10-K Annual Report for
the year ended December 31, 1996, and any and all amendments, exhibits and
supplementary information thereto, with the Securities and Exchange Commission
pursuant to the Securities Exchange Act of 1934, with full power and authority
to do and perform any and all acts and things whatsoever requisite and necessary
to be done in the premises and the undersigned hereby ratifies and approves the
acts of each such attorney and any such substitute or substitutes.

         IN WITNESS WHEREOF, the undersigned hereby has signed his or her name
this 28th day of February, 1997.





                                              ROBERT J.FARLING
                                              ----------------------------------
                                              Robert J. Farling
                                              Chairman, Chief Executive Officer
                                              and Director




Signed and acknowledged in the presence of:   J.T. PERCIO
                                              --------------------------------

<PAGE>   2


                                                                EXHIBIT 24 (CEI)

                 POWER OF ATTORNEY OF DIRECTOR AND/OR OFFICER OF
                 -----------------------------------------------

                   THE CLEVELAND ELECTRIC ILLUMINATING COMPANY
                   -------------------------------------------






         The undersigned, being a director or officer or both (as stated under
his or her signature below) of The Cleveland Electric Illuminating Company, an
Ohio corporation (hereinafter called the "Company"), does hereby constitute and
appoint each of Robert J. Farling, Murray R. Edelman, Fred J. Lange, Jr., Gary
R. Leidich, Terrence G. Linnert, David M. Blank, E. Lyle Pepin, Janis T. Percio,
Ronald J. Studeny, Mary E. O'Reilly and Paul N. Edwards as an attorney of the
undersigned with power to act alone for and in the name, place and stead of the
undersigned, with power of substitution and resubstitution, to sign and file,
including electronic filing, on behalf of the undersigned acting in his or her
capacity as such director or officer the Company's Form 10-K Annual Report for
the year ended December 31, 1996, and any and all amendments, exhibits and
supplementary information thereto, with the Securities and Exchange Commission
pursuant to the Securities Exchange Act of 1934, with full power and authority
to do and perform any and all acts and things whatsoever requisite and necessary
to be done in the premises and the undersigned hereby ratifies and approves the
acts of each such attorney and any such substitute or substitutes.

         IN WITNESS WHEREOF, the undersigned hereby has signed his or her name
this 6th day of March, 1997.





                                           TERRENCE G. LINNERT
                                           ----------------------------------
                                           Terrence G. Linnert
                                           Vice President and Chief Financial
                                           Officer





Signed and acknowledged in the presence of:    JEAN M. LeMAY
                                            -----------------------------
<PAGE>   3


                                                                EXHIBIT 24 (CEI)

                 POWER OF ATTORNEY OF DIRECTOR AND/OR OFFICER OF
                 -----------------------------------------------

                   THE CLEVELAND ELECTRIC ILLUMINATING COMPANY
                   -------------------------------------------






         The undersigned, being a director or officer or both (as stated under
his or her signature below) of The Cleveland Electric Illuminating Company, an
Ohio corporation (hereinafter called the "Company"), does hereby constitute and
appoint each of Robert J. Farling, Murray R. Edelman, Fred J. Lange, Jr., Gary
R. Leidich, Terrence G. Linnert, David M. Blank, E. Lyle Pepin, Janis T. Percio,
Ronald J. Studeny, Mary E. O'Reilly and Paul N. Edwards as an attorney of the
undersigned with power to act alone for and in the name, place and stead of the
undersigned, with power of substitution and resubstitution, to sign and file,
including electronic filing, on behalf of the undersigned acting in his or her
capacity as such director or officer the Company's Form 10-K Annual Report for
the year ended December 31, 1996, and any and all amendments, exhibits and
supplementary information thereto, with the Securities and Exchange Commission
pursuant to the Securities Exchange Act of 1934, with full power and authority
to do and perform any and all acts and things whatsoever requisite and necessary
to be done in the premises and the undersigned hereby ratifies and approves the
acts of each such attorney and any such substitute or substitutes.

         IN WITNESS WHEREOF, the undersigned hereby has signed his or her name
this 3rd day of March, 1997.





                                           E LYLE  PEPIN
                                           ---------------------------------
                                           E. Lyle Pepin
                                           Controller



Signed and acknowledged in the presence of:   RUTH A. HARNER
                                            -------------------------

<PAGE>   4



                                                                EXHIBIT 24 (CEI)

                 POWER OF ATTORNEY OF DIRECTOR AND/OR OFFICER OF
                 -----------------------------------------------

                   THE CLEVELAND ELECTRIC ILLUMINATING COMPANY
                   -------------------------------------------






         The undersigned, being a director or officer or both (as stated under
his or her signature below) of The Cleveland Electric Illuminating Company, an
Ohio corporation (hereinafter called the "Company"), does hereby constitute and
appoint each of Robert J. Farling, Murray R. Edelman, Fred J. Lange, Jr., Gary
R. Leidich, Terrence G. Linnert, David M. Blank, E. Lyle Pepin, Janis T. Percio,
Ronald J. Studeny, Mary E. O'Reilly and Paul N. Edwards as an attorney of the
undersigned with power to act alone for and in the name, place and stead of the
undersigned, with power of substitution and resubstitution, to sign and file,
including electronic filing, on behalf of the undersigned acting in his or her
capacity as such director or officer the Company's Form 10-K Annual Report for
the year ended December 31, 1996, and any and all amendments, exhibits and
supplementary information thereto, with the Securities and Exchange Commission
pursuant to the Securities Exchange Act of 1934, with full power and authority
to do and perform any and all acts and things whatsoever requisite and necessary
to be done in the premises and the undersigned hereby ratifies and approves the
acts of each such attorney and any such substitute or substitutes.

         IN WITNESS WHEREOF, the undersigned hereby has signed his or her name
this 21st day of March, 1997.





                                             MURRAY R EDELMAN
                                             ---------------------------
                                             Murray R. Edelman
                                             President and Director




Signed and acknowledged in the presence of:   J T PERCIO
                                            ---------------------------

<PAGE>   5


                                                                EXHIBIT 24 (CEI)

                 POWER OF ATTORNEY OF DIRECTOR AND/OR OFFICER OF
                 -----------------------------------------------

                   THE CLEVELAND ELECTRIC ILLUMINATING COMPANY
                   -------------------------------------------






         The undersigned, being a director or officer or both (as stated under
his or her signature below) of The Cleveland Electric Illuminating Company, an
Ohio corporation (hereinafter called the "Company"), does hereby constitute and
appoint each of Robert J. Farling, Murray R. Edelman, Fred J. Lange, Jr., Gary
R. Leidich, Terrence G. Linnert, David M. Blank, E. Lyle Pepin, Janis T. Percio,
Ronald J. Studeny, Mary E. O'Reilly and Paul N. Edwards as an attorney of the
undersigned with power to act alone for and in the name, place and stead of the
undersigned, with power of substitution and resubstitution, to sign and file,
including electronic filing, on behalf of the undersigned acting in his or her
capacity as such director or officer the Company's Form 10-K Annual Report for
the year ended December 31, 1996, and any and all amendments, exhibits and
supplementary information thereto, with the Securities and Exchange Commission
pursuant to the Securities Exchange Act of 1934, with full power and authority
to do and perform any and all acts and things whatsoever requisite and necessary
to be done in the premises and the undersigned hereby ratifies and approves the
acts of each such attorney and any such substitute or substitutes.

         IN WITNESS WHEREOF, the undersigned hereby has signed his or her name
this 28th day of February, 1997.





                                           FRED J LANGE JR
                                           -----------------------------------
                                           Fred J. Lange, Jr.
                                           Vice President and Director




Signed and acknowledged in the presence of:   KENDRA STANO
                                             ----------------