<PAGE>   1
                                                              Exhibit 24(CEI)
<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 Kevin P. Murphy 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, 1995, 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 1st day of March, 1996.





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




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

<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 Kevin P. Murphy 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, 1995, 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 29th day of February, 1996.





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



Signed and acknowledged in the presence of: JEAN M. LeMAY
                                            ----------------------------
<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 Kevin P. Murphy 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, 1995, 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 29th day of February, 1996.





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



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



<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 Kevin P. Murphy 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, 1995, 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, 1996.





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




Signed and acknowledged in the presence of: MARIA-ELENA G. JANSEN
                                            --------------------------
<PAGE>   6

                                                                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 Kevin P. Murphy 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, 1995, 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, 1996.





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




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