<PAGE>   1

                                                                     EXHIBIT 24

                              PENNZOIL COMPANY

                              POWER OF ATTORNEY


         WHEREAS, PENNZOIL COMPANY, a Delaware corporation (Company), intends
to file with the Securities and Exchange Commission (Commission) under the
Securities Exchange Act of 1934, as amended (Act), an Annual Report on Form
10-K for the fiscal year ended December 31, 1997, as prescribed by the
Commission pursuant to the Act and the rules and regulations of the Commission
promulgated thereunder, with such amendments, supplements or appendices thereto
as may be necessary or appropriate, together with any and all exhibits and
other documents having relation to said Annual Report;

         NOW, THEREFORE, the undersigned in his capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint DAVID
P. ALDERSON, II, STEPHEN D. CHESEBRO' and JAMES L. PATE and each of them
severally, his true and lawful attorney or attorneys with power to act with or
without the others, and with full power of substitution and resubstitution, to
execute in his name, place and stead, in his capacity as a director or officer,
or both, as the case may be, of the Company, said Annual Report and any and all
amendments, supplements or appendices thereto as said attorneys or any of them
shall deem necessary or incidental in connection therewith and to file the same
or cause the same to be filed with the Commission.  Each of said attorneys
shall have full power and authority to do and perform in the name and on behalf
of the undersigned in any and all capacities, every act whatsoever necessary or
desirable to be done to the premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby
ratifying and approving the acts of said attorneys and each of them.

         IN WITNESS WHEREOF, the undersigned has executed this instrument on 
this 17th day of February, 1998.





                                        /s/ HOWARD H. BAKER, JR.
                                        ----------------------------
                                            Howard H. Baker, Jr.
<PAGE>   2
                               
                               PENNZOIL COMPANY

                              POWER OF ATTORNEY


         WHEREAS, PENNZOIL COMPANY, a Delaware corporation (Company), intends
to file with the Securities and Exchange Commission (Commission) under the
Securities Exchange Act of 1934, as amended (Act), an Annual Report on Form
10-K for the fiscal year ended December 31, 1997, as prescribed by the
Commission pursuant to the Act and the rules and regulations of the Commission
promulgated thereunder, with such amendments, supplements or appendices thereto
as may be necessary or appropriate, together with any and all exhibits and
other documents having relation to said Annual Report;

         NOW, THEREFORE, the undersigned in his capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint DAVID
P. ALDERSON, II, STEPHEN D. CHESEBRO' and JAMES L. PATE and each of them
severally, his true and lawful attorney or attorneys with power to act with or
without the others, and with full power of substitution and resubstitution, to
execute in his name, place and stead, in his capacity as a director or officer,
or both, as the case may be, of the Company, said Annual Report and any and all
amendments, supplements or appendices thereto as said attorneys or any of them
shall deem necessary or incidental in connection therewith and to file the same
or cause the same to be filed with the Commission.  Each of said attorneys
shall have full power and authority to do and perform in the name and on behalf
of the undersigned in any and all capacities, every act whatsoever necessary or
desirable to be done to the premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby
ratifying and approving the acts of said attorneys and each of them.

         IN WITNESS WHEREOF, the undersigned has executed this instrument on 
this 17th day of February, 1998.





                                        /s/ W. J. BOVAIRD
                                        -------------------------
                                            W. J. Bovaird
<PAGE>   3
                               PENNZOIL COMPANY

                              POWER OF ATTORNEY


         WHEREAS, PENNZOIL COMPANY, a Delaware corporation (Company), intends
to file with the Securities and Exchange Commission (Commission) under the
Securities Exchange Act of 1934, as amended (Act), an Annual Report on Form
10-K for the fiscal year ended December 31, 1997, as prescribed by the
Commission pursuant to the Act and the rules and regulations of the Commission
promulgated thereunder, with such amendments, supplements or appendices thereto
as may be necessary or appropriate, together with any and all exhibits and
other documents having relation to said Annual Report;

         NOW, THEREFORE, the undersigned in his capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint DAVID
P. ALDERSON, II, STEPHEN D. CHESEBRO' and JAMES L. PATE and each of them
severally, his true and lawful attorney or attorneys with power to act with or
without the others, and with full power of substitution and resubstitution, to
execute in his name, place and stead, in his capacity as a director or officer,
or both, as the case may be, of the Company, said Annual Report and any and all
amendments, supplements or appendices thereto as said attorneys or any of them
shall deem necessary or incidental in connection therewith and to file the same
or cause the same to be filed with the Commission.  Each of said attorneys
shall have full power and authority to do and perform in the name and on behalf
of the undersigned in any and all capacities, every act whatsoever necessary or
desirable to be done to the premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby
ratifying and approving the acts of said attorneys and each of them.

         IN WITNESS WHEREOF, the undersigned has executed this instrument on 
this 17th day of February, 1998.





                                        /s/ CHARLES BERDON LAWRENCE 
                                        -----------------------------
                                            Charles Berdon Lawrence
<PAGE>   4
                               PENNZOIL COMPANY

                              POWER OF ATTORNEY


         WHEREAS, PENNZOIL COMPANY, a Delaware corporation (Company), intends
to file with the Securities and Exchange Commission (Commission) under the
Securities Exchange Act of 1934, as amended (Act), an Annual Report on Form
10-K for the fiscal year ended December 31, 1997, as prescribed by the
Commission pursuant to the Act and the rules and regulations of the Commission
promulgated thereunder, with such amendments, supplements or appendices thereto
as may be necessary or appropriate, together with any and all exhibits and
other documents having relation to said Annual Report;

         NOW, THEREFORE, the undersigned in his capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint DAVID
P. ALDERSON, II, STEPHEN D. CHESEBRO' and JAMES L. PATE and each of them
severally, his true and lawful attorney or attorneys with power to act with or
without the others, and with full power of substitution and resubstitution, to
execute in his name, place and stead, in his capacity as a director or officer,
or both, as the case may be, of the Company, said Annual Report and any and all
amendments, supplements or appendices thereto as said attorneys or any of them
shall deem necessary or incidental in connection therewith and to file the same
or cause the same to be filed with the Commission.  Each of said attorneys
shall have full power and authority to do and perform in the name and on behalf
of the undersigned in any and all capacities, every act whatsoever necessary or
desirable to be done to the premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby
ratifying and approving the acts of said attorneys and each of them.

         IN WITNESS WHEREOF, the undersigned has executed this instrument on
this 17th day of February, 1998.





                                        /s/ BRENT SCOWCROFT 
                                        ----------------------------
                                            Brent Scowcroft
<PAGE>   5
                               PENNZOIL COMPANY

                              POWER OF ATTORNEY


         WHEREAS, PENNZOIL COMPANY, a Delaware corporation (Company), intends
to file with the Securities and Exchange Commission (Commission) under the
Securities Exchange Act of 1934, as amended (Act), an Annual Report on Form
10-K for the fiscal year ended December 31, 1997, as prescribed by the
Commission pursuant to the Act and the rules and regulations of the Commission
promulgated thereunder, with such amendments, supplements or appendices thereto
as may be necessary or appropriate, together with any and all exhibits and
other documents having relation to said Annual Report;

         NOW, THEREFORE, the undersigned in his capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint DAVID
P. ALDERSON, II, STEPHEN D. CHESEBRO' and JAMES L. PATE and each of them
severally, his true and lawful attorney or attorneys with power to act with or
without the others, and with full power of substitution and resubstitution, to
execute in his name, place and stead, in his capacity as a director or officer,
or both, as the case may be, of the Company, said Annual Report and any and all
amendments, supplements or appendices thereto as said attorneys or any of them
shall deem necessary or incidental in connection therewith and to file the same
or cause the same to be filed with the Commission.  Each of said attorneys
shall have full power and authority to do and perform in the name and on behalf
of the undersigned in any and all capacities, every act whatsoever necessary or
desirable to be done to the premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby
ratifying and approving the acts of said attorneys and each of them.

         IN WITNESS WHEREOF, the undersigned has executed this instrument on 
this 17th day of February, 1998.





                                        /s/ W. L. LYONS BROWN, JR.
                                        ---------------------------------
                                            W. L. Lyons Brown, Jr.
<PAGE>   6
                               PENNZOIL COMPANY

                              POWER OF ATTORNEY


         WHEREAS, PENNZOIL COMPANY, a Delaware corporation (Company), intends
to file with the Securities and Exchange Commission (Commission) under the
Securities Exchange Act of 1934, as amended (Act), an Annual Report on Form
10-K for the fiscal year ended December 31, 1997, as prescribed by the
Commission pursuant to the Act and the rules and regulations of the Commission
promulgated thereunder, with such amendments, supplements or appendices thereto
as may be necessary or appropriate, together with any and all exhibits and
other documents having relation to said Annual Report;

         NOW, THEREFORE, the undersigned in his capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint DAVID
P. ALDERSON, II, STEPHEN D. CHESEBRO' and JAMES L. PATE and each of them
severally, his true and lawful attorney or attorneys with power to act with or
without the others, and with full power of substitution and resubstitution, to
execute in his name, place and stead, in his capacity as a director or officer,
or both, as the case may be, of the Company, said Annual Report and any and all
amendments, supplements or appendices thereto as said attorneys or any of them
shall deem necessary or incidental in connection therewith and to file the same
or cause the same to be filed with the Commission.  Each of said attorneys
shall have full power and authority to do and perform in the name and on behalf
of the undersigned in any and all capacities, every act whatsoever necessary or
desirable to be done to the premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby
ratifying and approving the acts of said attorneys and each of them.

         IN WITNESS WHEREOF, the undersigned has executed this instrument on 
this 17th day of February, 1998.





                                        /s/ HARRY H. CULLEN
                                        ----------------------------
                                            Harry H. Cullen
<PAGE>   7
                               PENNZOIL COMPANY

                              POWER OF ATTORNEY


         WHEREAS, PENNZOIL COMPANY, a Delaware corporation (Company), intends
to file with the Securities and Exchange Commission (Commission) under the
Securities Exchange Act of 1934, as amended (Act), an Annual Report on Form
10-K for the fiscal year ended December 31, 1997, as prescribed by the
Commission pursuant to the Act and the rules and regulations of the Commission
promulgated thereunder, with such amendments, supplements or appendices thereto
as may be necessary or appropriate, together with any and all exhibits and
other documents having relation to said Annual Report;

         NOW, THEREFORE, the undersigned in his capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint DAVID
P. ALDERSON, II, STEPHEN D. CHESEBRO' and JAMES L. PATE and each of them
severally, his true and lawful attorney or attorneys with power to act with or
without the others, and with full power of substitution and resubstitution, to
execute in his name, place and stead, in his capacity as a director or officer,
or both, as the case may be, of the Company, said Annual Report and any and all
amendments, supplements or appendices thereto as said attorneys or any of them
shall deem necessary or incidental in connection therewith and to file the same
or cause the same to be filed with the Commission.  Each of said attorneys
shall have full power and authority to do and perform in the name and on behalf
of the undersigned in any and all capacities, every act whatsoever necessary or
desirable to be done to the premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby
ratifying and approving the acts of said attorneys and each of them.

         IN WITNESS WHEREOF, the undersigned has executed this instrument on 
this 17th day of February, 1998.





                                        /s/ CYRIL WAGNER, JR.    
                                        ---------------------------------
                                            Cyril Wagner, Jr.
<PAGE>   8
                               PENNZOIL COMPANY

                               POWER OF ATTORNEY


         WHEREAS, PENNZOIL COMPANY, a Delaware corporation (Company), intends
to file with the Securities and Exchange Commission (Commission) under the
Securities Exchange Act of 1934, as amended (Act), an Annual Report on Form
10-K for the fiscal year ended December 31, 1997, as prescribed by the
Commission pursuant to the Act and the rules and regulations of the Commission
promulgated thereunder, with such amendments, supplements or appendices thereto
as may be necessary or appropriate, together with any and all exhibits and
other documents having relation to said Annual Report;

         NOW, THEREFORE, the undersigned in his capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint DAVID
P. ALDERSON, II, STEPHEN D. CHESEBRO' and JAMES L. PATE and each of them
severally, his true and lawful attorney or attorneys with power to act with or
without the others, and with full power of substitution and resubstitution, to
execute in his name, place and stead, in his capacity as a director or officer,
or both, as the case may be, of the Company, said Annual Report and any and all
amendments, supplements or appendices thereto as said attorneys or any of them
shall deem necessary or incidental in connection therewith and to file the same
or cause the same to be filed with the Commission.  Each of said attorneys
shall have full power and authority to do and perform in the name and on behalf
of the undersigned in any and all capacities, every act whatsoever necessary or
desirable to be done to the premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby
ratifying and approving the acts of said attorneys and each of them.

         IN WITNESS WHEREOF, the undersigned has executed this instrument on 
this 17th day of February, 1998.





                                        /s/ ERNEST H. COCKRELL
                                        -----------------------------------
                                            Ernest H. Cockrell
<PAGE>   9
                               PENNZOIL COMPANY

                              POWER OF ATTORNEY


         WHEREAS, PENNZOIL COMPANY, a Delaware corporation (Company), intends
to file with the Securities and Exchange Commission (Commission) under the
Securities Exchange Act of 1934, as amended (Act), an Annual Report on Form
10-K for the fiscal year ended December 31, 1997, as prescribed by the
Commission pursuant to the Act and the rules and regulations of the Commission
promulgated thereunder, with such amendments, supplements or appendices thereto
as may be necessary or appropriate, together with any and all exhibits and
other documents having relation to said Annual Report;

         NOW, THEREFORE, the undersigned in his capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint DAVID
P. ALDERSON, II, STEPHEN D. CHESEBRO' and JAMES L. PATE and each of them
severally, his true and lawful attorney or attorneys with power to act with or
without the others, and with full power of substitution and resubstitution, to
execute in his name, place and stead, in his capacity as a director or officer,
or both, as the case may be, of the Company, said Annual Report and any and all
amendments, supplements or appendices thereto as said attorneys or any of them
shall deem necessary or incidental in connection therewith and to file the same
or cause the same to be filed with the Commission.  Each of said attorneys
shall have full power and authority to do and perform in the name and on behalf
of the undersigned in any and all capacities, every act whatsoever necessary or
desirable to be done to the premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby
ratifying and approving the acts of said attorneys and each of them.

         IN WITNESS WHEREOF, the undersigned has executed this instrument on 
this 17th day of February, 1998.





                                        /s/ ALFONSO FANJUL
                                        ---------------------------
                                            Alfonso Fanjul
<PAGE>   10
                               PENNZOIL COMPANY

                              POWER OF ATTORNEY


         WHEREAS, PENNZOIL COMPANY, a Delaware corporation (Company), intends
to file with the Securities and Exchange Commission (Commission) under the
Securities Exchange Act of 1934, as amended (Act), an Annual Report on Form
10-K for the fiscal year ended December 31, 1997, as prescribed by the
Commission pursuant to the Act and the rules and regulations of the Commission
promulgated thereunder, with such amendments, supplements or appendices thereto
as may be necessary or appropriate, together with any and all exhibits and
other documents having relation to said Annual Report;

         NOW, THEREFORE, the undersigned in his capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint DAVID
P. ALDERSON, II, STEPHEN D. CHESEBRO' and JAMES L. PATE and each of them
severally, his true and lawful attorney or attorneys with power to act with or
without the others, and with full power of substitution and resubstitution, to
execute in his name, place and stead, in his capacity as a director or officer,
or both, as the case may be, of the Company, said Annual Report and any and all
amendments, supplements or appendices thereto as said attorneys or any of them
shall deem necessary or incidental in connection therewith and to file the same
or cause the same to be filed with the Commission.  Each of said attorneys
shall have full power and authority to do and perform in the name and on behalf
of the undersigned in any and all capacities, every act whatsoever necessary or
desirable to be done to the premises, as fully and to all intents and purposes
as the undersigned might or could do in person, the undersigned hereby
ratifying and approving the acts of said attorneys and each of them.

         IN WITNESS WHEREOF, the undersigned has executed this instrument on 
this 17th day of February, 1998.





                                        /s/ GERALD B. SMITH      
                                        ----------------------------------
                                            Gerald B. Smith