<PAGE>

                                                                      EXHIBIT 24

                            LYONDELL CHEMICAL COMPANY

                                POWER OF ATTORNEY

     WHEREAS, LYONDELL CHEMICAL COMPANY, a Delaware corporation (the "Company"),
intends to file with the Securities and Exchange Commission (the "Commission")
under the Securities Act of 1933, as amended (the "Act"), a Registration
Statement on Form S-8, together with any and all exhibits and other documents
having relation to said Registration Statement (collectively, the "Registration
Statement"), in connection with the Company's 1999 Long-Term Incentive Plan
adopted, as amended and restated.

     NOW, THEREFORE, the undersigned, in his or her capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint DAN F.
SMITH, T.KEVIN DENICOLA, CHARLES L. HALL and KERRY A. GALVIN, and each of them
severally, his or her true and lawful attorneys or attorney with power to act
with or without the others and with full power of substitution and
resubstitution, to execute in his or her name, place and stead, in his or her
capacity as a director or officer or both, as the case may be, of the Company,
the Registration Statement and all instruments necessary or incidental in
connection therewith, with such amendment or amendments thereto in each case as
may be necessary or appropriate, together with any and all exhibits and other
documents relating 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.

                                       1

<PAGE>

     IN WITNESS WHEREOF, the undersigned has executed this instrument on this
11th day of July, 2002.

   /s/ Dr. William T. Butler
-----------------------------------------------------
DR. WILLIAM T. BUTLER

   /s/ Dan F. Smith
-----------------------------------------------------
DAN F. SMITH

   /s/ Carol A. Anderson
-----------------------------------------------------
CAROL A. ANDERSON

   /s/ Travis Engen
-----------------------------------------------------
TRAVIS ENGEN

   /s/ Stephen F. Hinchliffe, Jr.
-----------------------------------------------------
STEPHEN F. HINCHLIFFE, JR.

   /s/ David J. Lesar
-----------------------------------------------------
DAVID J. LESAR

   /s/ Dudley C. Mecum II
-----------------------------------------------------
DUDLEY C. MECUM II

   /s/ Dr. William R. Spivey
-----------------------------------------------------
DR. WILLIAM R. SPIVEY

   /s/ T. Kevin DeNicola
-----------------------------------------------------
T. KEVIN DENICOLA

   /s/ Charles L. Hall
-----------------------------------------------------
CHARLES L. HALL

                                        2

<PAGE>

                                                                      EXHIBIT 24

                            LYONDELL CHEMICAL COMPANY

                                POWER OF ATTORNEY

     WHEREAS, LYONDELL CHEMICAL COMPANY, a Delaware corporation (the "Company"),
intends to file with the Securities and Exchange Commission (the "Commission")
under the Securities Act of 1933, as amended (the "Act"), a Registration
Statement on Form S-8, together with any and all exhibits and other documents
having relation to said Registration Statement (collectively, the "Registration
Statement"), in connection with the Company's 1999 Long-Term Incentive Plan
adopted, as amended and restated.

     NOW, THEREFORE, the undersigned, in his or her capacity as a director or
officer, or both, as the case may be, of the Company, does hereby appoint DAN F.
SMITH, T.KEVIN DENICOLA, CHARLES L. HALL and KERRY A. GALVIN, and each of them
severally, his or her true and lawful attorneys or attorney with power to act
with or without the others and with full power of substitution and
resubstitution, to execute in his or her name, place and stead, in his or her
capacity as a director or officer or both, as the case may be, of the Company,
the Registration Statement and all instruments necessary or incidental in
connection therewith, with such amendment or amendments thereto in each case as
may be necessary or appropriate, together with any and all exhibits and other
documents relating 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
3/rd/ day of October, 2002.


   /s/ Dr. Ray R. Irani
-----------------------------------------------------
DR. RAY R. IRANI

   /s/ Stephen I. Chazen
-----------------------------------------------------
STEPHEN I. CHAZEN