<PAGE>


                                                                      Exhibit 24

                            LYONDELL CHEMICAL COMPANY

                                POWER OF ATTORNEY

     Each person whose signature appears below hereby constitutes and appoints
Dan F. Smith, T. Kevin DeNicola, Charles L. Hall, and Kerry A. Galvin and each
of them, his or her true and lawful attorneys-in-fact and agents, with full
power of substitution and resubstitution, for him or her and in his or her name,
place and stead, in any and all capacities, in connection with any outstanding
securities of Lyondell Chemical Company (the "Company"), or any public offering
or other issuance of any securities of the Company authorized by the Board of
Directors of the Company, or by the Executive Committee thereof pursuant to due
authorization by such Board, (1) to execute and file, or cause to be filed, with
the United States Securities and Exchange Commission (the "Commission"), (A)
registration statements and any and all amendments (including post-effective
amendments), and exhibits thereto and any and all other documents in connection
therewith as required by the Commission in connection with such registration
under the Securities Act of 1933, as amended, and (B) any report or other
document required to be filed by the Company with the Commission pursuant to the
Securities Exchange Act of 1934, as amended, (2) to execute and file, or cause
to be filed, any application for registration or exemption therefrom, any report
or any other document required to be filed by the Company under the Blue Sky or
securities law of any state and to furnish any other information required in
connection therewith, (3) to execute and file, or cause to be filed, any
application for registration or exemption therefrom under the securities laws of
any jurisdiction outside the United States of America, including any reports or
other documents required to be filed subsequent to the issuance of such
securities, and (4) to execute and file, or cause to be filed, any application
for listing such securities on the New York Stock Exchange, or any other
securities exchange in any other jurisdiction where any such securities are
proposed to be sold, granting to such attorneys-in-fact and agents, and each of
them,


<PAGE>



Page 2 of 3

full power and authority to do and perform each and every act required to be
done as he or she might or could do in person, hereby ratifying and confirming
all that such attorneys-in-fact and agents, and each of them, may lawfully do or
cause to be done by virtue of this power of attorney. Each person whose
signature appears below may at any time revoke this power of attorney as to
himself or herself only by an instrument in writing specifying that this power
of attorney is revoked as to him or her as of the date of execution of such
instrument or at a subsequent specified date. This power of attorney shall be
revoked automatically with respect to any person whose signature appears below
effective on the date he or she ceases to be a member of the Board of Directors
or an officer of the Company. Any revocation hereof shall not void or otherwise
affect any acts performed by any attorney-in-fact and agent named herein
pursuant to this power of attorney prior to the effective date of such
revocation.

Dated:  March 6, 2003

        Signature                                   Title
        ---------                                   -----

 /s/ DAN F. SMITH             President, Chief Executive Officer and Director
-------------------------
Dan F. Smith


 /s/ T. KEVIN DENICOLA        Senior Vice President and Chief Financial Officer
-------------------------
T. Kevin DeNicola


 /s/ CHARLES L. HALL                   Vice President and Controller
-------------------------
Charles L. Hall


 /s/ KERRY A. GALVIN        Senior Vice President, General Counsel and Secretary
-------------------------
Kerry A. Galvin


<PAGE>


Page 3 of 3


        Signature                                   Title
        ---------                                   -----

 /s/ DR. WILLIAM T. BUTLER                 Chairman and Director
--------------------------------
Dr. William T. Butler


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


 /s/ STEPHEN CHAZEN                                Director
-------------------------------
Stephen Chazen


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


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


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


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


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

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