<PAGE>

                                                                    Exhibit 24.1

                           LYONDELL CHEMICAL COMPANY

                               POWER OF ATTORNEY

         Each person whose signature appears below hereby constitutes and
appoints Dan F. Smith, Robert T. Blakely, 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,
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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:  February 8, 2002


<TABLE>
<CAPTION>

                         Signature                                                    Title
<S>                                                              <C>
/s/ DAN F. SMITH                                                 President, Chief Executive Officer and Director
-------------------------------
Dan F. Smith

/s/ ROBERT T. BLAKELY                                                      Executive Vice President and
-------------------------------                                               Chief Financial Officer
Robert T. Blakely


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

/s/ KERRY A. GALVIN                                               Vice President, General Counsel and Secretary
-------------------------------
Kerry A. Galvin
</TABLE>
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<TABLE>
<CAPTION>

                         Signature                                                    Title
<S>                                                                          <C>
/s/ DR. WILLIAM T. BUTLER                                                     Chairman and Director
-------------------------------
Dr. William T. Butler


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

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

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

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



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



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



/s/ PAUL R. STALEY                                                                   Director
-------------------------------
Paul R. Staley


</TABLE>