EXHIBIT 24
 
                           LYONDELL CHEMICAL COMPANY

                               POWER OF ATTORNEY


     Each person whose signature appears below hereby constitutes and appoints
Dan F. Smith, Jeffrey R. Pendergraft, Robert J. Millstone, Van Billet, and
Edward W. Rich 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 

 
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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, 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 4, 1999

          SIGNATURE                                     TITLE


/s/ Dan F. Smith
_______________________________       President, Chief Executive Officer and 
Dan F. Smith                                          Director
 

/s/ Jeffrey R. Pendergraft
_______________________________            Executive Vice President and
Jeffrey R. Pendergraft                     Chief Administrative Officer
 

/s/ Robert J. Millstone
_______________________________    Vice President, General Counsel and Secretary
Robert J. Millstone
 
 
/s/ Van Billet
_______________________________           Vice President and Controller
Van Billet
 

 
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          SIGNATURE                                     TITLE 


/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/ Stephen F. Hinchliffe, Jr.
_______________________________                        Director
Stephen F. Hinchliffe, Jr.
 
 
/s/ Dudley C. Mecum II
_______________________________                        Director
Dudley C. Mecum II
 
 
/s/ Frank Savage
_______________________________                        Director
Frank Savage
 
 
/s/ Paul R. Stanley
_______________________________                        Director 
Paul R. Staley