LYONDELL PETROCHEMICAL CO
DEF 14A, 1998-04-06
PETROLEUM REFINING
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<PAGE>
 
                           SCHEDULE 14A INFORMATION

          Proxy Statement Pursuant to Section 14(a) of the Securities
                    Exchange Act of 1934 (Amendment No.  )
        
Filed by the Registrant [X]

Filed by a Party other than the Registrant [_] 

Check the appropriate box:

[_]  Preliminary Proxy Statement         [_]  CONFIDENTIAL, FOR USE OF THE
                                              COMMISSION ONLY (AS PERMITTED BY
                                              RULE 14A-6(E)(2))

[X]  Definitive Proxy Statement 

[_]  Definitive Additional Materials 

[_]  Soliciting Material Pursuant to Section 240.14a-11(c) or Section 240.14a-12

                        LYONDELL PETROCHEMICAL COMPANY
- --------------------------------------------------------------------------------
               (Name of Registrant as Specified In Its Charter)

                                Not Applicable
- --------------------------------------------------------------------------------
   (Name of Person(s) Filing Proxy Statement, if other than the Registrant)

   
Payment of Filing Fee (Check the appropriate box):

[X]  No fee required

[_]  Fee computed on table below per Exchange Act Rules 14a-6(i)(4) and 0-11.

   
     (1) Title of each class of securities to which transaction applies:

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     (2) Aggregate number of securities to which transaction applies:

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     (3) Per unit price or other underlying value of transaction computed
         pursuant to Exchange Act Rule 0-11 (Set forth the amount on which
         the filing fee is calculated and state how it was determined):

     -------------------------------------------------------------------------
      

     (4) Proposed maximum aggregate value of transaction:

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     (5) Total fee paid:

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[_]  Fee paid previously with preliminary materials.
     
[_]  Check box if any part of the fee is offset as provided by Exchange
     Act Rule 0-11(a)(2) and identify the filing for which the offsetting fee
     was paid previously. Identify the previous filing by registration statement
     number, or the Form or Schedule and the date of its filing.
     
     (1) Amount Previously Paid:
 
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     (2) Form, Schedule or Registration Statement No.:

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     (3) Filing Party:
      
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     (4) Date Filed:

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Notes:

<PAGE>

[LOGO OF LYONDELL APPEARS HERE] 
 
LYONDELL
PETROCHEMICAL
COMPANY
 
 
 
NOTICE OF
ANNUAL MEETING
OF STOCKHOLDERS
TO BE HELD
ON MAY 15, 1998
AND PROXY STATEMENT
 
                     PLEASE COMPLETE, SIGN, DATE AND RETURN
                              YOUR PROXY PROMPTLY
 
<PAGE>
 
 
                        LYONDELL PETROCHEMICAL COMPANY
                       1221 MCKINNEY STREET, SUITE 1600
                             HOUSTON, TEXAS 77010
 
March 31, 1998
 
Dear Stockholder:
 
  The 1998 Annual Meeting of Stockholders will be held on Friday, May 15,
1998, beginning at 10:00 a.m. at the Four Seasons Hotel, 1300 Lamar in
Houston, Texas. This booklet includes the Notice of the Meeting and the Proxy
Statement, which contains information about the formal business to be acted
upon by the stockholders. We do not anticipate any other business except for
the two regularly scheduled items.
 
  It is important that your shares be voted whether or not you plan to be
present at the meeting. Please complete, sign, date and return the enclosed
form of proxy promptly. If you do plan to attend, we would appreciate your
checking the appropriate box on the enclosed proxy card.
 
Sincerely yours,
 
/s/ Dan F. Smith
 
Dan F. Smith
President and Chief Executive Officer
<PAGE>
 
 
                        LYONDELL PETROCHEMICAL COMPANY
 
                   NOTICE OF ANNUAL MEETING OF STOCKHOLDERS
 
                                 MAY 15, 1998
 
TO THE STOCKHOLDERS:
 
  The Annual Meeting of Stockholders of Lyondell Petrochemical Company will be
held at the Four Seasons Hotel, 1300 Lamar, in Houston, Texas, at 10:00 a.m.,
Houston time, on Friday, May 15, 1998, for the following purposes, as more
fully described in the attached Proxy Statement.
 
  (1) To elect six directors to serve until the 1999 Annual Meeting of
      Stockholders or until their earlier resignation or removal;
 
  (2) To ratify the joint appointment of Coopers & Lybrand L.L.P. and Price
      Waterhouse LLP, independent auditors, including any successor merged
      entity of the two firms, as the Company's auditors for the year 1998;
      and
 
  (3) To transact such other business as may properly come before the meeting
      or any adjournment thereof.
 
  Stockholders of record at the close of business on March 18, 1998 will be
entitled to notice of and to vote at the meeting and any adjournment thereof.
 
  PLEASE READ THE PROXY STATEMENT, THEN COMPLETE, SIGN AND DATE THE FORM OF
PROXY AND RETURN IT IN THE ENCLOSED SELF-ADDRESSED POSTPAID ENVELOPE.
 
BY ORDER OF THE BOARD OF DIRECTORS,

/s/ Kerry A. Galvin
Kerry A. Galvin                                           Houston, Texas
Secretary                                                 March 31, 1998
<PAGE>
 
 
                        LYONDELL PETROCHEMICAL COMPANY
                             1221 MCKINNEY STREET
                                  SUITE 1600
                             HOUSTON, TEXAS 77010
 
                               ----------------
 
                                PROXY STATEMENT
                                MARCH 31, 1998
 
                               ----------------
 
                                 INTRODUCTION
 
 
  The accompanying proxy is solicited by the Board of Directors of Lyondell
Petrochemical Company ("Lyondell" or the "Company"). When a proxy is returned
properly dated and signed, the shares represented thereby will be voted by the
persons named as proxies in accordance with each stockholder's directions. If
a proxy is dated, signed and returned without specifying choices, the shares
will be voted as recommended by the directors of the Company. As to other
items of business that may come before the meeting or any adjournment thereof,
the persons named in the accompanying form of proxy will vote in accordance
with their best judgment. It is expected that proxy materials will be mailed
to stockholders beginning on or about April 6, 1998.
 
                               VOTING PROCEDURES
 
  Holders of record of Common Stock at the close of business on March 18, 1998
will be entitled to one vote per share. The Company had 78,491,488 shares of
Common Stock outstanding on such record date. Fractional shares will not be
voted. The presence, in person or by proxy, of stockholders entitled to cast
at least a majority of the votes that all stockholders are entitled to cast
will constitute a quorum. Abstentions and broker non-votes are counted as
present in determining whether the quorum requirement is satisfied.
 
  The directors will be elected by a plurality of the shares of Common Stock
cast in person or represented by proxy at the meeting. Adoption of the
proposal to ratify the appointment of the independent auditors will require
the affirmative vote of a majority of the shares present in person or
represented by proxy at the meeting.
 
  Abstentions from voting on any matter will be included in the voting tally
and will have the same effect as a vote withheld on the election of directors
or against the ratification of the appointment of the independent auditors, as
the case may be. Because broker non-votes (instances where brokers are
prohibited from exercising discretionary authority for beneficial owners who
have not returned a proxy) are not considered "shares present" with respect to
a matter requiring the affirmative vote of a majority of shares present in
person or by proxy at the meeting, broker non-votes will not affect the
outcome with respect to the ratification of the appointment of the independent
auditors.
 
  The Company's 401(k) and Savings Plan, in which employees, including
executive officers, have account balances, permits plan participants to direct
the plan trustees how to vote the Common Stock allocated to their accounts.
The trustee will vote all shares of Common Stock for which no participant
directions are received as directed by the Plan's Benefits Administrative
Committee which is comprised of executive officers of the Company.
 
  The proxy may be revoked by the stockholder at any time prior to the time it
is voted by giving notice of such revocation in writing to the Secretary of
Lyondell, by submitting another valid proxy bearing a later date or by voting
in person at the meeting.
<PAGE>
 
                            PRINCIPAL STOCKHOLDERS
 
  The table below sets forth certain information as of December 31, 1997 (the
most recent date as of which the Company has information except as otherwise
noted below) regarding the beneficial ownership of the Common Stock by persons
known by the Company to beneficially own more than five percent of its
outstanding shares of Common Stock. Information in the table and footnotes is
based on the most recent respective Statement on Schedule 13G or 13D or
amendment thereto filed by such persons with the Securities and Exchange
Commission (the "SEC"), except as otherwise known to the Company.
 
<TABLE>
<CAPTION>
                                                                    PERCENTAGE
                                                          NUMBER OF  OF SHARES
                       NAME AND ADDRESS                    SHARES   OUTSTANDING
                       ----------------                   --------- -----------
      <S>                                                 <C>       <C>
      Wellington Management Company, LLP(a).............. 9,189,403    11.6%
      75 State Street, Boston, Massachusetts 02109
      Brinson Partners, Inc.(b).......................... 6,450,925     8.2%
      209 South LaSalle, Chicago, Illinois 60604-1295
      State Street Bank and Trust Company(c)............. 5,703,392     7.2%
      225 Franklin Street, Boston, Massachusetts 02110
      Scudder Kemper, Investments, Inc.(d)............... 4,963,389     6.3%
      345 Park Avenue, New York, New York 10154
</TABLE>
- --------
(a) Wellington Management Company, LLP ("WMC") (together with its wholly-owned
    subsidiary, Wellington Trust Management Company, N.A.) may be deemed a
    beneficial owner of the 9,189,403 shares by virtue of the direct or
    indirect investment and/or voting discretion they possess pursuant to the
    provisions of investment advisory agreements with clients, including the
    Vanguard/Windsor Fund, Inc. ("Vanguard"). WMC has shared dispositive power
    over the 9,189,403 shares and shared voting power over 600 shares.
    Vanguard has shared dispositive power over 9,188,803 shares and sole
    voting power over 9,188,803 shares.
(b) Brinson Partners, Inc. ("BPI"), and its parent holding companies, Brinson
    Holdings, Inc. ("BHI", SBC Holding (USA), Inc. ("SBCUSA") and Swiss Bank
    Corporation ("SBC") may be deemed a beneficial owner of the 6,450,925
    shares by virtue of the direct or indirect investment and/or voting
    discretion they possess pursuant to the provisions of investment advisory
    agreements with clients. BPI, SBCUSA, SBC and BHI have shared voting and
    shared dispositive power over all 6,450,925 shares.
(c) State Street Bank and Trust Company ("State Street"), (i) Trustee for the
    Lyondell Petrochemical Company 401(k) and Savings Plan; (ii) Trustee for
    the LYONDELL-CITGO Refining Company Ltd. 401(k) and Savings Plan; (iii)
    Trustee or Discretionary Advisor for various collective investment funds
    for employee benefit plans and other index accounts; and (iv) Trustee or
    Co-Trustee for various trust accounts, may be deemed a beneficial owner of
    the 5,703,392 shares by virtue of the direct or indirect investment and/or
    voting discretion it possesses pursuant to the provisions of investment
    advisory agreements with clients. State Street has sole voting power over
    2,553,006 shares and shared voting power over 3,118,586 shares, sole
    dispositive power over 2,582,506 shares and shared dispositive power over
    3,120,886 shares.
(d) Scudder Kemper Investments, Inc. ("Scudder Kemper") may be deemed a
    beneficial holder of 4,963,389 shares. Scudder Kemper has sole voting
    power over 1,824,948 shares and shared voting power over 2,657,553 shares,
    and has sole dispositive power over all 4,963,389 shares.
 
                                       2
<PAGE>
 
                       SECURITY OWNERSHIP OF MANAGEMENT
 
  The following table sets forth the number of shares of Common Stock owned
beneficially as of February 1, 1998 by each director or nominee, each of the
executive officers named in the Summary Compensation Table and by all
directors and executive officers as a group. As of February 1, 1998, the
percentage of shares of Common Stock beneficially owned by any director or
nominee, named executive officer or by all directors and executive officers as
a group, did not exceed one percent of the issued and outstanding Common
Stock. Unless otherwise noted, each individual has sole voting and investment
power.
 
<TABLE>
<CAPTION>
                                                         SHARES OF COMMON STOCK
                                                         OWNED BENEFICIALLY AS
                                                             OF FEBRUARY 1,
                                                               1998(A)(B)
                                                         ----------------------
      <S>                                                <C>
      William T. Butler.................................          5,553
      Curtis J. Crawford................................          2,243
      Travis Engen......................................          3,243
      Stephen F. Hinchliffe, Jr.........................          8,143(c)
      Dudley C. Mecum II................................          2,943
      Richard W. Park...................................         53,502
      Jeffrey R. Pendergraft............................         37,444
      Dan F. Smith......................................         87,882
      Paul R. Staley....................................          2,493
      Debra L. Starnes..................................         68,089(d)
      Russell S. Young..................................         72,624(e)
      All directors and executive officers as a
       group(14)........................................        370,552(f)
</TABLE>
- --------
(a) Includes shares held by the trustee under the Lyondell 401(k) and Savings
    Plan for the accounts of participants as of December 31, 1997.
(b) The amounts shown include shares that may be acquired within 60 days
    following February 1, 1998 through the exercise of stock options, as
    follows: Mr. Smith, 32,200; Mr. Pendergraft, 25,300; Mr. Young, 39,400;
    Ms. Starnes, 32,500; Mr. Park, 31,100 and all directors and executive
    officers as a group, including those just named, 169,277.
(c) Does not include 1,000 shares held by a trust of which Mr. Hinchliffe is a
    trustee, as to which shares he disclaims beneficial ownership.
(d) Does not include approximately 8,000 shares owned by Ms. Starnes' spouse,
    as to which shares she disclaims beneficial ownership.
(e) Does not include 1,100 shares owned by Mr. Young's spouse, as to which
    shares he disclaims beneficial ownership.
(f) Does not include the approximately 10,100 shares owned by spouses and a
    trust, as to which shares beneficial ownership is disclaimed.
 
                                       3
<PAGE>
 
SECTION 16(A) BENEFICIAL OWNERSHIP REPORTING COMPLIANCE
 
  Section 16(a) of the Exchange Act requires the Company's directors and
executive officers, and persons who own more than ten percent of a registered
class of the Company's equity securities, to file with the SEC and the New
York Stock Exchange initial reports of ownership and reports of changes in
ownership of Common Stock of the Company. Officers, directors and greater than
ten-percent stockholders are required by SEC regulation to furnish the Company
with copies of all Section 16(a) forms they file.
 
  To the Company's knowledge, based solely on review of the copies of such
reports furnished to the Company and written representations that such reports
accurately reflect all reportable transactions and holdings, during the fiscal
year ended December 31, 1997, all Section 16(a) filing requirements applicable
to its officers, directors and greater than ten-percent beneficial owners were
complied with.
 
                              BOARD OF DIRECTORS
 
DIRECTORS' MEETINGS
 
  An annual meeting of the Board of Directors is held each year in conjunction
with the annual meeting of stockholders for the purposes of the organization
of committees, election or appointment of officers and the transaction of
other business. Regular meetings of the Board of Directors may be held without
notice at such times as the Board of Directors may determine. Special meetings
may be called by the Chairman of the Board of Directors, the President or a
majority of the directors in office. The By-Laws permit action to be taken
without a meeting if all members of the Board of Directors consent to such
action in writing. During 1997, the Board of Directors held eleven meetings.
All of the Company's incumbent directors attended 75 percent or more of the
aggregate of all meetings of the Board and committees on which they served
during 1997.
 
AUDIT COMMITTEE
 
  The Audit Committee of the Board of Directors was established for the
general purpose of reviewing the integrity of the Company's accounting and
financial reporting, maintaining communications between the Board of Directors
and external and internal auditors, and initiating special investigations as
deemed necessary. The independent accountants and the internal auditors have
full and free access to the Audit Committee and meet with it, with and without
management being present, to discuss all appropriate matters. No member of the
Committee is an officer or employee of the Company. The Audit Committee held
six meetings during 1997. The Audit Committee currently consists of Messrs.
Engen, Staley and Mecum, who serves as Chairman.
 
COMPENSATION COMMITTEE
 
  The Compensation Committee of the Board of Directors adopts, amends,
administers and terminates compensation and benefit plans, makes
recommendations to the Board of Directors as to management succession plans
and administers the Company's pay performance and incentive plans for
executive officers. The Committee also reviews pay performance and incentive
plans for the Company's joint ventures. No member of the Committee is an
officer or employee of the Company and no member is eligible to participate in
any benefit plan of the Company that is administered by the Committee. The
Compensation Committee held eight meetings during 1997. The Compensation
Committee currently consists of Messrs. Butler, Crawford and Hinchliffe, who
serves as Chairman.
 
CORPORATE GOVERNANCE COMMITTEE
 
  The Corporate Governance Committee considers and makes recommendations to
the Board of Directors as to the number of Directors to constitute the whole
Board, the selection criteria for membership and the names of persons whom it
concludes should be considered for membership on the Board of Directors. The
Corporate Governance Committee also recommends matters relating to committee
assignments and the roles and responsibilities of the Board and of the
Directors. The Corporate Governance Committee makes determinations
 
                                       4
<PAGE>
 
on compensation for Non-Employee Directors and is responsible for evaluating
the Board's performance and assessing the effectiveness of its structure and
governance. The Corporate Governance Committee held five meetings during 1997.
The Corporate Governance Committee currently consists of Messrs. Crawford,
Butler and Staley, who serves as Chairman. Stockholders of the Company who
wish to nominate persons for election to the Board of Directors must comply
with the provisions of the By-Laws that are described more fully at page 23 of
this Proxy Statement.
 
EXECUTIVE COMMITTEE
 
  The Executive Committee has and may exercise all the authority of the Board
of Directors in the management of the Company in the interim between meetings
of the Board of Directors (except to the extent of certain exceptions set
forth in Delaware law and the Company's By-laws) and formerly was responsible
for determining compensation of the Non-Employee Directors. The Executive
Committee did not meet during 1997. The Executive Committee currently consists
of Messrs. Smith, Engen and Butler, who serves as Chairman.
 
                        CORPORATE GOVERNANCE GUIDELINES
 
  The Board of Directors has adopted a formal statement of the roles and
responsibilities of the Board and adopted Corporate Governance Guidelines. The
following are the statement on roles and responsibilities as well as excerpts
from the Guidelines adopted by the Board:
 
ROLE OF THE BOARD
 
  The Board of Directors represents the interests of shareholders in
perpetuating a successful business and optimizing long term financial returns.
In furtherance of this objective, it is the responsibility of the Board to
select management, oversee corporate strategy and performance, and act as a
resource to management in matters of planning and policy. The Board also will
participate in management's succession planning, including specifically the
evaluation of the Chief Executive Officer. To assure success, Board members
will act not only as advisors, but also as active participants and decision
makers in matters of governance and corporate strategy.
 
  While the Board's primary role is to foster increased shareholder value, the
Board also recognizes that the Company has responsibilities to other
constituencies, including customers, employees, suppliers, creditors and the
communities where it operates--all of whom are essential to a successful
business.
 
RESPONSIBILITIES OF DIRECTORS
 
  Directors owe a duty of care and a duty of loyalty to the Company.
Therefore, Directors are expected to do the following:
 
  . act in the best interests of all shareholders;
 
  . exercise informed and independent judgment;
 
  . be knowledgeable about the businesses;
 
  . participate in the development of the Company's mission, aspirations,
    values and strategies;
 
  . maintain an understanding of general economic trends and conditions, and
    trends in corporate governance;
 
  . study materials presented for Board consideration;
 
  . actively participate in an objective and constructive manner in meetings
    of the Board and its committees; and
 
  . assist in representing the Company to the outside world.
 
                                       5
<PAGE>
 
GOVERNANCE GUIDELINES
 
  The following is a synopsis of key provisions of the Corporate Governance
Guidelines for the Board of Directors:
 
    Board membership will consist of no more than ten to twelve Board members
  including no more than two present or former members of Company management.
 
    Desired characteristics of potential new Board members will be reviewed
  on at least an annual basis. Potential new Board members may be nominated
  by any Director for screening, selection and recommendation for election by
  the Board. Invitation to join the Board of Directors will be extended by
  the Chairman of the Board and the Chairman of the Corporate Governance
  Committee. New Directors will undergo a Company orientation.
 
    Whether the Chairman of the Board and the Chief Executive Officer
  positions should be held by separate individuals will be addressed in the
  best interest of the Company under the circumstances at the time. A lead
  Director may be chosen by outside Directors when the Chairman of the Board
  is an employee of the Company.
 
    There are no term limits for Board members. Annually, each Director will
  be asked to confirm his/her desire to continue as a member of the Board.
  The Corporate Governance Committee will review the continued
  appropriateness of Board membership for Directors who change the job
  responsibilities held when last elected to the Board. Retirement age for
  Board members is age 72.
 
    Compensation for Board members will be reviewed annually for
  competitiveness. All Directors will be compensated equally and portions of
  that compensation will be in the form of Company stock.
 
    Performance of the Board will be reported annually to the Board by the
  Corporate Governance Committee in order to increase the Board's
  effectiveness.
 
    The Chief Executive Officer will be evaluated annually by the full Board.
  The evaluation will be used in considering compensation of the Chief
  Executive Officer.
 
    The Chief Executive Officer will provide an annual reporting to the
  Compensation Committee on succession planning and management development.
  This information will be shared with the full Board.
 
                                       6
<PAGE>
 
                             ELECTION OF DIRECTORS
 
                             Item 1 on Proxy Card
 
  Pursuant to the Company's Certificate of Incorporation and its By-Laws, the
members of the Board of Directors serve for one-year terms, and until their
successors are elected and qualified. The Board of Directors has selected the
persons listed below as nominees for election to the Board. Mr. Curtis J.
Crawford will not be standing for reelection to the Board of Directors.
 
  Unless authority to vote for directors is withheld in the proxy, the persons
named in the accompanying proxy intend to vote for the election of the six
nominees listed below. The directors will be elected by a plurality of the
shares of Common Stock cast in person or by proxy at the meeting.
 
  All nominees have indicated a willingness to serve as directors, but if any
of them should decline or be unable to act as a director, the persons named in
the proxy will vote for the election of another person or persons as the Board
of Directors recommends.
 
  THE BOARD OF DIRECTORS RECOMMENDS THAT YOU VOTE FOR ELECTION OF EACH NOMINEE
LISTED BELOW. PROPERLY DATED AND SIGNED PROXIES WILL BE SO VOTED UNLESS
STOCKHOLDERS SPECIFY OTHERWISE.
 
  The following biographical information is furnished with respect to each of
the nominees for election at the annual meeting. The information includes age
as of March 1, 1998, present position, if any, with Lyondell, period served as
director, and other business experience during the past five years. The
positions referred to beneath a director's name refer to positions with
Lyondell unless stated otherwise.
 
William T. Butler, 65........  Dr. Butler was elected Chairman of the Board of
                               Directors of the Company on June 30, 1997. He
                               has served as a Director of the Company since
                               his election on December 21, 1988, effective as
                               of January 25, 1989. Dr. Butler became
                               Chancellor of Baylor College of Medicine in
                               January 1996. From 1979 until January 1996, he
                               served as President and Chief Executive Officer
                               of Baylor College of Medicine. He is also a
                               director of C. R. Bard, Inc. and Browning-
                               Ferris Industries Inc.
 
                               Dr. Butler is a member of the Compensation
                               Committee and the Corporate Governance
                               Committee, and is Chairman of the Executive
                               Committee.
 
Travis Engen, 53.............  Mr. Engen was elected a Director of the Company
                               effective as of April 1, 1995. He has held his
                               current position as Chairman, President and
                               Chief Executive of ITT Industries, Inc. (a
                               diversified manufacturing company) since
                               December 1995. From 1991 until December 1995,
                               he served as Executive Vice President and a
                               member of the Management Policy Committee of
                               ITT Corporation. He held the position of Senior
                               Vice President of ITT Corporation and President
                               and Chief Executive Officer of ITT Defense,
                               Inc. from 1987 to 1991. Mr. Engen is also a
                               director of Alcan Aluminium Limited.
 
                               Mr. Engen is a member of the Audit Committee
                               and the Executive Committee.
 
Stephen F. Hinchliffe, Jr.,
64...........................  Mr. Hinchliffe was elected a Director of the
                               Company on March 1, 1991. Since 1988, he has
                               held his current position of Chairman of the
                               Board and Chief Executive Officer of BHH
                               Management, Inc.,
 
                                       7
<PAGE>
 
                               the managing partner of Leisure Group, Inc. (a
                               manufacturer of consumer products). Previously,
                               he served as Chairman of the Board of Leisure
                               Group, Inc., which he founded in 1964.
 
                               Mr. Hinchliffe is Chairman of the Compensation
                               Committee.
 
Dudley C. Mecum II, 63.......  Mr. Mecum was elected a Director of the Company
                               on November 28, 1988, effective as of January
                               25, 1989. Since July 1997, Mr. Mecum has been a
                               managing director of Capricorn Holdings LLC (a
                               firm specializing in leveraged buyouts). From
                               August 1989 until January 1997, Mr. Mecum was a
                               partner with the merchant banking firm of G. L.
                               Ohrstrom & Company. He served as Group Vice
                               President and director of Combustion
                               Engineering Inc. from 1985 to December 1987,
                               and as a managing partner of the New York
                               region of Peat, Marwick, Mitchell & Co. from
                               1979 to 1985. He is also a director of The
                               Travelers Group, Dyncorp, VICORP Restaurants,
                               Inc., Fingerhut Companies, Inc., Travelers
                               Property Casualty Corporation, Metris
                               Companies, Inc. and Suburban Propane LLP.
 
                               Mr. Mecum is Chairman of the Audit Committee.
 
Dan F. Smith, 51.............  Mr. Smith was named Chief Executive Officer of
 President and Chief           the Company on December 6, 1996 and has served
 Officer                       as President of the Company since August 31,
                               1994. He has served as a Director of the
                               Company since October 24, 1988. Since December
                               1, 1997, Mr. Smith has also served as the Chief
                               Executive Officer of Equistar Chemicals, LP
                               ("Equistar"), a petrochemicals and polymers
                               joint venture owned 57 percent by the Company.
                               Mr. Smith served as Chief Operating Officer of
                               the Company from May 1993 to December 1996. He
                               served as Vice President Corporate Planning of
                               Atlantic Richfield Company ("ARCO") from
                               October 1991 until May 1993. He previously
                               served as Executive Vice President and Chief
                               Financial Officer of the Company from October
                               1988 to October 1991 and as Senior Vice
                               President of Manufacturing of the Company, and
                               its predecessor, the Lyondell Division of ARCO,
                               from June 1986 to October 1988. From April 1985
                               to June 1986 Mr. Smith held executive positions
                               in manufacturing, control and administration.
                               Prior to 1985, he served in various financial,
                               planning and manufacturing positions with ARCO.
                               Mr. Smith is also a director of ABS Group of
                               Companies, Inc., a subsidiary of American
                               Bureau of Shipping, and ChemFirst, Inc.
 
                               Mr. Smith is a member of the Executive
                               Committee.
 
Paul R. Staley, 68...........  Mr. Staley was elected a Director of the
                               Company on November 28, 1988, effective as of
                               January 25, 1989. He has held his current
                               position as Chairman of the National Vision
                               Foundation since August 1994. He held the
                               position of Chairman of the Executive Committee
                               of the Board of Directors of P. Q. Corporation
                               (an industry supplier of silicates) from
                               January 1991 until August 1994. He also held
                               the positions of President and Chief Executive
                               Officer of P.Q. Corporation from 1973 and 1981,
                               respectively, until January 1991.
 
                               Mr. Staley is Chairman of the Corporate
                               Governance Committee and a member of the Audit
                               Committee.
 
                                       8
<PAGE>
 
          PROPOSAL TO RATIFY THE APPOINTMENT OF INDEPENDENT AUDITORS
 
                             Item 2 on Proxy Card
 
  The Board of Directors has recommended the joint appointment of Coopers &
Lybrand L.L.P. ("Coopers & Lybrand") and Price Waterhouse LLP ("Price
Waterhouse"), including any successor merged entity of the two firms, to audit
the financial statements of Lyondell for the year 1998.
 
  Pursuant to the terms of the Equistar Partnership Agreement, Millennium
Chemicals Inc. ("Millennium") and the Company are required to jointly select
the independent public accountants for Equistar, the Company's petrochemical
joint venture which was formed December 1, 1997. The managements of the
Company and Equistar, with the approval of the Company's Audit Committee and
the Equistar Partnership Governance Committee, solicited proposals for the
1998 annual audits of the Company and Equistar from several independent public
accounting firms. In that process, the Company requested that Coopers &
Lybrand and Price Waterhouse submit a joint proposal because of their
announcement of a plan to merge. Coopers & Lybrand are the Company's present
independent public accountants and Price Waterhouse are the independent public
accountants for Millennium. In addition, from time to time, Coopers & Lybrand
performs consulting work for the Company and Equistar.
 
  It is the view of the Company's management that the firm that serves as
independent public accountants for Equistar should also serve as the
independent public accountants for the Company because of the materiality of
Equistar to the Company. As a result of the process described in the foregoing
paragraph, the Company's Audit Committee and the Equistar Partnership
Governance Committee approved managements' recommendations of the selection of
Coopers & Lybrand and Price Waterhouse jointly as the independent public
accountants for the Company and Equistar. (Although such selection anticipates
the merger of Coopers & Lybrand and Price Waterhouse, the Company intends to
utilize both firms regardless of the outcome of the plan to merge.)
 
  Representatives of each of Coopers & Lybrand and Price Waterhouse will be
present at the meeting and will have the opportunity to make a statement if
they desire to do so. These representatives will also be available to respond
to appropriate questions.
 
  The proposal will be approved if it receives the affirmative vote of a
majority of the shares of Common Stock present in person or by proxy at the
meeting.
 
  THE BOARD OF DIRECTORS RECOMMENDS THAT YOU VOTE FOR RATIFICATION OF THE
JOINT APPOINTMENT OF COOPERS & LYBRAND AND PRICE WATERHOUSE, INCLUDING ANY
SUCCESSOR MERGED ENTITY OF THE TWO FIRMS. PROPERLY DATED AND SIGNED PROXIES
WILL BE SO VOTED UNLESS STOCKHOLDERS SPECIFY OTHERWISE.
 
                                       9
<PAGE>
 
                            EXECUTIVE COMPENSATION
 
  The following table sets forth information as to the Chief Executive Officer
during 1997 and the next four most highly compensated executive officers of
the Company.
 
                          SUMMARY COMPENSATION TABLE
 
<TABLE>
<CAPTION>
                                                                 LONG-TERM
                                                                COMPENSATION
                                                            ---------------------
                                   ANNUAL COMPENSATION        AWARDS    PAYOUTS
                                 ------------------------------------------------------------
                                                            RESTRICTED LONG-TERM
                                               OTHER ANNUAL   STOCK    INCENTIVE  ALL OTHER
   NAME AND PRINCIPAL          SALARY   BONUS  COMPENSATION   AWARDS    PAYOUTS  COMPENSATION
        POSITION          YEAR   ($)     ($)      ($)(A)      ($)(B)    ($)(C)      ($)(D)
   ------------------     ---- ------- ------- ------------ ---------- --------- ------------
<S>                       <C>  <C>     <C>     <C>          <C>        <C>       <C>
Dan F. Smith............  1997 651,734 548,900    11,360     277,325   5,079,354     85,712
President &               1996 490,886 241,932    11,026     370,813     221,613     61,556
Chief Executive Officer   1995 473,905 370,813     7,945     383,175     115,382     56,519
Russell S. Young(e).....  1997 297,130 182,967    32,359      96,514   1,721,777  2,931,109
Senior Vice President,    1996 275,400  90,725    24,297     139,055      83,127     43,844
Chief Financial Officer   1995 269,385 139,055    16,990     143,691     120,269     41,199
& Treasurer
Jeffrey R. Pendergraft..  1997 282,556 182,967    14,129      96,514   1,721,777     45,178
Senior Vice President     1996 255,000  90,725    14,707     139,055      83,127     40,845
and Chief Administration
 Officer                  1995 249,885 139,055     8,868     143,691     149,277     38,854
Debra L. Starnes(f).....  1997 270,598 182,967    16,310      96,514   1,721,777     42,686
Senior Vice President,    1996 214,200  90,725    15,444     139,055      83,127     39,109
Petrochemicals            1995 209,904 139,055    10,387     143,691     110,174     34,108
Richard W. Park(g)......  1997 223,419 109,780    25,262      57,904   1,033,077  3,057,062
Vice President,           1996 207,060  54,535    29,824      83,433      49,867     38,209
Human Resources           1995 203,000  83,433    12,102      86,214     107,488     35,540
</TABLE>
- --------
(a) Includes imputed income in respect of the Long-Term Disability Plan, tax
    gross-ups in respect of financial counseling reimbursements and in respect
    of other miscellaneous items, and the amount of incremental interest
    accrued under the Executive Deferral Plan that exceeds 120 percent of a
    specified IRS rate. "Tax gross-ups" refers to the additional reimbursement
    paid to a recipient to cover the federal income tax obligations associated
    with the underlying benefit, including an additional amount based on
    maximum applicable income tax rates.
(b) The restricted stock is awarded as part of the award under the Company's
    Value Share Plan. The dollar value included in the table reflects the
    valuation at the time of the award. The Value Share Plan was terminated in
    December 1997 and all unvested outstanding restricted stock was vested at
    such time.
(c) Amounts shown in the Long-Term Incentive Payouts column for 1997 represent
    the deferred cash payments made in 1997 in accordance with the normal
    operation of the Value Share Plan, together with payments made in December
    1997 in connection with the termination of the Value Share Plan. Pursuant
    to the term of the Value Share Plan, in connection with its termination,
    in December 1997 each executive received a payment equivalent to the sum
    of the estimated pro-rated Value Share Plan awards for the years 1998
    through 2001. Awards under the Value Share Plan are calculated based on
    five year Performance Cycles and the payments made in December 1997
    acknowledge each executive's contributions to the Company through December
    1997 for the Cycles ending in each of the years 1998 through 2001.
    Accordingly, each received a pro-rated award in the amount of the sum of
    80% of the estimated award otherwise payable to such executive in 1999 for
    1998; 60% of the estimated award payable to such executive in 2000 for
    1999; 40% of the estimated award payable to such executive in 2001 for
    2000; and 20% of the estimated award payable to such executive in 2002 for
    2001. Amounts shown in the Long-Term Incentive Payouts column for 1996 and
    1995 represent payment of the associated cash portion under the Value
    Share Plan that was paid in December 1996 and December 1995, respectively,
    in connection with the vesting of such executive
 
                                      10
<PAGE>
 
   officers' restricted stock. The amounts for 1995 also include the payout of
   performance units (including associated dividend share credits) previously
   awarded under the Company's Executive Long-Term Incentive Plan (the "LTIP")
   (except with respect to Mr. Smith, who was not an executive officer of the
   Company at the time those performance units were granted). Dividend share
   credits are allocated to an optionee's account whenever dividends are
   declared on shares of Common Stock. The number of dividend share credits to
   be allocated on each record date to an optionee's account is computed by
   multiplying the dividend rate per share of Common Stock by the sum of (i) the
   number of shares subject to outstanding options, (ii) the number of dividend
   share credits then credited to the optionee's account and dividing the
   resulting figure by the fair market value of a share of Common Stock on such
   dividend record date. As future dividends are declared, the participant will
   receive dividend share credits not only on the number of shares covered by
   unexercised options and the number of performance units but also on the
   number of dividend share credits in the participant's account. The dividend
   crediting mechanism will continue to operate in this manner with respect to
   options, until the participant exercises such options or the options expire.
   Dividend share credits do not represent earned compensation and have no
   definite value, if any, until the date on which the options in respect of
   which such credits have been allocated are exercised. See footnote (b) to the
   Aggregated Option Exercises and Fiscal Year-End Option Values Table. Dividend
   share credits are canceled upon an optionee's termination of employment under
   certain specified circumstances. The number of dividend share credits accrued
   to the accounts of the named executives during 1997, 1996 and 1995,
   respectively, is as follows: Mr. Smith: 1,399, 1,233 and 2,149; Mr. Young:
   1,740, 1,589 and 2,182; Mr. Pendergraft: 2,273, 2,125 and 2,567; Ms. Starnes:
   1,455, 1,358 and 1,523; Mr. Park: 1,416, 1,322 and 1,759. (d) Includes
   contributions to the Executive Supplementary Savings Plan, incremental
   executive medical plan premiums, financial counseling reimbursements and
   certain amounts in respect to the Executive Life Insurance Plan, as follows:
 
<TABLE>
<CAPTION>
                             YEAR MR. SMITH MR. YOUNG MR. PENDERGRAFT MS. STARNES MR. PARK
                             ---- --------- --------- --------------- ----------- --------
   <S>                       <C>  <C>       <C>       <C>             <C>         <C>
   Executive Supplementary
    Savings Plan...........  1997  $52,563   $23,770      $22,712       $21,648   $17,874
   Incremental Medical Plan
    Premiums...............  1997  $ 8,712   $ 8,712      $ 8,712       $ 8,712   $ 8,712
   Financial Counseling
    Reimbursement..........  1997  $ 7,680   $ 6,900      $ 8,125       $ 8,330   $ 7,860
   Executive Life Insurance
    Plan...................  1997  $16,757   $ 8,157      $ 5,629       $ 3,996   $ 8,413
</TABLE>
 
  See "EXECUTIVE SEVERANCE ARRANGEMENTS--Payments to Former Executive
  Officers" for additional information regarding Mr. Young and Mr. Park.
 
(e) Mr. Young retired at the end of 1997.
(f) Ms. Starnes served as Senior Vice President, Petrochemicals, of the
    Company, until Equistar commenced operations on December 1, 1997. She
    currently serves as Senior Vice President, Polymers, of Equistar. The
    summary compensation information presented above includes compensation
    paid to Ms. Starnes by the Company for her services as an Equistar officer
    during December 1997.
(g) Mr. Park retired at the end of 1997.
 
                                      11
<PAGE>
 
            PAY AND PERFORMANCE PLANS AND LONG-TERM INCENTIVE PLANS
 
VALUE SHARE PLAN
 
  In 1995 the Company adopted a performance driven pay plan for executive
officers (the "Value Share Plan"). In connection with the significant
reorganization of the Company as a result of the creation of Equistar, the
Value Share Plan was terminated effective December 1, 1997. In connection with
such termination, all unvested restricted stock outstanding was immediately
vested, and the associated deferred cash piece was paid out. Pursuant to the
terms of the plan, each participant received a payment equivalent to the sum
of the estimated pro-rated Value Share Plan awards for the years 1998 through
2001. Awards under the Value Share Plan were calculated based on five year
Performance Cycles and the payments made in December 1997 acknowledge each
participant's contributions to the Company through December 1997 for the
Cycles ending in each of the years 1998 through 2001. Accordingly, each
received a pro-rated award in the amount of the sum of 80% of the estimated
award otherwise payable to such participant in 1999 for 1998; 60% of the
estimated award payable to such participant in 2000 for 1999; 40% of the
estimated award payable to such participant in 2001 for 2000; and 20% of the
estimated award payable to such participant in 2002 for 2001.
 
  The Value Share Plan was designed to provide participants with an incentive
to maximize long-term shareholder value and to encourage significant ownership
of Company stock. The Value Share Plan established Performance Cycles and at
the beginning of each Cycle, participants were assigned an allocation
percentage indicating the extent to which each participant shares in the
amounts generated by the Value Share Plan. At the end of the Performance Cycle
two award pools are created: (i) a Value Award Pool and (ii) an Operating
Award Pool.
 
  The Value Award Pool equaled the sum of 4.0% of Average EVA ("economic value
added") and 1.25% of MVA ("market value added"). EVA measures the Company's
cash flow performance in excess of a capital charge, which is calculated by
multiplying the capital invested in the Company times the Company's weighted
average cost of capital. MVA measures changes in the market value of the
Company's equity, plus the value of dividends as if they had been reinvested
in the Company's Common Stock.
 
  An Operating Award Pool was created if certain minimum criteria were
satisfied. The size of the pool was based on the Compensation Committee's
evaluation of Lyondell's operating performance in the final year of any Cycle
in the areas of customer satisfaction, corporate responsibility (including
safety and environmental performance), employee productivity and financial
performance. The Operating Award Pool maximum is $1,000,000 for any
Performance Cycle and could be adjusted downward by the Compensation Committee
based on its assessment of the Company's performance in the final year of the
Cycle.
 
  Following the completion of a Performance Cycle, the Value Share Plan
provided that the sum of the Pools be awarded to Participants in accordance
with their allocation percentages. Awards were designed to be paid out: (a)
one-third in cash, to be paid within 90 days following the end of a
Performance Cycle; (b) one-third in restricted stock, issued within 90 days
following the end of a Performance Cycle; and (c) one-third in cash, to be
paid at the time that the related award of restricted stock vests. The award
for the Performance Cycle ended in 1997 was paid entirely in cash and such
award payment is set forth in the "Bonus" column under the Summary
Compensation Table.
 
  Upon termination of the Value Share Plan, cash payments were made for the
participant's contribution to the Company through December 1997 for each of
the Performance Cycles that would have ended in the years 1998 through 2001.
For purposes of calculating such payments, the share price for calculating MVA
was held at $23.943, the average price for 1997, and EVA for the remaining
Performance Cycles was deemed to be the same as for 1997.
 
                                      12
<PAGE>
 
LONG-TERM INCENTIVE PLAN--AWARDS IN LAST FISCAL YEAR
 
<TABLE>
<CAPTION>
                                                                    PERIOD UNTIL
                                                                     MATURATION
                          NAME                     NUMBER OF SHARES  OR PAYOUT
                          ----                     ---------------- ------------
      <S>                                          <C>              <C>
      Mr. Smith...................................      10,950            *
      Mr. Young...................................       4,107            *
      Mr. Pendergraft.............................       4,107            *
      Ms. Starnes.................................       4,107            *
      Mr. Park....................................       2,464            *
</TABLE>
- --------
* These shares were granted in 1997 for the Performance Cycle ended in 1996.
 All shares were vested December 1, 1997 in connection with the termination of
 the plan.
 
EXECUTIVE LONG-TERM INCENTIVE PLAN
 
  Prior to its replacement by the Value Share Plan, the LTIP provided for the
granting of stock options, the right to receive performance units under
certain circumstances and a cash payment in respect of dividend share credits.
Additional information with respect to the payout of performance units
previously granted under the LTIP is contained in the Summary Compensation
Table. No performance units are currently outstanding. Commencing in 1995, no
additional grants of stock options or performance units have been made to
executive officers pursuant to the LTIP, although dividend share credits will
continue to accrue on outstanding stock options.
 
  No stock options were exercised during 1997. The following table shows the
number of shares of Common Stock represented by outstanding stock options held
by each of the named executive officers as of December 31, 1997. Also reported
are the values for "in-the-money" options which represent the positive spread
between the exercise price of any such existing stock options and the year end
price of the Common Stock.
 
                      AGGREGATED OPTION EXERCISES IN 1997
                       AND FISCAL YEAR-END OPTION VALUES
 
<TABLE>
<CAPTION>
                              NUMBER OF SECURITIES      VALUE OF UNEXERCISED
                             UNDERLYING UNEXERCISED    IN-THE-MONEY OPTIONS AT
                                OPTIONS AT FISCAL      FISCAL YEAR-END ($) (A)
                                  YEAR-END (#)                   (B)
                            ------------------------- -------------------------
              NAME          EXERCISABLE UNEXERCISABLE EXERCISABLE UNEXERCISABLE
              ----          ----------- ------------- ----------- -------------
      <S>                   <C>         <C>           <C>         <C>
      Mr. Smith............   32,200         -0-       $129,375        -0-
      Mr. Young............   39,400         -0-       $101,513        -0-
      Mr. Pendergraft......   25,300         -0-       $ 73,181        -0-
      Ms. Starnes..........   32,500         -0-       $ 87,850        -0-
      Mr. Park.............   31,100         -0-       $ 94,238        -0-
</TABLE>
- --------
(a) The last reported closing sales price, as reported on the NYSE, of
    Lyondell Common Stock on December 31, 1997 was $26.50 per share.
(b) Each option carries with it the right to dividend share credits, as
    described in footnote (c) to the Summary Compensation Table. Set forth
    below is a calculation of the value of accrued dividend share credits,
    assuming exercise at December 31, 1997, of the in-the-money options. These
    hypothetical values have been calculated for illustration purposes only.
 
<TABLE>
<CAPTION>
                                                       EXERCISABLE UNEXERCISABLE
                                                       ----------- -------------
      <S>                                              <C>         <C>
      Mr. Smith.......................................  $170,448      $   -0-
      Mr. Young.......................................  $226,867      $   -0-
      Mr. Pendergraft.................................  $320,889      $   -0-
      Ms. Starnes.....................................  $201,448      $   -0-
      Mr. Park........................................  $212,980      $   -0-
</TABLE>
 
                                      13
<PAGE>
 
                            ANNUAL PENSION BENEFITS
 
  The following table shows estimated annual pension benefits payable to the
Company's employees, including executive officers of the Company upon
retirement at age 65 based on credited service as of January 1, 1998, under
the provisions of the Lyondell Retirement Plan and the Supplementary Executive
Retirement Plan.
 
                              PENSION PLAN TABLE
 
<TABLE>
<CAPTION>
   AVERAGE FINAL EARNINGS
  (BASE SALARY PLUS ANNUAL
   INCENTIVE PLAN AWARDS)
  HIGHEST THREE CONSECUTIVE
 YEARS OUT OF LAST TEN YEARS     APPROXIMATE ANNUAL BENEFIT FOR YEARS OF MEMBERSHIP SERVICE INDICATED(A)(B)(C)
 --------------------------- -------------------------------------------------------------------------------
                                15 YEARS        20 YEARS        25 YEARS        30 YEARS        35 YEARS
                             --------------- --------------- --------------- --------------- ---------------
<S>                          <C>             <C>             <C>             <C>             <C>
        $1,400,000                  $322,239        $429,652        $537,065        $644,478        $751,891
         1,300,000                   299,139         398,852         498,565         598,278         698,991
         1,200,000                   276,039         368,052         460,065         552,078         644,091
         1,100,000                   252,939         337,252         421,565         505,878         590,191
         1,000,000                   229,839         306,452         383,065         459,678         536,291
           900,000                   206,739         275,652         344,565         413,478         482,391
           800,000                   183,639         244,852         306,065         367,278         428,491
           700,000                   160,539         214,052         267,565         321,078         374,591
           600,000                   137,439         183,252         229,065         274,878         320,691
           500,000                   114,339         152,452         650,565         228,678         266,791
           400,000                    91,239         121,652         152,065         182,478         212,891
           300,000                    68,139          90,852         113,565         136,278         159,991
           200,000                    45,039          60,052          75,065          90,078         105,091
</TABLE>
- --------
(a) The amounts shown in the above table are necessarily based upon certain
    assumptions, including retirement of the employee at age 65, based on
    credited services as of January 1, 1998 and payment of the benefit under
    the basic form of allowance provided under the Lyondell Retirement Plan
    (payment for the life of the employee only with a guaranteed minimum
    payment period of 60 months). The amounts will change if the payment is
    made under any other form of allowance permitted by the Lyondell
    Retirement Plan, or if an employee's actual retirement occurred after
    January 1, 1997, since the "annual covered compensation level" of such
    employee (one of the factors used in computing the annual retirement
    benefits) may change during the employee's subsequent years of membership
    service. The benefits shown are not subject to deduction for Social
    Security benefits or other offset amounts. The plans, however, provide a
    higher level of benefits for the portion of compensation above the
    compensation levels on which Social Security benefits are based.
(b) As of December 31, 1997, the credited years of service (rounded to the
    nearest whole number) under the Lyondell Retirement Plan for the named
    executive officers were: Mr. Smith, 21; Mr. Young, 18; Mr. Pendergraft,
    25; Mr. Park, 32; and Ms. Starnes, 23.
(c) All employees' (including executive officers') years of service with ARCO
    prior to the creation of Lyondell have been credited under the Company's
    retirement plans.
 
                                      14
<PAGE>
 
                       EXECUTIVE SEVERANCE ARRANGEMENTS
 
SEVERANCE AGREEMENTS
 
  In September 1997, the Company terminated the severance agreements
previously in effect with each of its executive officers. No severance
agreement with any executive officer of Lyondell is currently in existence.
 
PAYMENTS TO FORMER EXECUTIVE OFFICERS
 
  Effective December 1997, Mr. Park and Mr. Young each entered into a
Voluntary Separation Agreement and Release ("Separation Agreement") with
Lyondell. Under the terms of these agreements, each received severance
payments equal to those payable under his existing severance agreement upon a
change of control of Lyondell. Such payments were equivalent to three times
each such executive's respective current annual base salary and average Value
Share Plan Award (calculated as the average of the annual cash award paid for
the previous three year's performance cycles). Mr. Park received an amount
equal to $906,435 and Mr. Young received an amount equal to $1,288,842. Mr.
Park and Mr. Young were each eligible for accrued benefits under the Lyondell
Retirement Plan. In addition, each was eligible for accrued benefits under the
Lyondell Supplementary Executive Retirement Plan ("SERP") and received
$531,522 and $783,050, respectively. In addition to the normal SERP benefits,
each received a special supplementary benefit payment equal to $379,839 and
$684,797, respectively. Each executive may continue to participate in
Lyondell's Executive Medical Plan and in Lyondell's Long-Term Disability Plan,
and will continue to be covered under the terms of the Executive Life
Insurance Plan for a period of two years. They also are eligible for full
benefits under Lyondell's Financial Counseling Policy for 1998. In addition,
Messrs. Park and Young also received $683,367 and $639,921, respectively, to
cover, on a "grossed-up" basis, federal income tax payable with respect to
their Executive Deferral Plan balances accrued as of September 1, 1996.
 
                                      15
<PAGE>
 
                               PERFORMANCE GRAPH
 
  The graph below compares the cumulative total return to stockholders of the
Company with the cumulative total return to stockholders of the S&P 500 Stock
Index and a group of 13 peer companies ("Peer Group").
 
  The Peer Group is a composite index composed of commodity chemical
manufacturers and independent refiners. The Peer Group consists of Ashland
Oil, Inc.; Crown Central Petroleum Corporation; Utramar-Diamond Shamrock,
Inc.; Eastman Chemical; FINA, Inc; The Geon Company; Georgia Gulf Corporation;
Methanex Corporation; Nova Corporation of Alberta; Sun Company, Inc.; Tosco
Corporation; Union Carbide Corporation and Valero Energy Corporation. During
1997, Rexene Corporation, formerly a member of the Peer Group, ceased to be a
publicly-traded company and was therefore eliminated from the Peer Group.
 
 
                       [PERFORMANCE GRAPH APPEARS HERE]
 
<TABLE>
<CAPTION>
                                  1992    1993    1994    1995    1996    1997
                                 ------- ------- ------- ------- ------- -------
<S>                              <C>     <C>     <C>     <C>     <C>     <C>
LYONDELL........................ $100.00 $ 91.43 $115.29 $105.61 $105.97 $131.81
S&P 500......................... $100.00 $110.08 $111.53 $153.45 $188.68 $251.63
PEER GROUP(a)................... $100.00 $114.29 $137.37 $147.16 $164.92 $197.66
</TABLE>
 
(a) Group total returns are weighted by average annual market capitalization
    for Peer Group companies as of the beginning of each year and assume
    reinvestment of dividends. None of the Peer Companies constituted more
    than 20 percent of the market capitalization of the entire Peer Group in
    1997.
 
  PURSUANT TO SEC RULES, THIS SECTION OF THE PROXY STATEMENT (INCLUDING THE
  COMPENSATION COMMITTEE REPORT THAT FOLLOWS) IS NOT DEEMED "FILED" WITH THE
  SEC AND IS NOT INCORPORATED BY REFERENCE WITH THE COMPANY'S REPORT ON FORM
  10-K.
 
                                      16
<PAGE>
 
                         COMPENSATION COMMITTEE REPORT
 
  The Compensation Committee of the Board of Directors (the "Committee") has
responsibility for establishing and administering the pay philosophy,
policies, and plans for the executive officers of the Company. The Committee
conducts an annual review of executive pay and approves all salary changes,
grants and awards to executive officers of Lyondell. The Committee is
comprised of three non-employee directors: Mr. Stephen F. Hinchliffe, Jr.,
Chairman, Dr. William T. Butler and Mr. Curtis J. Crawford.
 
EXECUTIVE PAY PHILOSOPHY
 
  The overriding principle behind the Company's pay philosophy is that pay
must support the Company's primary objective of creating shareholder value and
that premium pay will be provided for premium performance. Specific elements
of this philosophy are:
 
  . Performance should be defined in terms of measures that directly link to
    or strongly influence Lyondell's shareholder value and achievement of
    strategic business and other performance objectives
 
  . Executive base salaries should be comparable to salaries for similar
    positions in a broad group of industrial and chemical companies that are
    similar to Lyondell, with incentives varying substantially commensurate
    with the Company's performance and designed to account for the cyclical
    nature of the Company's businesses
 
  . The pay programs should foster a team orientation and a high degree of
    cooperation and coordination among top management
  . Substantial ownership in the Company's stock among executives should be
    highly encouraged so that management interests are closely aligned with
    shareholders in terms of both risk and reward
 
  Driven by this philosophy, the Company's executive pay program has been
designed to encourage a long-term performance orientation, with performance
measures strongly related to shareholder value creation. Further, the program
is designed to facilitate ownership of Company stock. As a result, the
Company's total pay package is designed to be highly sensitive to the
Company's performance, defined in terms of shareholder value creation.
 
 Base Salary
 
  Pursuant to the pay philosophy, Lyondell's executive base salaries generally
are positioned at the 50th percentile of the market according to nationally
recognized surveys for industrial and chemical companies. Salaries for
executives who are new to their positions may initially be set at below market
levels.
 
  Generally, the Compensation Committee assesses market pay by position by
relying on published surveys. Published surveys cover a group of industrial
and chemical companies. Using this data, salary adjustments are generally made
such that salaries for most executives are set at the median of the market.
Salaries for those new in their positions, however, are set below the median
of the market.
 
  In the years in which external salary assessments are not conducted, the
Compensation Committee adjusts executive salaries commensurate with the
increases reported by at least two nationally recognized surveys. This was
done in 1997.
 
 Incentives
 
  Value Share Plan
 
  For 1997, Lyondell executives participated in the Value Share Plan, an
incentive compensation program originally adopted and approved by the
shareholders in 1995. The Value Share Plan was designed to provide
participants with an incentive to maximize the long-term creation of
shareholder value and encourage significant ownership of Company stock.
 
                                      17
<PAGE>
 
  Pursuant to the Value Share Plan, each year an award pool was created,
comprised of 4.0% of Lyondell's Economic Value Added (EVA), averaged over the
last five years, and 1.25% of Lyondell's five-year Market Value Added (MVA).
EVA measures the Company's cash flow performance (which exceeds the cost of
capital) and was calculated by multiplying the capital invested in the Company
by the Company's weighted average cost of capital. MVA measures changes in the
market value of the Company's equity, plus dividends as if they had been
reinvested in the Company's stock. Based on this formula, an award pool of
$4,337,000 was created for 1997. This award pool represents 4.0% of five-year
average EVA, which was $3,296,000 and 1.25% of five-year MVA, which was
$1,041,000.
 
  In addition, an annual award pool of $1,000,000 was created for 1997, based
on the Committee's assessment of Lyondell's accomplishments over the course of
the year. The Company must satisfy certain minimum criteria relating to these
areas to be eligible for this pool, which in any event may not exceed
$1,000,000. In determining the size of this pool, the Committee took into
account accomplishments relating to customer satisfaction, corporate
responsibility, including safety and environmental performance, employee
productivity and overall performance, including particularly the successful
completion of the Equistar joint venture.
 
  The award pools were allocated to a total of 10 executives, who in the
opinion of the Committee, had the opportunity to significantly impact the
long-range success and value of the Company in accordance with pre-established
allocation percentages. Initially, one-third of the calculated value of each
individual's award was paid out in cash and two-thirds was paid in equal
amounts of deferred cash and restricted stock. In connection with the
completion of the Equistar transaction and the subsequent reorganization of
the Company, the Value Share Plan was terminated in December 1997. All shares
previously restricted under that plan were vested as of December 1 and the
associated deferred cash portion was paid out at that time. The award for 1997
was made entirely in cash and also was paid as of December 1. In addition,
pursuant to the terms of the plan, each participant received a pro rata share
of the estimated awards that would have been paid for the cycles ending in the
years 1998 through 2001. For purposes of calculating those estimated awards
certain assumptions were made about the price of the Company's stock and the
Company's earnings levels for those future years. For purposes of calculating
such payments, the share price for calculating MVA was held at $23.943, the
average price for 1997, and EVA for the remaining Performance Cycles was
deemed to be the same as for 1997. These awards also were paid in cash.
 
  1998 Incentive Compensation Plan
 
  The termination of the Value Share Plan in December 1997 necessitated the
adoption of a new incentive compensation for Lyondell executive officers. As a
result of the creation of Equistar and the concurrent reorganization of the
Company, the pool of executive officers at Lyondell initially was reduced to
five persons. The Board has subsequently approved the creation of one
additional executive officer position. The Company is reviewing stock-based
alternatives to the Value Share Plan, consistent with its focus on improved
shareholder return. For 1998, the Compensation Committee has approved an
executive incentive compensation plan that is based on substantially the same
principles as the Value Share Plan. The extent to which awards will be made
will be based on achievement of specific MVA, EVA and operating targets. The
elements of the pool are weighted to emphasize maximization of shareholder
returns as the driver. The weighting of the pool is as follows: MVA, 50%; EVA,
25% and operating targets, 25%, in the aggregate.
 
  Awards will have an up front cash portion, as well as long-term portion. The
long-term portion will consist of restricted stock that vests over a three
year period, accompanied by an equivalent amount of deferred cash that is paid
out as the restricted shares vest. The shares will be paid out of the
Company's restricted stock plan, which plan was approved by the shareholders
in 1995.
 
                                      18
<PAGE>
 
 Stock Ownership Guidelines
 
  In 1995, the Committee adopted stock ownership guidelines for executive
officers. The current ownership targets are as follows:
<TABLE>
<CAPTION>
                                                                NUMBER OF SHARES
                                                                REQUESTED TO BE
      POSITION                                                       OWNED
      --------                                                  ----------------
      <S>                                                       <C>
      Chief Executive Officer..................................     110,000
      Senior Vice President....................................      25,000
      Vice President...........................................      15,000
</TABLE>
 
  All shares which are beneficially owned, including, if applicable, shares of
unvested restricted stock, and shares held in the Company's 401(k) plan, but
excluding unexercised stock options, count toward fulfillment of the ownership
guidelines.
 
CHIEF EXECUTIVE OFFICER'S 1997 PAY
 
  In September 1997, Mr. Smith's salary was raised from $624,000 to $780,000.
This increase was merited because of Mr. Smith's role as both CEO of Lyondell
and CEO of Equistar Chemicals, LP, the Company's $5 billion chemical joint
venture. Equistar reimburses a portion of Mr. Smith's salary to the Company,
in consideration for his services as Chief Executive Officer of Equistar.
 
  In December 1997, Mr. Smith received an incentive award for 1997 under the
Company's Value Share Plan. Pursuant to the termination of the Value Share
Plan, which is discussed above, Mr. Smith's award was made entirely in cash,
in the amount of $1,646,700. The Committee believes that this award was
appropriate given the Company's achievements in creating value, as measured by
EVA and MVA, as well as its financial and strategic success, particularly his
key role in the successful negotiation and completion of the Equistar joint
venture and the completion of the LCR $1.1 billion upgrade project. In
addition, pursuant to the terms of the Value Share Plan, Mr. Smith received a
pro rata share of his awards for the years 1998 through 2001.
 
  Going forward, Mr. Smith's pay package is expected to continue to include a
large portion that is at risk as to its ultimate value. The Compensation
Committee believes that Mr. Smith's pay mix, coupled with the design of his
pay package, continues to align his rewards and incentives with shareholder
interests. Consistent with the Company's pay philosophy, Mr. Smith's total pay
package will be highly sensitive to the Company's performance, defined in
terms of shareholder value as measured by MVA and EVA.
 
OMNIBUS BUDGET RECONCILIATION ACT OF 1993
 
  Section 162(m) of the Omnibus Budget Reconciliation Act of 1993 (the "1993
Act") limits the deductibility of pay in excess of $1 million paid to the
Company's chief executive officer and the next four highest paid officers
during any fiscal year, beginning with 1994, unless such pay meets certain
requirements.
 
  The Committee seeks to qualify for deductibility where feasible, but retains
the discretion to pay non-deductible amounts if that would be in the best
interests of the Company and shareholders under the circumstances. The amounts
paid in 1997 under the Value Share Plan and in connection with the termination
of the Value Share Plan generally were not deductible.
 
COMPENSATION COMMITTEE MEMBERS
 
  The Compensation Committee strongly believes that shareholders are well
served by Lyondell's executive management team and that the executive pay
philosophy and programs that have been established support the long-term
success of the Company. This report is submitted by the Compensation Committee
of the Board of Directors of Lyondell.
 
  Respectfully submitted,
 
  Stephen F. Hinchliffe, Jr. (Chairman)
  Dr. William T. Butler
  Curtis J. Crawford
 
  THE COMPENSATION COMMITTEE
 
                                      19
<PAGE>
 
                           COMPENSATION OF DIRECTORS
 
DIRECTORS' FEES
 
  Directors who are employees of the Company are not paid any fees or
additional compensation for service as members of the Board of Directors or
any committee thereof. During 1997, directors who were not employees of the
Company ("Non-Employee Directors") were paid an annual retainer of $40,000 (of
which $10,000 was paid in shares of restricted stock) and $1,250 for each
Board or committee meeting attended, and were reimbursed for travel and other
related expenses incurred in attending such meetings. In addition, the non-
employee directors who served as Chairman of the Audit, Compensation and
Corporate Governance Committees, respectively, received $7,500, $7,500 and
$5,000 per year. The non-employee Chairman of the Board received an additional
$15,000 and an additional $5,000 of restricted stock.
 
RESTRICTED STOCK GRANTS
 
  The Company believes paying a portion of the directors' compensation in
stock further aligns the directors' interests with the shareholders' interests
and accordingly, has adopted stock ownership guidelines for its Non-Employee
Directors. Restricted Shares were granted as part of the annual retainer for
1998 and were valued at approximately $10,000 (which are subject to transfer
restrictions and risk of forfeiture for a period (the "restricted period") of
at least one year from the date of grant). During the restricted period, the
director has the right to receive dividends on and the right to vote the
Restricted Shares. The Restricted Shares will be forfeited if the director's
service terminates (other than for retirement, death or disability) prior to
the end of the restricted period. It is intended that the directors will
continue to hold the Restricted Shares beyond the termination of the
restricted period.
 
RETIREMENT PLAN FOR NON-EMPLOYEE DIRECTORS
 
  The Lyondell Petrochemical Company Retirement Plan for Non-Employee
Directors (the "Directors' Retirement Plan") is a non-qualified retirement
plan for directors who are not employees of the Company. The annual retirement
benefit is equal to the director's annual retainer fee immediately preceding
the director's retirement from the Board of Directors. A director vests in the
benefit upon serving three years as a member of the Board of Directors, or, in
the case of a retired Company officer, three years following retirement as an
officer of the Company. The benefit is payable for a period of time equal to a
director's service on the Board of Directors, or, in the case of retired
officers of the Company, to the director's service on the Board of Directors
following retirement as an officer. However, if a director has served for at
least 15 years as a member of the Board of Directors, excluding years of
service when the director was also an officer of the Company, the benefit
shall be paid for the greater of the period described in the preceding
sentence or until death. Benefits commence at age 65, or, if later, at the
time the director retires from the Board of Directors. A surviving spouse is
entitled to receive 50 percent of the benefits otherwise payable to a director
with payment up to a maximum of 15 years if the director dies prior to
retirement from the Board of Directors or if he dies after retirement from the
Board of Directors the benefits otherwise payable to the director up to a
maximum of 15 years. The benefits under the Directors' Retirement Plan are
secured through a grantor trust.
 
DEFERRAL PLAN FOR NON-EMPLOYEE DIRECTORS
 
  The Lyondell Petrochemical Company Elective Deferral Plan for Non-Employee
Directors (the "Directors' Deferral Plan") provides directors who are not
employees of the Company with the opportunity to defer all or a portion of
their retainer and meeting fees. Under the Directors' Deferral Plan, the
minimum amount that may be elected to be deferred is $8,000 and the maximum is
100 percent of the director's retainer and meeting fees per year. Amounts may
be deferred until retirement from their regular employment or resignation from
the Board, unless the director has suffered a financial hardship or elected an
early distribution at the time the deferral commitment is made. Upon the
director's death, retirement or resignation, benefits are payable, in
accordance with the director's prior election, either in a lump sum or in
substantially equal monthly payments over five, ten or fifteen years. The
benefits under the Directors' Deferral Plan are secured through a grantor
trust. A participant's account under the Deferral Plan will accrue interest at
a rate established by the Company annually prior to the commencement of each
year. The guaranteed minimum rate of interest is not less than the Citibank
base rate. The interest rate for 1997 was 9.3 percent.
 
                                      20
<PAGE>
 
TRANSACTIONS BETWEEN THE COMPANY AND ARCO
 
  Lyondell was a division of ARCO until July 1988 when ARCO transferred the
assets of its Lyondell division to a wholly-owned subsidiary, Lyondell
Petrochemical Company. In January 1989, ARCO completed an initial public
offering of Lyondell's Common Stock. On September 15, 1997, ARCO divested of
substantially all of its remaining holdings of the Lyondell Common Stock
pursuant to the terms of notes issued by ARCO in August 1994 (the "ARCO Note
Offering"), which were exchanged for Lyondell Common Stock. ARCO thereupon
publicly reported that it had ceased to beneficially own more than five
percent of Lyondell's Common Stock.
 
  For the period from January 1, 1997 through September 30, 1997, Lyondell
(including LCR) paid ARCO and its direct or indirect subsidiaries, including
ARCO Chemical Company (together, "ARCO Affiliates"), an aggregate of
approximately $160 million. For the same period, Lyondell recorded revenues of
approximately $206 million from sales to ARCO Affiliates, all of which
represented sales to ARCO Chemical Company ("ARCO Chemical"). Such sales to
ARCO Chemical accounted for approximately 10 percent of total revenues from
sales of petrochemical products (including intersegment sales) for the first
three quarters of 1997 and approximately 8.8 percent of total revenues for the
first three quarters of 1997.
 
  THE FOLLOWING IS A SUMMARY OF CERTAIN AGREEMENTS, ARRANGEMENTS AND
TRANSACTIONS AMONG THE COMPANY AND ARCO AFFILIATES EFFECTIVE THROUGH SEPTEMBER
30, 1997.
 
REGISTRATION RIGHTS AGREEMENT
 
  In connection with the ARCO Note Offering, Lyondell and ARCO entered into a
registration rights agreement ("Registration Rights Agreement"). Pursuant to
the Registration Rights Agreement, ARCO had certain "demand" and "piggyback"
registration rights. Pursuant to the Registration Rights Agreement, ARCO
agreed that it would not, without the prior approval of Lyondell's Board of
Directors, prior to the maturity of the ARCO Notes, take certain actions with
respect to Lyondell, including the solicitation of proxies or acquisition
proposals. ARCO also agreed that it would not, without the prior approval of
Lyondell's Board of Directors dispose of all or any portion of its Lyondell
Common Stock except under certain circumstances.
 
CROSS-INDEMNITY AGREEMENT
 
  In connection with the transfer of assets and liabilities from ARCO to
Lyondell, Lyondell agreed to assume certain liabilities arising out of the
operation of the Company's integrated petrochemicals and petroleum processing
business prior to July 1, 1988. At that time, the Company and ARCO entered
into an agreement ("Cross-Indemnity Agreement") whereby the Company agreed to
defend and indemnify ARCO against certain uninsured claims and liabilities
which ARCO may incur relating to the operation of the business of the Company
prior to July 1, 1988. Effective in September 1997, the Company and ARCO
entered into an amendment to the Cross-Indemnity Agreement ("Revised Cross-
Indemnity Agreement"). For current and future cases related to Company
products and Company operations, ARCO and the Company will bear a
proportionate shares of judgment and settlement costs according to a formula
which allocates responsibility based on years of ownership during the relevant
time period. The party with the most significant potential liability exposure
will be responsible for case management and associated costs although
provisions have been made to allow the non-case managing party to protect its
interests. Under the Revised Cross-Indemnity Agreement, both ARCO and the
Company waived any claim for reimbursement under the existing Cross-Indemnity
Agreement for any prior defense and settlement costs associated with waste
site matters, and the Company assumed responsibility for its proportionate
share of future costs for waste site matters not covered by ARCO insurance.
 
SERVICES AGREEMENTS
 
  During the first half of 1997, ARCO provided various employee benefits
administration services pursuant to the "Employee Services Agreement" and
investment services with regard to the management of Lyondell's qualified
employee pension benefit plan funds pursuant to the "Investment Management
Agreement". Such agreements were terminated as of July 1, 1997. The Employee
Services Agreement provided for substantially all
 
                                      21
<PAGE>
 
services to be provided at a fee based on ARCO's costs and for the other
services to be provided at mutually-agreed fees. The Investment Management
Agreement provided for a renegotiation of fees from time to time. During the
first three quarters of 1997, Lyondell paid ARCO an aggregate of $395,000 for
services under these agreements.
 
TECHNOLOGY TRANSFERS AND LICENSES
 
  Effective July 1, 1988, ARCO assigned to the Company numerous domestic and
foreign trademarks and certain U.S. and foreign patents and granted the
Company a nonexclusive license to use other trademarks containing the word
"ARCO," to use ARCO's spark symbol as a logo and to use ARCO's color striping
scheme. The Company subsequently assigned this license to LCR and LCR paid
ARCO approximately $100,000 under the terms of this license during 1997.
 
  In connection with the transfer of assets and liabilities from ARCO to the
Company, effective July 1, 1988, the Company and ARCO entered into certain
technology licenses, assignments and other related agreements. In addition,
Lyondell and ARCO have executed a patent maintenance agreement pursuant to
which ARCO agreed to maintain certain patents licensed to Lyondell. Lyondell
and ARCO also entered into a letter agreement granting Lyondell the right to
obtain additional licensing rights. During 1997, no payments were made by
either party under any of such agreements.
 
AGREEMENTS BETWEEN THE COMPANY AND ARCO PIPELINE COMPANY
 
  The Company has entered into several contracts with ARCO PipeLine Company
("ARCO PipeLine") pursuant to which the Company: (i) leases certain pipelines
and pipeline segments from ARCO PipeLine at annual rental rates which include
recovery of operating costs, return on capital investment and inflation
escalators; (ii) obtains services from ARCO PipeLine to operate various groups
of pipelines owned by the Company; and (iii) throughputs volumes at tariff
rates for transportation of crude oil and other products. Certain of these
contracts that relate to the refining business were assigned to LCR as of July
1, 1993. ARCO PipeLine also owns various easements and licenses for its
pipelines and related equipment located on the property of the Company or LCR
and has performed services relating to the pipeline systems. The Company
(including LCR) also ships products over common carrier pipelines owned and
operated by ARCO PipeLine pursuant to filed tariffs on the same basis as other
non-affiliated customers. Beginning in January 1997, ARCO PipeLine began
providing terminalling and delivery of crude oil to LCR under the terms of
crude oil terminally agreement that extends through 2010. During the first
three quarters of 1997, the Company and LCR paid ARCO PipeLine approximately
$22 million for rental fees and services under these contracts.
 
AGREEMENTS BETWEEN THE COMPANY AND ARCO CHEMICAL
 
  Lyondell provides to ARCO Chemical large volumes of the feedstocks
(including benzene, ethylene, propylene and methanol) purchased by ARCO
Chemical for its manufacturing facilities located at Channelview, Texas.
Pricing arrangements under these contracts are generally representative of
prevailing market prices. Lyondell also provides certain nominal plant
services at the aforementioned plants. ARCO Chemical in turn provides to
Lyondell certain feedstocks and supplies at market-based prices.
 
  The Company sells MTBE (produced at one of the Company's two MTBE units) to
ARCO Chemical at market-based prices. Production from the Company's second
MTBE unit is dedicated to LCR.
 
OTHER AGREEMENTS BETWEEN THE COMPANY AND ARCO
 
  Lyondell has a nine year supply agreement through 2005 with ARCO Products
Company ("ARCO Products") wherein Lyondell is committed to sell and ARCO
Products is committed to buy approximately 6,000 barrels of alkylate per day
at market-based prices.
 
  LCR purchases certain of its crude oil requirements from ARCO Affiliates
under short-term arrangements at prices based on market values at the time of
delivery. LCR also purchases crude oil from ARCO Affiliates
 
                                      22
<PAGE>
 
from time to time on the spot market at then-current spot market prices. The
Company and LCR also purchased natural gas and natural gas liquids from ARCO
Affiliates during 1997 on the spot market at then-current spot market prices.
 
  The Company (including LCR) also sold products to ARCO Affiliates, including
crude oil resales and sales of heating oil and lube oil at market-based
prices.
 
  In April 1993, the Company, ARCO and ARCO Chemical entered into a Dispute
Resolution Agreement that mandates a procedure for negotiation and binding
arbitration of significant commercial disputes among any two or more of the
parties.
 
                                OTHER BUSINESS
 
  The Board of Directors is not aware of any other matters to be presented at
the meeting. If any other matters should properly come before the meeting, the
persons named in the enclosed proxy will vote the proxies in accordance with
their best judgment.
 
                              PROXY SOLICITATION
 
  The expense of soliciting proxies will be paid by the Company. The Company
has retained Georgeson & Company Inc. to solicit proxies at an estimated fee
of $9,500 plus expenses. Some of the executive officers and other employees of
the Company also may solicit proxies personally, by telephone and by mail, if
deemed appropriate. The Company will reimburse brokers or other persons
holding stock in their names or in the names of their nominees for their
reasonable expenses in forwarding proxy material to beneficial owners of
stock.
 
                 STOCKHOLDER PROPOSALS FOR 1999 ANNUAL MEETING
                           AND DIRECTOR NOMINATIONS
 
  Stockholder proposals intended to be presented at the 1999 Annual Meeting
must be received by the Company, at the address set forth on the first page of
this Proxy Statement, no later than December 7, 1998, in order to be included
in the Company's proxy material and form of proxy relating to such meeting.
Such proposals should be addressed to the Secretary. Stockholder proposals
must otherwise be eligible for inclusion. The 1999 Annual Meeting is scheduled
to take place in May 1999.
 
  Pursuant to the By-Laws of the Company, a stockholder wishing to nominate a
candidate for election to the Board is required to give written notice to the
Secretary of the Company of his or her intention to make such a nomination.
The notice of nomination must be received by the Company not less than 90 days
in advance of such meeting, or if the meeting was not publicly announced by a
mailing to the stockholders, in a press release reported by the Dow Jones New
Service, the Associated Press or a comparable national news service or a
filing with the Securities and Exchange Commission more than 90 days prior to
the meeting, must be delivered to the Board of Directors not later than the
close of business on the tenth day following the day on which the date of the
meeting was first so publicly announced. The notice of nomination is required
to contain certain information about both the nominee and the stockholder
making the nomination. A nomination that does not comply with the above
procedure will be disregarded. Compliance with the above procedures does not
require the Company to include the proposed nominee in the Company's proxy
solicitation material.
 
                       ADDITIONAL INFORMATION AVAILABLE
 
  THE COMPANY FILES AN ANNUAL REPORT ON FORM 10-K WITH THE SECURITIES AND
EXCHANGE COMMISSION. STOCKHOLDERS MAY OBTAIN A COPY OF THIS REPORT (WITHOUT
EXHIBITS), WITHOUT CHARGE, BY WRITING TO THE COMPANY'S INVESTOR RELATIONS
DEPARTMENT AT 1221 MCKINNEY STREET, SUITE 1600, HOUSTON, TEXAS 77010.
 
                                      23
<PAGE>
 
 
 
 
 
 
 

[LYONDELL LOGO APPEARS HERE]
                                                    [RECYCLED LOGO APPEARS HERE]
<PAGE>
 
[LYONDELL LOGO APPEARS HERE]


                        Lyondell Petrochemical Company
                        1221 McKinney Street, Suite 1600
                              Houston, Texas 77010

April 6, 1998

Dear Stockholder:

You are cordially invited to join us at the 1998 Annual Meeting of Stockholders
on Friday, May 15, 1998, beginning at 10:00 a.m. in the Austin Room of the Four
Seasons Hotel, 1300 Lamar, in Houston, Texas.

It is important that your shares be voted whether or not you plan to be present
at the meeting.  Please complete, sign, date and return the enclosed form of
proxy promptly.  If you do plan to attend, we would appreciate your checking the
appropriate box on the enclosed proxy card.

This booklet includes the Notice of the Meeting and the Proxy Statement, which
contains important information about the formal business to be acted upon by the
stockholders.  The official results of the voting at the meeting will be sent to
all stockholders as part of a subsequent stockholder report.

Sincerely yours,


DAN F. SMITH
President and Chief Executive Officer

                         PLEASE DETACH PROXY CARD HERE
- --------------------------------------------------------------------------------
1. ELECTION OF DIRECTORS

   FOR all nominees      WITHHOLD AUTHORITY to
   listed below   [ ]    vote for all nominees listed below [ ]  *EXCEPTIONS [ ]

   Nominees:  William T. Butler, Travis Engen, Stephen F. Hinchliffe, Jr.,
   Dudley C. Mecum II, Dan F. Smith, Paul R. Staley (INSTRUCTIONS: TO WITHHOLD
   AUTHORITY TO VOTE FOR ANY INDIVIDUAL NOMINEE MARK THE "EXCEPTIONS" BOX AND
   WRITE THAT NOMINEE'S NAME IN SPACE PROVIDED BELOW.)
   *Exceptions ___________________________________________________________

2. Proposal to ratify the joint appointment of Coopers & Lybrand and Price
   Waterhouse, independent accountants, including any successor merged entity of
   the two firms, as the Company's auditors for the fiscal year ending December,
   1998.

3. In their discretion, the Proxies are authorized to vote upon such other
   business as may properly come before the meeting.

  FOR   [ ]  AGAINST  [ ]   ABSTAIN  [ ]

I/we will attend the meeting.  [ ]    Address Change Mark Here [  ]

Please sign exactly as name appears.  When shares are held by joint tenants,
both should sign.  When signing as an attorney, executor, administrator, trustee
or guardian, please sign as such.

Dated: ____________________________, 1998

________________________________________
          Signature
________________________________________
     Signature if held jointly

PLEASE  SIGN, DATE AND RETURN THE PROXY       Votes MUST be indicated (x)
PROMPTLY USING THE ENCLOSED ENVELOPE.         in Black or Blue Ink.
<PAGE>
 
                         [LYONDELL LOGO APPEARS HERE]


                               One Houston Center
                           1221 McKinney, Suite 1600
                              Houston, Texas 77010

          This Proxy is Solicited on Behalf of the Board of Directors

     The undersigned hereby makes, constitutes and appoints Edward W. Rich and
Jeffrey R. Pendergraft and each of them, lawful attorney and proxies of the
undersigned, with full power of substitution, for and in name, place and stead
of the undersigned to attend the Special Meeting of Stockholders of Lyondell
Petrochemical Company (herein the "Company") in the Austin Room at the Four
Season's Hotel, 1300 Lamar, in Houston, Texas on Friday, May 15, 1998 at 10:00
a.m., local time, and at any adjournment(s) thereof, with all powers the
undersigned would be entitled to vote if personally present.

     This proxy when properly executed will be voted in the manner directed
herein by the undersigned stockholder.  If no direction is made, this proxy will
be voted FOR items 1 and 2.

     This card also constitutes your voting instructions for shares held in the
Lyondell Petrochemical Company 401(k) and Savings Plan, the Equistar Chemicals,
LP Savings and Investment Plan, the LYONDELL-CITGO Refining Company Ltd. 401(k)
and Savings Plan for Non-Represented Employees and the LYONDELL-CITGO Refining
Company Ltd. 401(k) and Savings Plan for Represented Employees, and the
undersigned hereby authorizes State Street Bank, as Trustee of such plans to
vote the shares held in the undersigned's accounts.

LYONDELL PETROCHEMICAL COMPANY
P.O. BOX 11244
NEW YORK, NY 10203-0244

                       (Continued, and to be signed and dated, on reverse side.)


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