LYONDELL CHEMICAL CO
DEF 14A, 1999-03-29
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 CHEMICAL 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:


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


     (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:


     (5) Total fee paid:

[_]  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:
 

     (2) Form, Schedule or Registration Statement No.:


     (3) Filing Party:
      

     (4) Date Filed:


<PAGE>
 
 
[LYONDELL LOGO APPEARS HERE]
 
LYONDELL
CHEMICAL
COMPANY
 
 
 
Notice of
Annual Meeting
of Stockholders
to be held
on May 6, 1999
and Proxy Statement
 
                     PLEASE COMPLETE, SIGN, DATE AND RETURN
                              YOUR PROXY PROMPTLY
 
<PAGE>
 
 
                           Lyondell Chemical Company
                       1221 McKinney Street, Suite 1600
                             Houston, Texas 77010
 
March 31, 1999
 
Dear Stockholder:
 
  The 1999 Annual Meeting of Stockholders will be held on Thursday, May 6,
1999, 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 three 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 Chemical Company
 
                   Notice of Annual Meeting of Stockholders
 
                                  May 6, 1999
 
To the Stockholders:
 
  The Annual Meeting of Stockholders of Lyondell Chemical Company will be held
at the Four Seasons Hotel, 1300 Lamar, in Houston, Texas, at 10:00 a.m.,
Houston time, on Thursday, May 6, 1999, for the following purposes, as more
fully described in the attached Proxy Statement:
 
  (1) To elect eight directors to serve until the 2000 Annual Meeting of
      Stockholders or until their earlier resignation or removal;
 
  (2) To ratify the appointment of PricewaterhouseCoopers LLP, independent
      auditors, as the Company's auditors for the year 1999;
 
  (3) To consider and act upon a proposal to adopt the Company's 1999 Long-
      Term Incentive Plan; and
 
  (4) 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 11, 1999, 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/ Robert J. Millstone
Robert J. Millstone                                       Houston, Texas
Secretary                                                 March 31, 1999
<PAGE>
 
                           Lyondell Chemical Company
                             1221 McKinney Street
                                  Suite 1600
                             Houston, Texas 77010
 
                               ----------------
                                PROXY STATEMENT
                                March 31, 1999
                               ----------------
 
                                 INTRODUCTION
 
  The accompanying proxy is solicited by the Board of Directors of Lyondell
Chemical 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 March 31, 1999.
 
                               VOTING PROCEDURES
 
  Holders of record of Common Stock at the close of business on March 11,
1999, will be entitled to one vote per share. The Company had 77,093,050
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. Broker
non-votes occur when a broker returns a proxy but does not have the authority
to vote on a particular matter.
 
  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. Adoption of the proposal to adopt the
Lyondell Chemical Company 1999 Long-Term Incentive Plan (the "1999 Long-Term
Incentive Plan" or the "Plan") will require approval by the holders of a
majority of the outstanding shares of Common Stock present, or represented,
and entitled to vote at the meeting, provided that the total votes cast must
also exceed fifty percent of the shares of Common Stock outstanding and
entitled to vote on the matter.
 
  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,
against the ratification of the appointment of the independent auditors, or
against approval of the 1999 Long-Term Incentive Plan, as the case may be.
Broker non-votes 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; accordingly, broker non-votes will not affect the
outcome with respect to the ratification of the appointment of the independent
auditors or the adoption of the 1999 Long-Term Incentive Plan.
 
  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 such Plan's Benefits Administrative
Committee which is made up of certain executive officers of the Company.
Similarly, the trustee will vote all shares of Common Stock held in benefits
plans of the Company's subsidiaries for which no participant directions are
received as directed by each plan's Benefits Administrative Committee, which
may be made up of certain executive officers of the Company.
 
  A proxy may be revoked by a 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, 1998 (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. On March 5,
1999, State Street Bank and Trust Company filed a Schedule 13G indicating its
beneficial ownership had dropped below five percent; accordingly, it has been
excluded from this table.
 
<TABLE>
<CAPTION>
                                                                    Percentage
                                                          Number of  of Shares
                       Name and Address                    Shares   Outstanding
                       ----------------                   --------- -----------
      <S>                                                 <C>       <C>
      Brinson Partners, Inc.(a).......................... 9,132,624    11.9%
      209 South LaSalle, Chicago, Illinois 60604-1295
 
      Scudder Kemper, Investments, Inc.(b)............... 8,330,769    10.8%
      345 Park Avenue, New York, New York 10154
 
      Sanford C. Bernstein & Co., Inc.(c)................ 7,882,077    10.3%
      767 Fifth Avenue, New York, New York 10153
 
      Wellington Management Company, LLP(d).............. 6,661,203     8.7%
      75 State Street, Boston, Massachusetts 02109
 
      Franklin Resources, Inc.(e)........................ 5,623,000     7.3%
      777 Mariners Island Blvd., San Mateo, CA 94404
</TABLE>
- --------
(a) Brinson Partners, Inc. ("BPI") and its indirect parent holding company,
    UBS AG, may be deemed the beneficial owners of the 9,132,624 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 and UBS AG have shared voting and shared dispositive power
    over all 9,132,624 shares.
(b) Scudder Kemper Investments, Inc. ("Scudder Kemper") may be deemed a
    beneficial holder of 8,330,769 shares. Scudder Kemper has sole voting
    power over 1,883,923 shares and shared voting power over 5,954,553 shares,
    and has sole dispositive power over all 8,330,769 shares.
(c) Sanford C. Bernstein & Co., Inc. ("Bernstein & Co.") may be deemed a
    beneficial holder of 7,882,077 shares. Bernstein & Co. has sole voting
    power over 4,951,215 shares and shared voting power over 524,685 shares,
    and has sole dispositive power over all 7,882,077 shares.
(d) Wellington Management Company, LLP ("WMC") (together with its wholly owned
    subsidiary, Wellington Trust Company, N.A.) may be deemed a beneficial
    owner of the 6,661,203 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 6,661,203 shares and shared voting power over 1,300 shares.
    Vanguard has shared dispositive power over 6,659,903 shares and sole
    voting power over 6,659,903 shares.
(e) Franklin Resources, Inc. (together with its principal shareholders,
    Charles B. Johnson and Rupert H. Johnson, Jr., and its advisory
    subsidiary, Templeton Global Advisors Limited ("TGAL")) may be deemed a
    beneficial owner of 5,623,000 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. TGAL has sole
    voting and dispositive power over 5,623,000 shares.
 
                                       2
<PAGE>
 
                       SECURITY OWNERSHIP OF MANAGEMENT
 
  The following table sets forth the number of shares of Common Stock owned
beneficially as of March 1, 1999, by each director or nominee, each of the
executive officers named in the Summary Compensation Table (the "named
executive officers") and by all directors and executive officers as a group.
As of March 1, 1999, 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 March 1, 1999(a)(b)
                                                        ----------------------
      <S>                                               <C>
      Carol A. Anderson................................          3,230(c)
      William T. Butler................................          8,105
      Travis Engen.....................................         11,600
      Morris Gelb......................................         25,569
      Stephen F. Hinchliffe, Jr........................         11,128(d)
      Dudley C. Mecum II...............................          3,510
      Jeffrey R. Pendergraft...........................         86,211(e)
      Joseph M. Putz...................................         65,867
      Frank Savage.....................................          2,408
      Dan F. Smith.....................................        172,728
      Paul R. Staley...................................         20,043
      Debra L. Starnes.................................         90,065(f)
      All directors and executive officers as a group
       (24)............................................        704,818(g)
</TABLE>
- --------
(a) Includes shares held by the trustees under the Lyondell 401(k) and Savings
    Plan and the ARCO Chemical Company Capital Accumulation and Savings Plans
    for the accounts of participants as of December 31, 1998.
(b) The amounts shown for the named executive officers include shares that (i)
    are restricted shares that are not fully vested, (ii) shares acquired
    under the Company's Dividend Reinvestment Plan and (iii) shares that may
    be acquired through the exercise of stock options. Those shares that may
    be acquired through the exercise of stock options include: Mr. Smith,
    32,200; Mr. Pendergraft, 50,600; Mr. Gelb, -0-; Ms. Starnes, 32,500; Mr.
    Putz, 25,600; and all executive officers as a group, including those just
    named, 144,919. The amounts shown for the directors include restricted
    shares which are not fully vested.
(c) Does not include 100 shares held by a trust of which Ms. Anderson is an
    indirect beneficiary, and as to which she disclaims beneficial ownership.
(d) 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.
(e) Does not include approximately 1,543 shares owned by Mr. Pendergraft's
    spouse, as to which shares he disclaims beneficial ownership.
(f) Does not include approximately 8,717 shares owned by Ms. Starnes' spouse,
    as to which shares she disclaims beneficial ownership.
(g) Does not include the approximately 11,562 shares owned by family members
    of certain executive officers and two trusts, as to which shares
    beneficial ownership is disclaimed.
 
Section 16(a) Beneficial Ownership Reporting Compliance
 
  Section 16(a) of the Securities Exchange Act of 1934, as amended (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 (the
"NYSE") 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.
 
  SEC regulations related to compliance with Section 16(a) of the Exchange Act
require the following disclosure: Carol A. Anderson, a director of the
Company, failed to file on a timely basis one report on Form 4 relating to a
purchase transaction involving 975 shares of Common Stock of the Company
directly owned by her.
 
  Except as described above, 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, 1998, all
Section 16(a) filing requirements applicable to its officers, directors and
greater than ten-percent beneficial owners were complied with.
 
                                       3
<PAGE>
 
                              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 Company's 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 1998, the Board of Directors held nine
meetings. All of the Company's incumbent directors attended seventy-five
percent or more of the aggregate of all meetings of the Board and committees
on which they served during 1998, except Mr. Savage.
 
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 1998. The Audit Committee currently comprises Messrs.
Savage, 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 ten meetings during 1998. The Compensation
Committee currently comprises Messrs. Butler, Engen and Hinchliffe. Mr.
Hinchliffe serves as Chairman.
 
Corporate Governance and Responsibility Committee
 
  The Corporate Governance and Responsibility 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 and Responsibility Committee also
recommends matters relating to committee assignments and the roles and
responsibilities of the Board and of the directors in addition to monitoring
the Company's legal compliance programs. The Corporate Governance and
Responsibility Committee makes determinations 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 and Responsibility Committee held seven meetings during 1998. The
Corporate Governance and Responsibility Committee currently comprises Ms.
Anderson and Messrs. Butler and Staley. Mr. Staley 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 Company's By-Laws
that are described more fully on page 32 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. The Executive Committee did
not meet during 1998. The Executive Committee currently comprises Messrs.
Smith, Engen and Butler. Dr. Butler serves as Chairman.
 
                                       4
<PAGE>
 
                        CORPORATE GOVERNANCE GUIDELINES
 
  The Board of Directors has adopted a formal statement of the roles and
responsibilities of the Board and has 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 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.
 
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 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 and
  Responsibility 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
 
                                       5
<PAGE>
 
  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 or her desire to continue as a member of the Board.
  The Corporate Governance and Responsibility 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 72.
 
    Compensation for Board members will be reviewed annually for
  competitiveness. A portion of the directors' compensation will be in the
  form of Company stock.
 
    Performance of the Board will be reported annually to the Board by the
  Corporate Governance and Responsibility 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 Restated Certificate of Incorporation, as amended
(the "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.
 
  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 eight
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, 1999, 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, 66........  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 has served as
                               Chancellor of Baylor College of Medicine since
                               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 and
                               Responsibility Committee, and is Chairman of
                               the Executive Committee.
 
Carol A. Anderson, 52........  Ms. Anderson was elected a director of the
                               Company effective December 11, 1998. She has
                               served as Managing Director of TSG
                               International, a subsidiary of The Springland
                               Group, which manages private equity investments
                               in high technology ventures since April 1998.
                               From 1993 until March 1998, Ms. Anderson served
                               as Managing Director of Merrill International,
                               Ltd., which develops energy projects worldwide.
                               Ms. Anderson is also a director of The Stroh
                               Brewery Co., The Stroh Companies and Merrill
                               International, Ltd.
 
                               Ms. Anderson is a member of the Corporate
                               Governance and Responsibility Committee.
 
Travis Engen, 54.............  Mr. Engen was elected a director of the Company
                               effective as of April 1, 1995. He has held his
                               current position as Chairman 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
 
                                       7
<PAGE>
 
                               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, Ltd.
 
                               Mr. Engen is a member of the Compensation
                               Committee and the Executive Committee.
 
Stephen F. Hinchliffe, Jr.,    Mr. Hinchliffe was elected a director of the
65...........................  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., 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 also a
                               director of BHH Management, Inc., Leisure
                               Group, Inc. and Relton Corp.
 
                               Mr. Hinchliffe is Chairman of the Compensation
                               Committee.
 
Dudley C. Mecum II, 64.......  Mr. Mecum was elected a director of the Company
                               on November 28, 1988, effective as of January
                               25, 1989. Since June 1997, Mr. Mecum has been
                               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 Dyncorp,
                               VICORP Restaurants, Inc., Travelers Property
                               Casualty Corporation, Metris Companies, Inc.,
                               Suburban Propane LLP, Citigroup and CCC
                               Information Services, Inc.
 
                               Mr. Mecum is Chairman of the Audit Committee.
 
Frank Savage, 60.............  Mr. Savage was elected a director of the
                               Company effective October 16, 1998. He has
                               served as the Chairman of Alliance Capital
                               Management International (financial services)
                               since 1993. From 1988 until 1996, Mr. Savage
                               was Senior Vice President of The Equitable Life
                               Assurance Society of the United States
                               (financial services). Mr. Savage served on the
                               Board of Directors of ARCO Chemical Company
                               ("ARCO Chemical") from 1993 until it was
                               acquired by the Company in July 1998. Mr.
                               Savage is a director of Alliance Capital
                               Management Corporation, Lockheed Martin
                               Corporation and Qualcomm, Inc.
 
                               Mr. Savage is a member of the Audit Committee.
 
Dan F. Smith, 52.............  Mr. Smith was named Chief Executive Officer of
                               the Company on December 6, 1996, and has served
                               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
 
                                       8
<PAGE>
 
                               also served as the Chief Executive Officer of
                               Equistar Chemicals, LP ("Equistar"), a
                               petrochemicals and polymers joint venture owned
                               41 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 Cooper
                               Industries, Inc. and ChemFirst, Inc.
 
                               Mr. Smith is a member of the Executive
                               Committee.
 
Paul R. Staley, 69...........  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 industrial 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 and Responsibility Committee and a
                               member of the Audit Committee.
 
          PROPOSAL TO RATIFY THE APPOINTMENT OF INDEPENDENT AUDITORS
 
                             Item 2 on Proxy Card
 
  The Board of Directors has recommended the appointment of
PricewaterhouseCoopers LLP ("PricewaterhouseCoopers") to audit the financial
statements of Lyondell for the year 1999. Prior to their merger, Coopers &
Lybrand L.L.P. ("Coopers & Lybrand") and Price Waterhouse LLP (including any
successor merged entity of the two firms), were jointly appointed to audit the
financial statements of Lyondell for the year 1998. Prior thereto, Coopers &
Lybrand had acted in this capacity since July 1988. In addition, from time to
time, PricewaterhouseCoopers performs consulting work for the Company.
 
  Representatives of PricewaterhouseCoopers 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
appointment of PricewaterhouseCoopers. Properly dated and signed proxies will
be so voted unless stockholders specify otherwise.
 
                                       9
<PAGE>
 
              PROPOSAL TO ADOPT THE 1999 LONG-TERM INCENTIVE PLAN
 
                             Item 3 on Proxy Card
 
  The Lyondell Chemical Company 1999 Long-Term Incentive Plan was adopted by
the Compensation Committee on December 9, 1998, subject to shareholder
approval, to provide for the grant of awards to employees of the Company and
its subsidiaries ("Employees"). The primary objectives of the Plan are to
focus Employees selected to participate on key measures of value creation for
the Company's shareholders, provide significant upside award potential
commensurate with shareholder value creation, encourage long-term management
perspective, reward sustained long-term performance, enhance the ability of
the Company to attract and retain highly talented individuals, reinforce a
team orientation among top management and encourage ownership of Company stock
among top management. The following summary of certain provisions of the Plan
does not purport to be complete and is qualified in its entirety by reference
to the Plan, a copy of which is attached as Exhibit A.
 
  Awards to Employees ("Awards") may be in the form of (i) rights to purchase
a specified number of shares of Common Stock at a specified price ("Options"),
(ii) rights to receive a payment, in cash or Common Stock, equal to the fair
market value or other specified value of a number of shares of Common Stock on
the exercise date of the rights over a specified strike price ("SARs"), (iii)
restricted grants of Common Stock or units denominated in Common Stock
("Restricted Stock Awards"), (iv) grants denominated in Common Stock or units
denominated in Common Stock, which are made subject to the attainment of one
or more goals ("Performance Shares"), (v) grants of rights to receive the
value of a specified number of shares of Common Stock ("Phantom Stock"), and
(vi) a cash payment ("Cash Award").
 
  The Plan is not qualified under Section 401(a) of the Internal Revenue Code
of 1986, as amended (the "Code"), and is not subject to the provisions of the
Employee Retirement Income Security Act of 1974, as amended ("ERISA").
 
Administration
 
  The Compensation Committee of the Board or another committee appointed by
the Board for this purpose (in either case, the "Committee") will administer
the Plan. The Committee has full and exclusive power to administer the Plan
and take all actions specifically contemplated thereby or necessary or
appropriate in connection with the administration thereof. The Committee has
the full and exclusive power to interpret the Plan and to adopt such rules,
regulations and guidelines for carrying out the Plan as the Committee may deem
necessary or proper in keeping with the objectives thereof. The Committee may,
in its discretion, extend or accelerate the exercisability of, accelerate the
vesting of, or eliminate or make less restrictive any restrictions contained
in any Award; waive any restriction or other provision of the Plan (insofar as
it relates to Awards) or in any Award or otherwise amend or modify any Award
in any manner that is either (i) not adverse to that Employee holding the
Award or (ii) consented to by that Employee. The Committee may delegate to the
chief executive officer and other senior officers of the Company its duties
under the Plan. Any decision of the Committee in the interpretation and
administration of the Plan shall lie within its sole and absolute discretion
and shall be final, conclusive and binding on all parties concerned.
 
Participation and Eligibility
 
  Employees eligible for selection to receive Awards under the Plan are
Employees whose performance, in the judgment of the Committee, can contribute
significantly to the Company's long-term profit and growth objectives.
 
Shares Subject to the Plan
 
  No Award shall be granted if it shall result in an aggregate number of
shares of Common Stock issued under the Plan plus the number of shares of
Common Stock covered by or subject to Awards then outstanding (after giving
effect to the grant of the Award in question) to exceed the lesser of ten
million or ten percent of the number of shares of Common Stock outstanding at
the time of granting such Award. No more than one million
 
                                      10
<PAGE>
 
shares of Common Stock shall be available for incentive stock options, as
defined below. No participant may be granted, during the term of the Plan,
Options covering or relating to more than two million shares of Common Stock.
No participant may be granted, during the term of the Plan, Awards in the form
of Performance Shares, Restricted Stock, Stock Appreciation Rights or Phantom
Stock covering or relating to more than one million shares of Common Stock. No
more than 2.5 million shares of Common Stock shall be available, in the
aggregate, for Awards in the form of Performance Shares, Restricted Stock,
Stock Appreciation Rights or Phantom Stock. No Participant may be granted Cash
Awards in respect of any calendar year having a value in excess of $2 million.
The number of shares authorized to be issued under the Plan is also subject to
adjustment as described under "--Adjustments" below. Shares subject to Awards
that are forfeited or terminated, exchanged for Awards that do not involve
Common Stock or expire unexercised, or are settled in cash in lieu of Common
Stock, or otherwise such that the shares covered thereby are not issued, again
become available for Awards.
 
Terms, Conditions and Limitations of Awards
 
  Generally. The Committee will determine the type or types of Awards made
under the Plan and will designate the Employees who are to be the recipients
of such awards. An Award (other than a Cash Award) shall be embodied in an
agreement (an "Award Agreement"), which will contain terms, conditions and
limitations as determined by the Committee. The Committee will establish
guidelines governing the issuance and payment of Cash Awards. At the
discretion of the Committee, an Employee may be offered an election to
substitute an Award for another Award or Awards of the same or different type.
Upon the termination of employment by an Employee, any unexercised, deferred,
unvested or unpaid Awards will be treated as set forth in the applicable Award
Agreement.
 
  Performance-Based Awards. Performance-based Awards consist of grants made to
an Employee subject to the attainment of one or more performance goals. A
performance-based Award will be paid, vested or otherwise deliverable solely
upon the attainment of one or more pre-established, objective performance
goals established by the Committee prior to the earlier of (i) 90 days after
the commencement of the period of service to which the performance goals
relate and (ii) the lapse of twenty-five percent of the period of service, and
in any event while the outcome is substantially uncertain. A performance goal
may be based upon one or more business criteria that apply to the Employee,
one or more business units of the Company or the Company as a whole, and may
include any of the following: economic value, economic value added, increased
revenue, net income, stock price, market share, earnings per share, return on
equity, return on assets, decrease in costs, shareholder value, net cash flow,
total shareholder return, return on capital, return on investors' capital,
operating income, funds from operations, cash flow, cash from operations,
after-tax operating income and total market value. Prior to the payment of any
compensation based on the achievement of such performance goals, the Committee
must certify in writing that the applicable performance goals and any of the
material terms thereof were, in fact, satisfied. Subject to the foregoing, the
terms, conditions and limitations applicable to any performance-based Awards
will be determined by the Committee. Performance-based Awards may be in the
form of Performance Shares, Options, Restricted Stock, Stock Appreciation
Rights, Cash Awards or Phantom Stock.
 
  Options. Options are rights to purchase a specified number of shares of
Common Stock at a specified price. An Option granted pursuant to the Plan may
consist of either an incentive stock option ("ISO") that complies with the
requirements of Section 422 of the Code or a non-qualified stock option
("NQSO") that does not comply with such requirements. The terms, conditions
and limitations applicable to any Options, including the term of any Options
and the date or dates upon which they become exercisable, will be determined
by the Committee; provided, however, that the exercise price of an Option may
not be less than the Fair Market Value of a share of Common Stock, as defined
in the Plan, on the date of grant and may not be less than the Fair Market
Value of a share of Common Stock on the grant date of any outstanding Option
that is relinquished in connection with a grant of a new Option. Unless
specified otherwise in the applicable Award Agreement, each Option shall
immediately terminate to the extent it is not vested and does not become
vested upon termination of employment on the date that a Participant
terminates employment with the Company or a subsidiary.
 
  SARs. SARs are rights to receive a payment, in cash or Common Stock, equal
to the excess of the Fair Market Value (or other specified valuation) of a
specified number of shares of Common Stock on the date the
 
                                      11
<PAGE>
 
rights are exercised over a specified strike price. The exercise price of an
SAR may not be less than the Fair Market Value of a share of Common Stock on
the date of grant. The terms, conditions and limitations applicable to any
SARs, including the term of any SARs and the date or dates upon which they
become exercisable, will be determined by the Committee.
 
  Restricted Stock Awards. Restricted Stock Awards consist of restricted
grants of Common Stock or units denominated in Common Stock. The terms,
conditions and limitations applicable to any Restricted Stock Awards will be
determined by the Committee.
 
  Performance Shares. Performance Shares consist of grants denominated in
Common Stock or units denominated in Common Stock made to an Employee subject
to the attainment of one or more performance goals. An Award of Performance
Shares will be paid, vested or otherwise deliverable solely upon the
attainment of one or more goals established by the Committee. Performance
Shares vested upon the achievement of performance goals may be paid, in the
discretion of the Committee, in shares of Common Stock, cash or a combination
thereof. Subject to the foregoing, the terms, conditions and limitations
applicable to any Performance Shares will be determined by the Committee.
 
  Phantom Stock. Phantom Stock means the right to receive the value of a
specified number of shares of Common Stock. The terms, conditions and
limitations applicable to any Phantom Stock will be determined by the
Committee.
 
  Cash Awards. Cash Awards are awards payable in cash. The terms, conditions
and limitations applicable to any Cash Award will be determined by the
Committee.
 
Exercise of Options
 
  The exercise price of any Option must be paid in full at the time the Option
is exercised in cash or, if permitted by the Committee, by means of tendering
Common Stock or surrendering another Award (including a Restricted Stock
Award). Unless otherwise provided in the applicable Award Agreement, in the
event shares of restricted stock are tendered as consideration for the
exercise of an Option, a number of the shares issued upon the exercise of the
Option, equal to the number of shares of restricted stock used as
consideration therefor, will be subject to the same restrictions as the
restricted stock so submitted as well as any other restrictions that may be
imposed by the Committee. The Committee may adopt additional rules and
procedures regarding the exercise of Options from time to time, provided that
such rules and procedures are not inconsistent with the provisions of this
paragraph.
 
Award Payments
 
  Deferral. With the approval of the Committee, payments in respect of Awards
may be deferred, either in the form of installments or a future lump sum
payment. Any deferred payment of an Award, whether elected by the participant
or specified by the Award Agreement or by the Committee, may be forfeited if
and to the extent that the Award Agreement so provides.
 
  Dividends and Interest. Dividends or dividend equivalent rights may be made
a part of any Award denominated in Common Stock or units of Common Stock,
subject to such terms, conditions and restrictions as the Committee may
establish. The Committee may establish rules for the crediting of interest on
deferred cash payments and dividend equivalents on deferred payments
denominated in Common Stock or units of Common Stock.
 
Assignment of Interests Prohibited
 
  Unless otherwise determined by the Committee and provided in the applicable
award agreement, no Award or any other benefit under the Plan shall be
assignable or otherwise transferable except by will or the laws of descent and
distribution. The Committee may prescribe and include in applicable award
agreements other restrictions on transfer. Any attempted assignment of an
Award or any other benefit under the Plan in violation
 
                                      12
<PAGE>
 
thereof will be null and void. Subject to approval by the Committee in its
sole discretion, a participant may transfer an Award to certain immediate
family members, as defined in the Plan, trusts for the exclusive benefit of
such immediate family members or a partnership which is owned by such
immediate family members.
 
Adjustments
 
  In the event of any subdivision or consolidation of outstanding shares of
Common Stock, declaration of a stock dividend payable in shares of Common
Stock or other stock split, any other recapitalization or capital
reorganization of the Company, any consolidation or merger of the Company with
another corporation or entity, the adoption by the Company of any plan of
exchange affecting the Common Stock or any distribution to holders of Common
Stock of securities or property, the Plan provides for the Committee to make,
in its sole discretion as it deems appropriate, adjustments to (i) the number
of shares of Common Stock reserved under the Plan, the number of shares of
Common Stock covered by outstanding Awards and related limitations on ISOs,
(ii) the exercise or other price in respect of such Awards, and (iii) the
appropriate Fair Market Value and other price determinations for such Awards.
In the event of a corporate merger, consolidation, acquisition of property or
stock, separation, reorganization or liquidation, the Board may (i) provide
for the issuance or assumption of Awards by means of substitution of new
Awards, as appropriate, for previously issued Awards or the assumption of
previously issued Awards as part of such adjustment, (ii) make provision,
prior to the transaction, for the acceleration of the vesting and
exercisability of, or lapse of restrictions with respect to, Awards, or (iii)
in the event that the Company is not the surviving corporation of any such
transaction, (A) cancel Awards that are Options or SARs and give the
Participants who are the holders of such Awards notice and opportunity to
exercise for 30 days prior to such cancellation, or (B) settle an Award that
is an Option or SAR by a cash payment equal to the difference between the Fair
Market Value per share of Common Stock on the date of such transaction and the
exercise price of the Award, multiplied by the number of shares subject to the
Award.
 
Amendment, Modification and Termination
 
  The Committee may amend, modify, suspend or terminate the Plan for the
purpose of addressing any changes in legal requirements or for any other
purpose permitted by law, except that (i) no amendment that would impair the
rights of any Participant with respect to any outstanding Award may be made
without the consent of such Participant and (ii) no amendment legally
requiring stockholder approval will be effective until such approval has been
obtained. No Awards may be granted more than ten years after the effective
date of the Plan.
 
Restrictions
 
  No payment or delivery of shares of Common Stock may be made unless the
Company is satisfied that such payment or delivery will comply with applicable
laws and regulations.
 
Tax Withholding
 
  The Company will have the right to deduct applicable taxes from any Award
payment and withhold, at the time of delivery or vesting of cash or shares of
Common Stock under the Plan, an appropriate amount of cash or number of shares
of Common Stock, or combination thereof, for the payment of taxes. The
Committee may also permit withholding to be satisfied by the transfer to the
Company of shares of Common Stock previously owned by the holder of the Award
for which withholding is required.
 
Unfunded Plan
 
  The Plan will be unfunded. Any bookkeeping accounts that are established
with respect to Participants for purposes of the Plan will be used merely as a
bookkeeping convenience. The Company is not required to segregate any assets
for purposes of the Plan or awards thereunder, nor will the Plan be construed
as providing for such segregation, nor will the Company, the Board or the
Committee be deemed to be a trustee of any benefit granted under the Plan. Any
liability or obligation of the Company to any participant under the Plan will
be based solely on any contractual obligations that may be created by the Plan
and any Award Agreement, and no such liability or obligation of the Company
will be deemed to be secured by any pledge or other encumbrance
 
                                      13
<PAGE>
 
on any property of the Company. Neither the Company, the Board nor the
Committee will be required to give any security or bond for the performance of
any obligation that may be created by the Plan.
 
Cancellation
 
  The adoption of the Plan is expressly conditioned on approval by holders of
a majority of the outstanding shares of Common Stock present, or represented,
and entitled to vote at the annual meeting of shareholders in 1999 and upon
shareholder approval at that annual meeting that satisfies applicable exchange
requirements for shareholder approval. If the shareholders of the Company
should fail to so approve the Plan at such annual meeting, the Plan shall
terminate and cease to be of any further force or effect and all grants of
Awards under the Plan shall be null and void.
 
Awards Granted Under the Plan
 
  Subject to stockholder approval of the Plan, the Committee granted Options
and Performance Shares under the Plan in January 1999 to seventeen executive
officers, including the named executive officers. The following table shows
the Options and Performance Shares granted under the Plan in January 1999 to
each of the named executive officers and all current executive officers as a
group. No Non-Employee Director will be granted an Award under the Plan. As of
March 15, 1998, no employee who is not an executive officer has been granted
Awards under the Plan. Prior to the date of the Annual Meeting, the Company
anticipates awarding Options for the purchase of up to approximately 800,000
shares of Common Stock and up to approximately 200,000 Performance Shares, in
the aggregate, to employees who are not executive officers. The last reported
sales price for the Company's Common Stock as reported on the New York Stock
Exchange Composite Transaction Tape on March 19, 1999 was $13 1/2 per share.
 
<TABLE>
<CAPTION>
 Awards Granted Under 1999 Long-Term Incentive
                     Plan
- ------------------------------------------------
                          Securities
                          Underlying Performance
Name                      Options(1)  Shares(2)
- ----                      ---------- -----------
<S>                       <C>        <C>
Mr. Smith...............    463,400    122,800
Mr. Pendergraft.........     79,100     21,000
Mr. Gelb................     91,700     24,300
Ms. Starnes.............     49,600     13,100
Mr. Putz................     30,700      8,100
All current executive
 officers as a group (17
 persons)...............  1,007,200    266,900
</TABLE>
- --------
(1) Number of shares of the Company's Common Stock.
(2) Number of Performance Shares subject to Award.
 
  Pursuant to the Plan, the Committee granted each executive officer a NQSO
Award and a Performance Share Award. The exercise price of the shares of
Common Stock underlying the Options is $18 1/8, representing the fair market
value of the Company's Common Stock on January 6, 1999. The Options vest
ratably over a three-year period beginning on the first anniversary date of
the awards, and have a ten-year term.
 
  The Performance Shares awarded to the executive officers represent the
number of Performance Shares each officer can earn during the calendar years
1999, 2000 and 2001 (the "Performance Period") if the Company achieves its
target performance. The Company's performance target is to achieve total
shareholder return during the Performance Period of at least the fiftieth
percentile, as compared to the companies in its peer group (as selected by the
Board of Directors). Total shareholder return is defined as the increase in
dollar value as of the end of the Performance Period of an initial $100.00
investment in the Company's Common Stock, as required to be calculated under
the Exchange Act for purposes of the Performance Graph contained in this Proxy
Statement.
 
  In order for any Performance Shares to be earned, the Company must achieve a
total shareholder return ranking of at least the thirtieth percentile. In such
event, twenty percent of the Performance Shares awarded will be deemed earned.
If, however, the Company achieves a total shareholder return ranking of at
least the eightieth percentile, the number of Performance shares earned by
each individual is increased to twice the number of Shares originally awarded
to each recipient. At the Committee's discretion, payment of the Performance
Shares will be paid in shares of Common Stock, in cash or a combination
thereof.
 
                                      14
<PAGE>
 
Federal Income Tax Consequences
 
  The following discussion summarizes some U.S. federal income tax
consequences to participants in the Plan. This summary is based on statutory
provisions, Treasury regulations thereunder, judicial decisions and rulings of
the Internal Revenue Service (the "IRS") in effect on the date hereof. This
summary does not purport to be complete, and does not cover, among other
things, state, local or foreign tax treatment of participation in the Plan.
Furthermore, differences in participants' financial situations may cause
federal, state and local tax consequences of participation in the Plan to
vary.
 
  Nonqualified Stock Options; Stock Appreciation Rights; Incentive Stock
Options. Participants will not realize taxable income upon the grant of an
NQSO or SAR. Upon the exercise of an NQSO or SAR, the Employee will recognize
ordinary income (subject to withholding by the Company) in an amount equal to
the excess of (i) the amount of cash and the Fair Market Value on the date of
exercise of the Common Stock received over (ii) the exercise price (if any)
paid therefor. The Employee will generally have a tax basis in any shares of
Common Stock received pursuant to the exercise of a SAR, or pursuant to the
cash exercise of a NQSO, that equals the Fair Market Value of such shares on
the date of exercise. Subject to the discussion under "--Certain Tax Code
Limitations on Deductibility" below, the Company (or a subsidiary) will be
entitled to a deduction for U.S. federal income tax purposes that corresponds
as to timing and amount with the compensation income recognized by the
participant under the foregoing rules.
 
  Employees will not have taxable income upon the grant of an ISO. Upon the
exercise of an ISO, the Employee will not have taxable income, although the
excess of the Fair Market Value of the shares of Common Stock received upon
exercise of the ISO ("ISO Stock") over the exercise price will increase the
alternative minimum taxable income of the Employee, which may cause such
Employee to incur alternative minimum tax. The payment of any alternative
minimum tax attributable to the exercise of an ISO would be allowed as a
credit against the Employee's regular tax liability in a later year to the
extent the Employee's regular tax liability is in excess of the alternative
minimum tax for that year.
 
  Upon the disposition of ISO Stock that has been held for the requisite
holding period (generally, at least two years from the date of grant and one
year from the date of exercise of the ISO), the Employee will generally
recognize capital gain (or loss) equal to the difference between the amount
received in the disposition and the exercise price paid by the Employee for
the ISO Stock. However, if an Employee disposes of ISO Stock that has not been
held for the requisite holding period (a "disqualifying disposition"), the
Employee will recognize ordinary income in the year of the disqualifying
disposition to the extent that the Fair Market Value of the ISO Stock at the
time of exercise of the ISO (or, if less, the amount realized in the case of
an arm's-length disqualifying disposition to an unrelated party) exceeds the
exercise price paid by the Employee for such ISO Stock. The Employee would
also recognize capital gain (or, depending on the holding period, additional
ordinary income) to the extent the amount realized in the disqualifying
disposition exceeds the Fair Market Value of the ISO Stock on the exercise
date. If the exercise price paid for the ISO Stock exceeds the amount realized
in the disqualifying disposition (in the case of an arm's-length disposition
to an unrelated party), such excess would ordinarily constitute a capital
loss.
 
  The Company and its subsidiaries will generally not be entitled to any
federal income tax deduction upon the grant or exercise of an ISO, unless the
Employee makes a disqualifying disposition of the ISO Stock. If an Employee
makes such a disqualifying disposition, the Company (or a subsidiary) will
then, subject to the discussion below under "--Certain Tax Code Limitations on
Deductibility," be entitled to a tax deduction that corresponds as to timing
and amount with the compensation income recognized by the Employee under the
rules described in the preceding paragraph.
 
  Under current rulings, if a participant transfers previously held shares of
Common Stock (other than ISO Stock that has not been held for the requisite
holding period) in satisfaction of part or all of the exercise price of an
NQSO or ISO, the participant will recognize income with respect to the Common
Stock received in the manner described above, but no additional gain will be
recognized as a result of the transfer of such previously
 
                                      15
<PAGE>
 
held shares in satisfaction of the NQSO or ISO exercise price. Moreover, that
number of shares of Common Stock received upon exercise which equals the
number of shares of previously held Common Stock surrendered therefor in
satisfaction of the NQSO or ISO exercise price will have a tax basis that
equals, and a holding period that includes, the tax basis and holding period
of the previously held shares of Common Stock surrendered in satisfaction of
the NQSO or ISO exercise price. Any additional shares of Common Stock received
upon exercise will have a tax basis that equals the amount of cash (if any)
paid by the participant, plus, in the case of a NQSO, the amount of ordinary
income recognized by the Participant with respect to the Common Stock
received.
 
  Awards Payable in Cash; Stock Unit Awards; Restricted Stock Awards. An
Employee will recognize ordinary compensation income upon receipt of cash
pursuant to an award payable in cash or, if earlier, at the time such cash is
otherwise made available for the Employee to draw upon it. An Employee will
not have taxable income upon the grant of an award of Performance Shares, a
Restricted Stock Award or Phantom Stock in the form of units denominated in
Common Stock ("Stock Unit Award") but rather will generally recognize ordinary
compensation income at the time the Employee receives Common Stock or cash in
satisfaction of such Stock Unit Award in an amount equal to the Fair Market
Value of the Common Stock or cash received. In general, a Participant will
recognize ordinary compensation income as a result of the receipt of Common
Stock pursuant to an award of Performance Shares, a Restricted Stock Award or
Performance Award in an amount equal to the Fair Market Value of the Common
Stock when such stock is received; provided, however, that if the stock is not
transferable and is subject to a substantial risk of forfeiture when received,
the Participant will recognize ordinary compensation income in an amount equal
to the Fair Market Value of the Common Stock when it first becomes
transferable or is no longer subject to a substantial risk of forfeiture,
unless the Participant makes an election to be taxed on the Fair Market Value
of the Common Stock when such stock is received.
 
  An Employee will be subject to withholding for federal, and generally for
state and local, income taxes at the time the Employee recognizes income under
the rules described above with respect to Common Stock or cash received
pursuant to a Cash Award, Performance Award, Restricted Stock Award or Stock
Unit Award. Dividends that are received by a Participant prior to the time
that the Common Stock is taxed to the Participant under the rules described in
the preceding paragraph are taxed as additional compensation, not as dividend
income. The tax basis of a Participant in the Common Stock received will equal
the amount recognized by the Employee as compensation income under the rules
described in the preceding paragraph, and the Employee's holding period in
such shares will commence on the date income is so recognized.
 
  Subject to the discussion under "--Certain Tax Code Limitations on
Deductibility" below, the Company (or a subsidiary) will be entitled to a
deduction for U.S. federal income tax purposes that corresponds as to timing
and amount with the compensation income recognized by the Participant under
the foregoing rules.
 
  Certain Tax Code Limitations on Deductibility. In order for the amounts
described above to be deductible by the Company (or a subsidiary), such
amounts must constitute reasonable compensation for services rendered or to be
rendered and must be ordinary and necessary business expenses. The ability of
the Company (or a subsidiary) to obtain a deduction for future payments under
the Plan could also be limited by Section 280G of the Code, which provides
that certain excess parachute payments made in connection with a change in
control of an employer are not deductible. The ability of the Company (or a
subsidiary) to obtain a deduction for amounts paid under the Plan could be
affected by Section 162(m) of the Code, which limits the deductibility, for
U.S. federal income tax purposes, of compensation paid to certain employees of
the Company to $1 million with respect to any such employee during any taxable
year of the Company. However, certain exceptions apply to this limitation in
the case of performance-based compensation. It is intended that the approval
of the Plan by the stockholders of the Company and the description of the Plan
contained in this Proxy will satisfy certain of the requirements for the
performance-based exception and the Company will be able to comply with the
requirements of the Code and Treasury Regulation Section 1.162-27 with respect
to the grant and payment of certain performance-based awards (including
certain options and SARs) so as to be eligible for the performance-based
exception. However, it may not be desirable in all cases to satisfy all of the
requirements for the exception and the Company may, in its sole discretion,
determine that in one or more cases it is in its best interests to not satisfy
the requirements for the performance-based exception.
 
                                      16
<PAGE>
 
  The proposal will be approved if it receives approval by the holders of a
majority of the outstanding shares of Common Stock present, or represented,
and entitled to vote at the meeting, provided that the total votes cast must
also exceed fifty percent of the shares of Common Stock outstanding and
entitled to vote on the matter.
 
  The Board of Directors recommends a vote FOR the adoption of the Lyondell
Chemical Company 1999 Long-Term Incentive Plan. Properly dated and signed
proxies will be so voted unless stockholders specify otherwise.
 
                                      17
<PAGE>
 
                             EXECUTIVE COMPENSATION
 
  The following table sets forth information as to the Chief Executive Officer
during 1998 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
                                                       Compensation   Awards    Payouts  Compensation
Name and Principal Position  Year Salary ($) Bonus ($)    ($)(a)      ($)(b)    ($)(c)      ($)(d)
- ---------------------------  ---- ---------- --------- ------------ ---------- --------- ------------
<S>                          <C>  <C>        <C>       <C>          <C>        <C>       <C>
Dan F. Smith...............  1998  804,000   1,094,000     8,516    1,094,000        -0-    87,578
President &                  1997  651,734     548,900    11,360      277,325  5,079,354    85,712
Chief Executive Officer      1996  490,886     241,932    11,026      370,813    221,613    61,556
 
Jeffrey R. Pendergraft.....  1998  350,468     327,000    26,358      326,995        -0-    50,536
Executive Vice President     1997  282,556     182,967    14,129       96,514  1,721,777    45,178
and Chief Administrative
 Officer                     1996  255,000      90,725    14,707      139,055     83,127    40,845
 
Morris Gelb(e).............  1998  142,464     179,900     3,029      706,440        -0-    22,984
Executive Vice President     1997       --          --        --           --         --        --
and Chief Operating Officer  1996       --          --        --           --         --        --
 
Debra L. Starnes(f)........  1998  297,356     201,000    21,693      200,996        -0-    43,046
Senior Vice President,       1997  270,598     182,967    16,310       96,514  1,721,777    42,686
Intermediate Chemicals       1996  214,200      90,725    15,444      139,055     83,127    39,109
 
Joseph M. Putz(g)..........  1998  259,284     155,000    30,733      154,997        -0-    42,997
Senior Vice President,       1997  211,084     154,837    22,061      154,837  1,042,455    30,215
Special Assignments          1996  189,720      49,867    15,889       49,867     83,433    25,946
</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) Messrs. Smith, Pendergraft and Putz and Ms. Starnes received restricted
    stock awards under the Lyondell Chemical Company Restricted Stock Plan (the
    "Restricted Stock Plan") as of March 4, 1999, in connection with their
    annual bonus for 1998. The valuations of such restricted stock awards in
    the table were calculated using a per share price of $14 1/4, the fair
    market value of the Company's Common Stock on the date of grant. Mr. Gelb
    was awarded 25,230 shares of restricted stock under the Restricted Stock
    Plan as a relocation bonus on July 24, 1998. The value of Mr. Gelb's award
    at December 31, 1998, based on the stock's closing price, was $454,140.
    None of the other named executive officers held any restricted stock at
    December 31, 1998. With the exception of Mr. Gelb's award, all of the
    restricted stock awarded to named executive officers with respect to 1998
    vests annually in three equal installments beginning on the first
    anniversary of the date of grant. Mr. Gelb's restricted stock award also
    vests in three equal installments. The vesting of the first third occurred
    on December 15, 1998, and the remaining two installments will vest on the
    second and third anniversary of the grant date. The restricted stock awards
    in the table for 1997 and 1996 were made pursuant to the Value Share Plan,
    which was terminated in 1997, at which time all unvested outstanding
    restricted stock became vested. The dollar value included in the table
    reflects the valuation at the time of the award. The named executive
    officers receive the dividends on shares of restricted stock at the same
    rate as all other stockholders.
(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 (as defined herein), together with
    payments made in December 1997 in accordance with the termination of the
    Value Share Plan. Amounts shown in the Long-Term Incentive Payouts column
    for 1996 represent payment of the associated
 
                                       18
<PAGE>
 
   cash portion under the Value Share Plan that was paid in December 1997 in
   connection with the vesting of such executive officers' restricted stock.
   Executive officers also accrued dividend share credits in each of 1998, 1997
   and 1996 for their outstanding options. 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 and (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 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 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 1998, 1997 and 1996, respectively, is as follows: Mr.
   Smith: 7,868, 1,399 and 1,233; Mr. Pendergraft: 14,441, 2,273 and 2,125; Ms.
   Starnes: 9,081, 1,455 and 1,358; Mr. Putz: 6,792, 278 and 290. Mr. Gelb did
   not hold any options during 1998 and accordingly he did not accrue any
   dividend share credits.
(d) Includes contributions to the Executive Supplementary Savings Plan,
    incremental executive medical plan premiums, financial counseling
    reimbursements, certain amounts in respect to the Executive Life Insurance
    Plan and the Optional Life Insurance Plan, in the case of each of Ms.
    Starnes and Mr. Putz, also includes such amounts with respect to the
    portion of 1998 during which they served as officers of Equistar, and, in
    the case of Mr. Gelb, also includes certain amounts paid under comparable
    ARCO Chemical plans, as follows:
 
<TABLE>
<CAPTION>
                             Year Mr. Smith Mr. Pendergraft Mr. Gelb Ms. Starnes Mr. Putz
                             ---- --------- --------------- -------- ----------- --------
   <S>                       <C>  <C>       <C>             <C>      <C>         <C>
   Executive Supplementary
    Savings Plan...........  1998  $64,320      $28,037      $8,038    $23,788   $20,743
   Incremental Medical Plan
    Premiums...............  1998  $ 8,441      $ 8,441      $4,983    $ 8,441   $ 8,441
   Financial Counseling
    Reimbursement..........  1998  $   -0-      $ 8,968      $2,500    $ 7,107   $ 7,107
   Executive and Optional
    Life Insurance Plans...  1998  $14,817      $ 5,090      $7,463    $ 3,710   $ 6,706
</TABLE>
(e) Mr. Gelb began serving as the Company's Executive Vice President and Chief
    Operating Officer in December 1998. From July 1998 through December 1998,
    Mr. Gelb served as Senior Vice President, Manufacturing, Process
    Development and Engineering. Prior thereto, Mr. Gelb served as an officer
    of ARCO Chemical, which was acquired by Lyondell in July 1998. The summary
    compensation information presented above includes compensation paid to Mr.
    Gelb by such subsidiary of Lyondell subsequent to the acquisition date. Mr.
    Gelb's 1998 Lyondell bonus was an amount based on his ARCO Chemical bonus
    target for 1998. The bonus amount in the table represents the pro-rata
    portion of such target bonus, which was paid to Mr. Gelb by the Company for
    the last five months of 1998.
(f) Ms. Starnes has served as Senior Vice President, Intermediate Chemicals
    since July 1998. From December 1, 1997, through June 1998, she served as
    Senior Vice President, Polymers, of Equistar. Prior thereto, Ms. Starnes
    served as Senior Vice President, Petrochemicals, of the Company. The
    summary compensation information presented above includes compensation paid
    to Ms. Starnes by the Company and Equistar in each of the foregoing
    capacities.
(g) Mr. Putz has served as Senior Vice President, Special Assignments since
    July 1998. From December 1, 1997, through June 1998, he served as Senior
    Vice President, Finance and Administration, of Equistar. Prior thereto, Mr.
    Putz served as Vice President, Control and Administration of the Company.
    The summary compensation information presented above includes compensation
    paid to Mr. Putz by the Company and Equistar in each of the foregoing
    capacities.
 
                                       19
<PAGE>
 
            PAY AND PERFORMANCE PLANS AND LONG-TERM INCENTIVE PLANS
 
1998 Bonus Awards
 
  For 1998, Lyondell executives (other than those executives, including Mr.
Gelb, who were executives of ARCO Chemical prior to its acquisition by
Lyondell) participated in the 1998 executive incentive plan (the "1998
Incentive Plan"). The 1998 Incentive Plan was designed to focus participants
on key measures of value creation for the Company's shareholders and on
operating measures that lead to the creation of value, encourage a long-term
management perspective, reward for sustained long-term performance; and
encourage significant ownership of Company stock.
 
  Pursuant to the 1998 Incentive Plan, financial measures were established,
based fifty percent on Lyondell's Market Value Added ("MVA"), twenty-five
percent on Lyondell's Economic Value Added ("EVA") and twenty-five percent on
certain operating targets. MVA measures changes in the market value of the
Company's equity based on average share price for the year, plus dividends as
if they had been reinvested in the Company's stock. EVA measures the Company's
cash flow performance (which exceeds the cost of capital) and is calculated by
multiplying the capital invested in the Company by the Company's weighted
average cost of capital. The operating targets focus on critical benchmarks
related to such items as attainment of synergies with Equistar, attainment of
cost savings for Lyondell-CITGO Refining LP, and selected financial results.
The Compensation Committee established an objective formula for determining
the resulting Performance Percentage corresponding with attained levels of
performance under these financial measures.
 
  The Compensation Committee assigned each participant a Target Bonus
Percentage of base salary commensurate with his or her position and other
considerations the Compensation Committee deemed appropriate. Based on
attainment of the established financial targets, the Compensation Committee
determined the Performance Percentage for 1998 performance. Each participant's
award was determined by multiplying the (a) participant's base salary for 1998
by (b) the Target Bonus Percentage, by (c) the Performance Percentage.
 
  Awards paid under the 1998 Incentive Plan have an up-front cash portion,
which amounts are included under the "Bonus" heading in the Summary
Compensation Table, as well as a long-term portion. The long-term portion
consists 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 restricted stock awards were made pursuant to the Restricted
Stock Plan.
 
1998 Incentive Plan--Awards in Last Fiscal Year
 
<TABLE>
<CAPTION>
                                                                    Period Until
                                                          Number     Maturation
      Name                                             of Shares(a)  or Payout
      ----                                             ------------ ------------
      <S>                                              <C>          <C>
      Mr. Smith.......................................    76,772        (b)
      Mr. Pendergraft.................................    22,947        (b)
      Mr. Gelb........................................        --        (b)
      Ms. Starnes.....................................    14,105        (b)
      Mr. Putz........................................    10,877        (b)
</TABLE>
- --------
(a) Represents the number of shares of Common Stock as to which the deferred
    cash portion of the awards made under the 1998 Incentive Plan is
    equivalent.
(b) These awards vest in annual one-third increments, beginning on December
    15, 2000.
 
Restricted Stock Plan
 
  The Restricted Stock Plan was approved by the stockholders in 1995. The
purpose of the Restricted Stock Plan is to provide executive officers and
other key employees with a proprietary interest in the Company's success and
progress by granting them shares of Common Stock. It is intended to further
align the interests of
 
                                      20
<PAGE>
 
such employees with the interests of the stockholders in terms of both risk
and reward and to strengthen the Company's ability to continue to attract and
retain highly qualified employees.
 
  Subject to the express provisions of the Restricted Stock Plan, the
Compensation Committee has the authority to select eligible executive officers
for participation in the Restricted Stock Plan and to determine all of the
terms and conditions of grants and awards. The Chief Executive Officer has
authority to select eligible non-officer key employees of the Company for
participation in the Restricted Stock Plan. The Compensation Committee also
has authority to prescribe rules and regulations for administering the
Restricted Stock Plan and to decide questions of interpretation of any
provision of the Restricted Stock Plan.
 
  Under the Restricted Stock Plan, fixed awards are made in the form of shares
of Common Stock that are issued to the employee but that are forfeitable and
subject to restrictions on transfer. Vesting of Restricted Stock awards is not
contingent on the achievement of specific objectives, but is contingent on the
participant's continuing in the Company's employ for a period specified in the
award. The restricted period will begin on the date of the grant and will
continue for a period of time determined on the date of grant.
 
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 eighty percent of the
estimated award otherwise payable to such participant in 1999 for 1998; sixty
percent of the estimated award payable to such participant in 2000 for 1999;
forty percent of the estimated award payable to such participant in 2001 for
2000; and twenty percent 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 stockholder 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 percent of Average EVA and 1.25
percent of MVA. 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 million 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
 
                                      21
<PAGE>
 
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.
 
Executive Long-Term Incentive Plan
 
  Prior to its replacement by the Value Share Plan, the Company's Executive
Long-Term Incentive 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. No performance units
are currently outstanding. Commencing in 1995, no additional grants of stock
options or performance units were 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 1998. 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, 1998. 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 1998
                       and Fiscal Year-End Option Values
 
<TABLE>
<CAPTION>
                              Number of Securities
                             Underlying Unexercised     Value of Unexercised
                                Options at Fiscal      In-The-Money Options at
                                  Year-End (#)        Fiscal Year-End ($)(a)(b)
                            ------------------------- -------------------------
              Name          Exercisable Unexercisable Exercisable Unexercisable
              ----          ----------- ------------- ----------- -------------
      <S>                   <C>         <C>           <C>         <C>
      Mr. Smith............   32,200         -0-         $-0-          -0-
      Mr. Pendergraft......   50,600         -0-         $-0-          -0-
      Mr. Gelb(c)..........       --          --           --           --
      Ms. Starnes..........   32,500         -0-         $-0-          -0-
      Mr. Putz.............   25,600         -0-         $-0-          -0-
</TABLE>
- --------
(a) The last reported closing sales price, as reported on the NYSE, of
    Lyondell Common Stock on December 31, 1998, was $18.00 per share. On
    December 31, 1998, none of the options held by the named executive
    officers was in-the-money.
(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, 1998, 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.......................................    $-0-         $-0-
      Mr. Pendergraft.................................    $-0-         $-0-
      Mr. Gelb........................................      --           --
      Ms. Starnes.....................................    $-0-         $-0-
      Mr. Putz........................................    $-0-         $-0-
</TABLE>
 
(c) The Company has not issued stock options to Mr. Gelb.
 
                                      22
<PAGE>
 
Equistar Long-Term Incentive Plan
 
  Ms. Starnes and Mr. Putz are entitled to awards under Equistar's long-term
incentive plan. Awards are based on whether Equistar reaches performance and
financial levels in two critical areas: economic value added ("Equistar EVA")
and the achievement of synergies. Equistar EVA measures Equistar's cash flow
performance in excess of a capital charge, which is calculated by multiplying
the capital invested in Equistar by Equistar's weighted average cost of
capital. Synergies include both one-time and on-going potential savings from
operating the businesses contributed by each of Equistar's owners.
 
  Equistar assigns a target award percentage to each plan participant based
primarily on the participant's salary and position. The target award
percentage is multiplied by a multiple (based on Equistar's achievement of
Equistar EVA and synergy goals) that is determined by Equistar's Partnership
Governance Committee, the product of which is multiplied by the participant's
base pay. Awards consist of a combination of current cash and deferred cash
compensation. For 1998, the annual cash portion of the awards paid to Ms.
Starnes and Mr. Putz was $105,000 and $91,000, respectively, which amounts are
included under the "Bonus" heading in the Summary Compensation Table. The
deferred component of the awards for Ms. Starnes and Mr. Putz (which would
otherwise be cash paid out over a three-year period, subject to certain
adjustments) was converted into long-term awards under the Lyondell 1998
Incentive Plan. Accordingly such deferred awards are reflected as a portion of
their restricted stock awards included in the Summary Compensation Table and
of their 1998 Incentive Plan Awards described under "1998 Incentive Plan--
Awards in Last Fiscal Year."
 
                                      23
<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, 1999, under
the provisions of the Lyondell Retirement Plan and the Supplementary Executive
Retirement Plan (together, the "Lyondell Retirement Plan").
 
                             Pension Plan Table(a)
 
<TABLE>
<CAPTION>
  Average Final Earnings (Base       Approximate Annual Benefit for Years of
Salary Plus Annual Bonus) Highest     Membership Service Indicated(c)(d)(e)
 Three Consecutive Years out of    --------------------------------------------
        Last Ten Years(b)          15 Years 20 Years 25 Years 30 Years 35 Years
- ---------------------------------  -------- -------- -------- -------- --------
<S>                                <C>      <C>      <C>      <C>      <C>
$1,400,000.......................  $322,169 $429,558 $536,948 $644,338 $751,727
 1,300,000.......................  $299,069 $398,758 $498,448 $598,138 $697,827
 1,200,000.......................  $275,969 $367,958 $459,948 $551,938 $643,927
 1,100,000.......................  $252,869 $337,158 $421,448 $505,738 $590,027
 1,000,000.......................  $229,769 $306,358 $382,948 $459,538 $536,127
   900,000.......................  $206,669 $275,558 $344,448 $413,338 $482,227
   800,000.......................  $183,569 $244,758 $305,948 $367,138 $428,327
   700,000.......................  $160,469 $213,958 $267,448 $320,938 $374,427
   600,000.......................  $137,369 $183,158 $228,948 $274,738 $320,527
   500,000.......................  $114,269 $152,358 $190,448 $228,538 $266,627
   400,000.......................  $ 91,169 $121,558 $151,948 $182,338 $212,727
   300,000.......................  $ 68,069 $ 90,758 $113,448 $136,138 $158,827
   200,000.......................  $ 44,969 $ 59,958 $ 74,948 $ 89,938 $104,927
</TABLE>
- --------
(a) Ms. Starnes and Mr. Putz were participants in Equistar's pension plan as a
    result of their one year of employment with Equistar. Benefits under the
    Equistar pension plan are calculated by multiplying the participant's
    years of service with Equistar by their final average earnings, the
    product of which is multiplied by a benefit percentage which is based on
    the age at which the participant begins to receive benefits. The estimated
    annual benefit payable to Ms. Starnes and Mr. Putz, assuming retirement at
    age 65, is $7,191 and $5,139, respectively. Ms. Starnes and Mr. Putz are
    participants in Equistar's Supplemental Executive Retirement Plan
    ("Equistar SERP"). Calculation of benefits under the Equistar SERP is
    based on the participant's base wage, salary deferrals and annual
    incentive awards. The Equistar SERP provides for two types of
    supplementary benefits: deferral/incentive supplements and qualification
    limitation supplements. The estimated annual benefit payable to Ms.
    Starnes and Mr. Putz, assuming retirement at age 65, is $4,977 and $2,925,
    respectively.
    Mr. Gelb is not a participant in the Lyondell Retirement Plan, but does
    participate in the ARCO Chemical Company Retirement Plan, which provides for
    benefits similar to those of the Lyondell Retirement Plan. Mr. Gelb also
    participates in the Lyondell Supplementary Executive Retirement Plan. The
    approximate annual benefits under the ARCO Chemical Retirement Plan do not
    differ significantly from those set forth in the table above with respect to
    the Lyondell Retirement Plan.
(b) The covered compensation for which retirement benefits are computed is the
    average of the participant's highest three consecutive years out of the
    last ten years of base salary plus annual bonus. Base salary and annual
    bonus amounts are set forth under the "Salary" and "Bonus" headings in the
    Summary Compensation Table.
(c) 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, 1999, 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, 1998, 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.
(d) As of December 31, 1998, the credited years of service (rounded to the
    nearest whole number) under the Lyondell Retirement Plan (or in the case
    of Mr. Gelb, under the ARCO Chemical Company Retirement Plan) for the
    named executive officers were: Mr. Smith, 24; Mr. Pendergraft, 26; Mr.
    Gelb, 29; Ms. Starnes, 23; and Mr. Putz, 32.
(e) 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.
 
                                      24
<PAGE>
 
                       EXECUTIVE SEVERANCE ARRANGEMENTS
 
  Certain employees (including Mr. Gelb and other executive officers) who are
former employees of ARCO Chemical are participants in the ARCO Chemical
Company Change of Control Plan (the "ACC Change of Control Plan"). The
Company's acquisition of ARCO Chemical in July 1998 was a change of control as
defined in such plan.
 
  Under the ACC Change of Control Plan, if an eligible employee is terminated
by the Company without cause or by the employee for good reason (which
includes certain "constructive" terminations) within two years following the
change of control, the employee will be entitled to receive one times to three
times pay, depending upon the employee's grade level. The definition of good
reason varies depending on the employee's grade level within the Company.
Severance payments are paid based upon length of service for employees who
were not executives or key managers of ARCO Chemical. As a former executive of
ARCO Chemical, Mr. Gelb would receive a payment equal to three times the sum
of his current base salary plus the greater of (i) the average of his bonuses
for the three years prior to termination or (ii) his target bonus for the year
in which the termination occurs. Former ARCO Chemical employees will receive
additional specified coverage under the Company's medical, dental and life
insurance plans, depending on the employee's grade level. Mr. Gelb will
receive 36 months of coverage. Mr. Gelb will also receive a gross-up payment
from the Company for the amount of the excise tax liability, if any, imposed
pursuant to Code Section 4999 with respect to any benefits paid in connection
with the change of control; however, due to the nature of the Company's
acquisition of ARCO Chemical, the Company does not believe that any payments
made pursuant to the ACC Change of Control Plan will result in excise tax
liability under Code Section 4999.
 
  On March 15, 1999, the Compensation Committee adopted the Lyondell Chemical
Company Executive Severance Pay Plan (the "Severance Plan"), which generally
applies to all executive officers of the Company, including Mr. Smith, Mr.
Pendergraft and Ms. Starnes, and certain other key members of management that
are designated by the Chief Executive Officer. Mr. Gelb is not eligible to
participate in the Severance Plan because no employee currently eligible for a
severance benefit under a plan or agreement established by ARCO Chemical is
eligible to participate. At the expiration of the ACC Change of Control Plan
in July 2000, Mr. Gelb and the other former ARCO Chemical executives will
automatically be covered under the Severance Plan. Mr. Putz is not currently
eligible to participate in the Severance Plan because he is eligible to
receive a severance benefit under an agreement between him and the Company as
described below. The Severance Plan provides for the payment of certain
benefits to covered employees upon certain terminations following a Change in
Control of the Company. Under the Severance Plan, a "Change in Control" of the
Company means any one of the following events: (i) the incumbent directors of
the Company (directors as of February 1, 1999 or individuals recommended or
approved by a majority of the then incumbent directors other than as a result
of either an actual or threatened election contest) cease to constitute at
least a majority of the Company's Board of Directors, (ii) the stockholders
approve (A) a merger, consolidation, or recapitalization of the Company, or a
sale of substantially all the Company's assets, unless immediately after the
consummation of the transaction, the shareholders of the Company immediately
prior to the transaction would own eighty percent or more of the resulting
entity, or the incumbent directors at the time of initial approval of the
transaction would, immediately after the transaction, constitute a majority of
the Board of Directors or similar managing group of such resulting entity, or
(B) any plan for the liquidation or dissolution of the Company, (iii) any
person shall become the beneficial owner of twenty percent or more of the
outstanding Common Stock or combined voting power of all voting securities of
the Company, unless such person reaches twenty percent ownership solely as a
result of (A) the Company acquiring securities and correspondingly reducing
the number of shares outstanding or (B) acquisition of securities directly
from the Company except for any conversion of a security that was not acquired
directly from the Company, provided that if a person referred to in subsection
(iii)(A) or (B) shall thereafter become the beneficial owner of any additional
shares of Common Stock or other voting securities (other than by stock split,
stock dividend or similar transaction), then a Change in Control will be
deemed to have occurred.
 
  If an employee covered under the Severance Plan is terminated by the Company
without cause or by the employee for good reason (which includes certain
"constructive" terminations) within two years following a Change in Control,
the employee will be entitled to receive a payment equal to one times to three
times annual
 
                                      25
<PAGE>
 
earnings, depending on the employee's position in the Company. Annual earnings
for this purpose is generally the sum of an employee's base pay plus target
annual bonus. Mr. Smith and Mr. Pendergraft will receive a payment equal to
three times their respective annual earnings, and Ms. Starnes will receive a
payment equal to two times her annual earnings. Outstanding option awards to
covered employees will be automatically vested. Covered employees will also
receive: (i) eligibility to commence vested early retirement benefits under
the Company's retirement plans, actuarially reduced for early commencement,
and retiree medical coverage; (ii) continuation of welfare benefit coverages
for a period of two years following termination; and (iii) outplacement
services for a period of one year, at a cost not to exceed $40,000. In
addition, covered employees will receive a gross-up payment from the Company
for the amount of the excise tax liability, if any, imposed pursuant to Code
Section 4999 with respect to any benefits paid in connection with the Change
in Control. In order to receive benefits under the Severance Plan, a covered
employee must sign a general release of claims against the Company and its
affiliates. Upon a Change in Control, the Company will also deposit into the
Company's Supplemental Executive Benefit Plans Trust any additional assets
necessary to fully fund the benefits due under the Supplementary Executive
Retirement Plan and the Executive Deferral Plan. The Severance Plan may be
amended or terminated at any time prior to a Change in Control or, if earlier,
prior to the date that a third party submits a proposal to the Board of
Directors that is reasonably calculated, in the judgment of the Compensation
Committee, to effect a Change in Control. The Severance Plan may not be
amended to deprive a covered employee of benefits after a Change in Control.
 
  Under the Severance Agreement with Mr. Putz, and in exchange for release of
liability, he is entitled to certain benefits if, during the term of such
agreement, he is involuntarily terminated or he elects to terminate for good
reason (which includes certain "constructive" terminations), or he terminates
due to death, disability or upon his contemplated retirement at December 31,
1999. Mr. Putz in such event, is entitled to receive (i) a payment equal to
three times his annual earnings, which for this purpose is generally the sum
of his base salary plus three-year average cash bonus paid; (ii) the immediate
vesting of all unvested stock options; (iii) an additional five years of age
and service credit under the Company's supplementary executive retirement
plan; (iv) a payment of all contributions and earnings accrued or credited to
his deferred compensation account; (v) two-thirds of an amount that is equal
to an income tax gross-up payment on the amount of contributions plus earnings
accrued or credited to such deferred compensation account as of September 1,
1996, for the payment of any federal, state, local or employment taxes
incurred; (vi) continuation of medical and welfare benefit coverages for a
period of two years following termination; (vii) financial counseling for a
period of one year following termination; and (viii) outplacement services for
a period of one year at a cost not to exceed $40,000. In addition, Mr. Putz
will receive, if applicable, a gross-up payment from the Company for the
amount of the excise tax liability, if any, imposed pursuant to Code Section
4999 with respect to any benefits paid pursuant to the agreement. The
agreement remains in effect until January 1, 2000.
 
                                      26
<PAGE>
 
                               PERFORMANCE GRAPH
 
  The graph below compares the cumulative total return to stockholders of the
Company for a five-year period (December 31, 1993 to December 31, 1998) with
the cumulative total return to stockholders of the S&P 500 Stock Index and a
group of 9 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,
Inc.; Crown Central Petroleum Corporation; Eastman Chemical; The Geon Company;
Georgia Gulf Corporation; Methanex Corporation; Sun Company, Inc.; Union
Carbide Corporation and Valero Energy Corporation. In 1998, FINA, Inc. and
Nova Corporation of Alberta, formerly members of the Peer Group, ceased to be
publicly traded and were therefore eliminated from the Peer Group.
 
 
 
                             [CHART APPEARS HERE]
 
<TABLE>
<CAPTION>
                                  1993    1994    1995    1996    1997    1998
                                 ------- ------- ------- ------- ------- -------
<S>                              <C>     <C>     <C>     <C>     <C>     <C>
LYONDELL........................ $100.00 $126.09 $115.51 $115.90 $144.15 $101.09
S&P 500......................... $100.00 $101.32 $139.40 $171.40 $228.59 $293.91
PEER GROUP(a)................... $100.00 $117.93 $127.96 $144.37 $173.00 $141.17
</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 the
     reinvestment of dividends. None of the Peer Companies constituted more
     than twenty percent of the market capitalization of the entire Peer Group
     in 1998.
 
  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.
 
                                      27
<PAGE>
 
                           LYONDELL CHEMICAL COMPANY
                      1999 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 composed
of three non-employee directors: Mr. Stephen F. Hinchliffe, Jr., Chairman, Dr.
William T. Butler and Mr. Travis Engen.
 
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 fiftieth percentile of the market according to
nationally recognized surveys for industrial and chemical companies. The
market data used are reflective of the Company's size, as measured by
revenues.
 
  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 these 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 1998, base salaries for most executive officers were
increased four percent.
 
1998 Executive Incentive Plan
 
  For 1998, Lyondell executives participated in the 1998 Executive Incentive
Plan. The Incentive Plan was designed to focus participants on key measures of
value creation for the Company's shareholders and on operating measures that
lead to the creation of value; encourage a long-term management perspective;
reward sustained long-term performance; and encourage significant ownership of
Company stock.
 
  Pursuant to the Incentive Plan, financial measures were established, based
fifty percent on Lyondell's Market Value Added (MVA), twenty-five percent on
Lyondell's Economic Value Added (EVA), and twenty-five percent on certain
operating targets. MVA measures changes in the market value of the Company's
equity based
 
                                      28
<PAGE>
 
on average share price for the year, plus dividends as if they had been
reinvested in the Company's stock. EVA measures the Company's cash flow
performance (that exceeds the cost of capital) and is calculated by
multiplying the capital invested in the Company by the Company's weighted
average cost of capital. The operating targets focus on critical benchmarks
related to such items as attainment of synergies with Equistar, attainment of
cost savings for Lyondell-CITGO Refining, and selected financial results. The
Committee established an objective formula for determining the resulting
Performance Percentage corresponding with attained levels of performance under
these financial measures.
 
  The Committee assigned each participant a Target Bonus Percentage of base
salary commensurate with his or her position and other considerations the
Committee deemed appropriate. Based on attainment of the established financial
targets, the Committee determined the Performance Percentage for 1998
performance. Each participant's award was determined by multiplying (a) the
participant's base salary for 1998, by (b) the Target Bonus Percentage, by (c)
the Performance Percentage.
 
  Awards paid under this plan have an up front cash portion, as well as a
long-term portion. The long-term portion consists 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 were
paid out of the Company's Restricted Stock Plan, which plan was approved by
the shareholders in 1995.
 
  In addition, special restricted stock grants were provided to several new
Lyondell executive officers who were formerly with ARCO Chemical Company.
These restricted stock awards and accompanying grants of deferred cash were
designed to induce these individuals to join Lyondell and had an initial
dollar value equivalent to the cash portion of the severance payment each
would have received under the ARCO Chemical Company Change of Control Plan.
 
1999 Long-Term Incentive Plan
 
  In late 1998, the Committee approved a new executive incentive compensation
program for the Company, subject to shareholder approval. Under this program,
incentive compensation opportunities for 1999 will be delivered in three
forms:
 
  . An executive Annual Incentive Plan, which rewards management for EVA
    performance and performance on selected business and operating
    objectives.
 
  . Stock options, granted at 100 percent of fair market value, having a term
    of ten years and vesting at a rate of one-third per year over three
    years, with accelerated vesting if the stock price increases 100 percent.
    The stock option awards are intended to incentivize participants to
    increase the Company's share price over time.
 
  . A performance share arrangement, under which executives earn a
    predetermined number of shares of Lyondell stock based on the Company's
    cumulative total shareholder return (stock price growth plus reinvested
    dividends) relative to an industry group comprising peer chemical
    companies. This plan is intended to incentivize participants to improve
    Lyondell's total shareholder return performance compared to comparable
    companies in the chemical industry.
 
  This Proxy Statement contains a copy of the proposed Long-Term Incentive
Plan for shareholder approval. If approved, this plan will provide the
Committee with sufficient incentive tools to provide long-term incentive
compensation that is closely tied to the creation of shareholder value. The
proposed plan allows for the Committee to make long-term incentive awards in
the form of stock options, restricted stock, performance shares, phantom stock
or stock appreciation rights, and to make cash bonus payments. Consequently,
the Committee made grants of stock options and performance shares under the
new plan to executive officers, and approved performance objectives for cash
awards, in January 1999. These grants are contingent upon shareholder approval
of the new 1999 Long-Term Incentive Plan. These contingent stock option and
performance share grants are described in the introduction to the proposed
1999 Long-Term Incentive Plan contained in this Proxy Statement.
 
                                      29
<PAGE>
 
As previously described, the Committee intends to rely on stock options and
performance shares as its primary long-term incentive vehicles in 1999.
 
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
      Position                                                       to be Owned
      --------                                                       -----------
      <S>                                                            <C>
      Chief Executive Officer.......................................   110,000
      Executive Vice President......................................    50,000
      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 1998 Pay
 
  In April, 1998, Mr. Smith's base salary was raised from $780,000 to
$811,200. This increase of four percent was based on the median rate of
increase in base salaries for executives in the marketplace, as determined
from published compensation surveys.
 
  In March 1999, Mr. Smith received an incentive award under the Company's
1998 Executive Incentive Plan. This award was paid thirty-three percent in
current cash and sixty-seven percent in the form of restricted stock and
deferred cash. The Committee believes that this award was appropriate given
the Company's achievements in creating value, as measured by EVA, MVA,
operating performance, as well as its financial and strategic success,
particularly his key role in the successful negotiation and completion of the
ARCO Chemical Company acquisition.
 
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 compensation for deductibility, but retains
the discretion to pay non-deductible amounts if that would be in the best
interests of the Company and shareholders. Certain amounts paid to the
Company's Chief Executive Officer for 1998 under the Executive Incentive Plan
were not deductible.
 
Compensation Committee Members
 
  The Compensation Committee 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
Travis Engen
 
The Compensation Committee
 
                                      30
<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 1998, 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 ("Restricted Shares"))
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 and Responsibility Committees each
received $7,500. The non-employee Chairman of the Board received an additional
$40,000, of which $10,000 was in the form of Restricted Shares.
 
Restricted Stock Grants
 
  The Company believes paying a portion of the directors' compensation in
stock further aligns the directors' interests with the stockholders' interests
and accordingly, has adopted stock ownership guidelines for its Non-Employee
Directors. Restricted Shares were granted as part of the annual retainer for
1999 and were valued at approximately $10,000 (and 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 Chemical 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 fifty 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 or she 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.
 
  In October 1998, the Board of Directors amended and restated the Directors'
Retirement Plan to close such plan to new directors, and give those directors
covered under the Plan the option of continuing to accrue benefits under the
Plan; retaining their existing benefits, as of December 31, 1998; or electing
to receive a payment equal to the present value of their benefits under the
Plan in the form of deferred compensation or Restricted Shares. Directors who
do not continue to accrue benefits under the Directors' Retirement Plan will
receive, in lieu of such a benefit, an annual award of Restricted Shares
valued at $25,000.
 
Deferral Plan for Non-Employee Directors
 
  The Lyondell Chemical 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
 
                                      31
<PAGE>
 
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 1998 was 8.9 percent.
 
                                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 2000 ANNUAL MEETING
                           AND DIRECTOR NOMINATIONS
 
  Stockholder proposals intended to be presented at the 2000 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 2, 1999, 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 2000 Annual Meeting is scheduled
to take place in May 2000.
 
  Pursuant to the By-Laws of the Company, a stockholder wishing to nominate a
candidate for election to the Board or bring a proposal before the 2000 Annual
Meeting is required to give written notice to the Secretary of the Company of
his or her intention to make such a nomination or present such a proposal. The
notice of intent to make a nomination or present a proposal at the 2000 Annual
Meeting 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 News 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 is required to contain certain
information about both the nominee or proposal, as applicable, and the
stockholder making the nomination or proposal. A nomination or proposal that
does not comply with the above procedures will be disregarded. Compliance with
the above procedures does not require the Company to include the proposed
nominee or proposal 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.
 
                                      32
<PAGE>
 
                                                                      EXHIBIT A
 
                           LYONDELL CHEMICAL COMPANY
                         1999 LONG-TERM INCENTIVE PLAN
 
  1. Objectives. This Lyondell Chemical Company 1999 Incentive Plan (the
"Plan") is intended to:
 
    . Focus Participants on key measures of value creation for the Company's
  shareholders
 
    . Provide significant upside and downside award potential commensurate
  with shareholder value creation
 
    . Encourage a long-term management perspective and reward for sustained
  long-term performance
 
    . Enhance the ability of Lyondell to attract and retain highly talented
  and competent individuals
 
    . Reinforce a team orientation among top management
 
    . Encourage ownership of the Company's stock among top management
 
  2. Definitions. As used herein, the terms set forth below shall have the
following respective meanings:
 
    "Award" means any Option, Performance Shares, Restricted Stock, Phantom
  Stock, Cash Award or Stock Appreciation Right, whether granted singly, in
  combination or in tandem, granted to a Participant pursuant to any
  applicable terms, conditions and limitations as the Committee may establish
  in order to fulfill the objectives of the Plan.
 
    "Award Agreement" means a written agreement between the Company and a
  Participant that sets forth the terms, conditions and limitations
  applicable to an Award.
 
    "Board" means the Board of Directors of the Company.
 
    "Cash Award" means an award payable in cash.
 
    "Code" means the United States Internal Revenue Code of 1986, as amended
  from time to time.
 
    "Common Stock" means the common stock, par value $1.00 per share, of the
  Company.
 
    "Committee" means the Compensation Committee of the Board or any person
  or persons appointed by the Board to administer the Plan.
 
    "Company" means Lyondell Chemical Company.
 
    "Effective Date" means January 1, 1999, subject to approval by the
  Company's shareholders as provided in Section 19.
 
    "Employee" means an individual employed by the Company or a Subsidiary.
 
    "Exercise Price" means the price at which the Option Shares may be
  purchased under the terms of the Award Agreement.
 
    "Fair Market Value" of a share of Common Stock means, as of a particular
  date, (i) if shares of Common Stock are listed on a national securities
  exchange, the closing price per share of Common Stock reported on the
  consolidated transaction reporting system for the principal national
  securities exchange on which shares of Common Stock are listed on that
  date, or, if there shall have been no such sale so reported on that date,
  on the last preceding date on which such a sale was so reported, (ii) if
  shares of Common Stock are not so listed but are quoted on the Nasdaq
  National Market, the closing price per share of Common Stock reported by
  the Nasdaq National Market on that date, or, if there shall have been no
  such sale so reported on that date, on the last preceding date on which
  such a sale was so reported, (iii) if the Common Stock is not so listed or
  quoted, the mean between the closing bid and asked price on that date, or,
  if there are no quotations available for such date, on the last preceding
  date on which such quotations are available, as reported by the Nasdaq
  Stock Market, or, if not reported by the Nasdaq Stock Market, by
 
                                      A-1
<PAGE>
 
  the National Quotation Bureau Incorporated or (iv) if shares of Common
  Stock are not publicly traded, the most recent value determined by an
  independent appraiser appointed by the Company for such purpose.
 
    "Grant Date" means the date on which an Award is granted by the
  Committee.
 
    "Option" means a right to purchase a particular number of shares of
  Common Stock at a particular Exercise Price, subject to certain terms and
  conditions as provided in the Plan and Award Agreement.
 
    "Option Shares" means the shares of Common Stock covered by a particular
  Option.
 
    "Participant" means an Employee to whom an Award has been granted under
  this Plan.
 
    "Performance-Based Award" means an Award that is paid, vested or
  otherwise deliverable solely based on the achievement of one or more
  Performance Goals as provided in Section 6(a).
 
    "Performance Goal" means a standard established by the Committee to
  determine in whole or in part whether Performance-Based Awards shall be
  earned.
 
    "Performance Shares" means the contingent right to receive an amount in
  cash or Common Stock, as determined by the Committee in its sole
  discretion, that is subject to the attainment of one or more Performance
  Goals.
 
    "Phantom Stock" means a right to receive the value of a specified number
  of shares of Common Stock.
 
    "Plan" means the Lyondell Chemical Company 1999 Long-Term Incentive Plan,
  as amended from time to time.
 
    "Restricted Stock" means shares of Common Stock that are restricted or
  subject to forfeiture provisions.
 
    "Stock Appreciation Rights" or "SARs" means the right to receive an
  amount in cash or Common Stock equal to the appreciation in value of a
  specified number of shares of Common Stock over a particular period of
  time.
 
    "Subsidiary" means (i) any corporation, limited liability company or
  similar entity of which the Company directly or indirectly owns shares
  representing more than fifty percent of the voting power of all classes or
  capital stock of such corporation which have the right to vote generally on
  matters submitted to a vote of the shareholders of such entity, (ii)
  Equistar Chemicals, LP or LYONDELL-CITGO Refining, LP so long as the
  Company maintains an equity ownership interest equal to at least twenty-
  five percent in such entities, or (iii) any other entity in which the
  Company has an equity ownership interest of at least twenty-five percent,
  so long as such entity is designated by the Committee as a Subsidiary for
  purposes of this Plan; provided, however, that with respect to Options
  intended to qualify as incentive stock options within the meaning of
  Section 422 of the Code, "Subsidiary" shall have the meaning set forth in
  Section 424(f) of the Code or any successor provision.
 
  3. Plan Administration and Designation of Participants.
 
  (a) Eligibility. All Employees of the Company and its Subsidiaries who, in
the judgment of the Committee, are in a position to contribute significantly
to its long-term profit and growth objectives are eligible for Awards under
this Plan. The Committee shall select the Participants from time to time by
the grant of Awards under the Plan and, subject to the terms and conditions of
the Plan, shall determine all terms and conditions of the Award.
 
  (b) Administration. The Plan shall be administered by the Committee, which
shall have full and exclusive power to interpret this Plan and to adopt such
rules, regulations and guidelines for carrying out this Plan as it may deem
necessary or appropriate. The Committee may delegate its duties hereunder to
the Chief Executive Officer or other senior officers of the Company subject to
such rules and regulations as the Committee establishes. The Committee may, in
its discretion, retain the services of an outside administrator for the
purpose
 
                                      A-2
<PAGE>
 
of performing any of its functions hereunder. The Committee may, in its
discretion, provide for the extension of the exercisability of an Award,
accelerate the vesting or exercisability of an Award, eliminate or make less
restrictive any restrictions contained in an Award Agreement, waive any
restriction or other provision of this Plan or an Award Agreement or otherwise
amend or modify an Award in any manner that is either (i) not adverse to the
Participant holding the Award or (ii) consented to by such Participant. The
Committee may grant an Award to an individual whom it expects to become an
Employee of the Company or any of its Subsidiaries within the following six
months, with such Award being subject to the individual's actually becoming an
Employee within such time period, and subject to such other terms and
conditions as may be established by the Committee. The Committee may correct
any defect or supply any omission or reconcile any inconsistency in this Plan
or in any Award Agreement in the manner and to the extent the Committee deems
necessary or desirable to further the Plan purposes. Any decision of the
Committee in the interpretation and administration of this Plan shall lie
within its sole and absolute discretion and shall be final, conclusive and
binding on all parties concerned.
 
  No member of the Committee and no officer of the Company to whom the
Committee has delegated authority in accordance with this Plan shall be liable
for anything done or omitted to be done by him or her in connection with the
performance of any duties under this Plan, except for his or her own willful
misconduct or as expressly provided by statute.
 
  4. Award Agreement. Each Award granted hereunder, other than a Cash Award,
shall be described in an Award Agreement, which shall be subject to the terms
and conditions of the Plan and shall be signed by the Participant and by the
appropriate officer for and on behalf of the Company. The Committee shall
authorize written guidelines for the issuance of a Cash Award.
 
  5. Shares of Common Stock Available for Awards. Subject to the provisions of
Section 11 hereof, no Award shall be granted if it shall result in the
aggregate number of shares of Common Stock issued under the Plan plus the
number of shares of Common Stock covered by or subject to Awards then
outstanding (after giving effect to the grant of the Award in question) to
exceed the lesser of ten million or ten percent of the number of shares of
Common Stock outstanding at the time of granting such Award. No Participant
may be granted, during the term of the Plan, Options covering or relating to
more than two million shares of Common Stock. No Participant may be granted,
during the term of the Plan, Awards in the form of Performance Shares,
Restricted Stock, Stock Appreciation Rights or Phantom Stock covering or
relating to more than one million shares of Common Stock. No more than 2.5
million shares of Common Stock shall be available for Awards in the form of
Performance Shares, Restricted Stock, Stock Appreciation Rights or Phantom
Stock. No Participant may be granted Cash Awards in respect of any calendar
year having a value in excess of $2 million. No more than one million shares
of Common Stock shall be available for Incentive Stock Options. The number of
shares of Common Stock that are the subject of Awards under this Plan that are
forfeited or terminated, expire unexercised, are settled in cash in lieu of
Common Stock or in a manner such that all or some of the shares covered by an
Award are not issued to a Participant or are exchanged for Awards that do not
involve Common Stock, shall again immediately become available for Awards
hereunder. The Committee may from time to time adopt and observe such
procedures concerning the counting of shares against the Plan maximum as it
may deem appropriate. The Board and the appropriate officers of the Company
shall from time to time take whatever actions are necessary to file any
required documents with governmental authorities, stock exchanges and
transaction reporting systems to ensure that shares of Common Stock are
available for issuance pursuant to Awards.
 
  6. Types of Awards.
 
  (a) Performance-Based Awards. Without limiting the type or number of Awards
that may be made under the other provisions of this Plan, an Award may be in
the form of a Performance-Based Award. Performance-Based Awards are Awards
that shall be paid, vested or otherwise deliverable solely on account of the
attainment of one or more pre-established, objective Performance Goals
established by the Committee prior to the earlier to occur of (i) 90 days
after the commencement of the period of service to which the Performance Goal
relates and (ii) the lapse of twenty-five percent of the period of service (as
scheduled in good faith at the time the goal is established), and in any event
while the outcome is substantially uncertain. A Performance Goal is objective
if a
 
                                      A-3
<PAGE>
 
third party having knowledge of the relevant facts could determine whether the
goal is met. Such a Performance Goal may be based on one or more business
criteria that apply to the Employee, one or more business units of the
Company, or the Company as a whole, and may include one or more of the
following: economic value, economic value added, increased revenue, net
income, stock price, market share, earnings per share, return on equity,
return on assets, decrease in costs, shareholder value, net cash flow, total
shareholder return, return on capital, return on investors' capital, operating
income, funds from operations, cash flow, cash from operations, after-tax
operating income, and total market value. Prior to the payment of any
compensation based on the achievement of Performance Goals, the Committee must
certify in writing that applicable Performance Goals and any of the material
terms thereof were, in fact, satisfied. In interpreting Plan provisions
applicable to Performance Goals and Performance-Based Awards, it is the intent
of the Plan to conform with the standards of Section 162(m) of the Code and
Treasury Regulation Section 1.162-27(e)(2)(i), and the Committee in
establishing such goals and interpreting the Plan shall be guided by such
provisions. A Performance-Based Award may include Performance Shares, Options,
Restricted Stock, Stock Appreciation Rights, Cash Awards or Phantom Stock.
 
  (b) Options. Options granted to Employees hereunder may be either incentive
stock options within the meaning of Section 422 of the Code or nonqualified
options within the meaning of Section 83 of the Code. The Exercise Price of an
Option shall not be less than the Fair Market Value of a share of Common Stock
on the Grant Date and shall not be less than the Fair Market Value of a share
of Common Stock on the Grant Date of any outstanding Option that is
relinquished in connection with a grant of a new Option. The terms, conditions
and limitations applicable to Options awarded to Employees shall be determined
by the Committee.
 
  (c) Performance Shares. An Award may be in the form of Performance Shares.
Performance Shares shall be payable, in the sole discretion of the Committee
in cash, shares of Common Stock, or any combination thereof. The terms,
conditions and limitations applicable to an Award of Performance Shares shall
be determined by the Committee.
 
  (d) Restricted Stock. An Award may be in the form of shares of Common Stock
or Restricted Stock. The terms, conditions, and limitations applicable to any
Award of shares of Common Stock or Restricted Stock pursuant to this Plan
shall be determined by the Committee.
 
  (e) Phantom Stock. An Award may be in the form of Phantom Stock, or other
bookkeeping account tied to the value of shares of Common Stock. The terms,
conditions, and limitations applicable to any Awards of Phantom Stock shall be
determined by the Committee.
 
  (f) Stock Appreciation Rights. An Award may be in the form of SARs. The
exercise price of an SAR shall not be less than the Fair Market Value of a
share of Common Stock on the Grant Date. The terms, conditions, and
limitations applicable to any Awards of SARs shall be determined by the
Committee.
 
  (g) Cash Awards. An Award may be in the form of a Cash Award. The terms,
conditions and limitations applicable to any Cash Awards shall be determined
by the Committee.
 
  7. Payment of Awards.
 
  (a) General. Payment of Awards may be made in the form of cash or Common
Stock or combinations thereof and may include such restrictions as the
Committee shall determine including, in the case of Common Stock, restrictions
on transfer and forfeiture provisions.
 
  (b) Deferral. The Committee may, in its discretion, (i) permit selected
Participants to elect to defer payments of some or all types of Awards in
accordance with procedures established by the Committee or (ii) provide for
the deferral of an Award in an Award Agreement or otherwise. Any such deferral
may be in the form of installment payments or a future lump sum payment. Any
deferred payment, whether elected by the Participant or specified by the Award
Agreement or by the Committee, may be forfeited if and to the extent that the
Award Agreement so provides.
 
  (c) Dividends and Interest. Dividends or dividend equivalent rights may be
extended to and made part of any Award denominated in Common Stock or units of
Common Stock, subject to such terms, conditions and restrictions as the
Committee may establish. The Committee may also establish rules and procedures
for the
 
                                      A-4
<PAGE>
 
crediting of interest on deferred cash payments and dividend equivalents for
deferred payment denominated in Common Stock or units of Common Stock.
 
  (d) Substitution of Awards. At the discretion of the Committee, a
Participant may be offered an election to substitute an Award for another
Award or Awards of the same or different type.
 
  8. Stock Option Exercise. The price at which shares of Common Stock may be
purchased under an Option shall be paid in full at the time of exercise in
cash or, if permitted by the Committee, by means of tendering Common Stock or
surrendering all or part of that or any other Award, including Restricted
Stock, valued at Fair Market Value on the date of exercise, or any combination
thereof. The Committee shall determine acceptable methods for tendering Common
Stock or Awards to exercise an Option as it deems appropriate. The Committee
may provide for procedures to permit the exercise or purchase of Awards by use
of the proceeds to be received from the sale of Common Stock issuable pursuant
to an Award. Unless otherwise provided in the applicable Award Agreement, in
the event shares of Restricted Stock are tendered as consideration for the
exercise of an Option, a number of the shares issued upon the exercise of the
Option, equal to the number of shares of Restricted Stock used as
consideration therefor, shall be subject to the same restrictions as the
Restricted Stock so submitted as well as any additional restrictions that may
be imposed by the Committee.
 
  9. Termination of Employment. Upon the termination of employment by a
Participant, any unexercised, deferred or unpaid Awards shall be treated as
provided in the specific Award Agreement evidencing the Award. Unless
otherwise specifically provided in the Award Agreement, each Award granted
pursuant to this Plan which is an Option shall immediately terminate to the
extent the Option is not vested (or does not become vested as a result of such
termination of employment) on the date the Participant terminates employment
with the Company or its Subsidiaries.
 
  10. Assignability. Except as otherwise provided herein, no Award granted
under this Plan shall be sold, transferred, pledged, assigned or otherwise
alienated or hypothecated by a Participant other than by will or the laws of
descent and distribution, and during the lifetime of a Participant, any Award
shall be exercisable only by him, or, in the case of a Participant who is
mentally incapacitated, the Award shall be exercisable by his guardian or
legal representative. The Committee may prescribe and include in applicable
Award Agreements other restrictions on transfer. Any attempted assignment or
transfer in violation of this Section shall be null and void. Upon the
Participant's death, the personal representative or other person entitled to
succeed to the rights of the Participant (the "Successor Participant") may
exercise such rights. A Successor Participant must furnish proof satisfactory
to the Company of his or her right to exercise the Award under the
Participant's will or under the applicable laws of descent and distribution.
 
  Subject to approval by the Committee in its sole discretion, all or a
portion of the Awards granted to a Participant under the Plan may be
transferable by the Participant, to the extent and only to the extent
specified in such approval, to (i) the children or grandchildren of the
Participant ("Immediate Family Members"), (ii) a trust or trusts for the
exclusive benefit of such Immediate Family Members ("Immediate Family Member
Trusts"), or (iii) a partnership or partnerships in which such Immediate
Family Members have at least ninety-nine percent of the equity, profit and
loss interests ("Immediate Family Member Partnerships"); provided that the
Award Agreement pursuant to which such Awards are granted (or an amendment
thereto) must expressly provide for transferability in a manner consistent
with this Section. Subsequent transfers of transferred Awards shall be
prohibited except by will or the laws of descent and distribution, unless such
transfers are made to the original Participant or a person to whom the
original Participant could have made a transfer in the manner described
herein. No transfer shall be effective unless and until written notice of such
transfer is provided to the Committee, in the form and manner prescribed by
the Committee. Following transfer, any such Awards shall continue to be
subject to the same terms and conditions as were applicable immediately prior
to transfer, and, except as otherwise provided herein, the term "Participant"
shall be deemed to refer to the transferee. The consequences of termination of
employment shall continue to be applied with respect to the original
Participant, following which the Awards shall be exercisable by the transferee
only to the extent and for the periods specified in this Plan and the Award
Agreement.
 
                                      A-5
<PAGE>
 
  11. Adjustments.
 
  (a) The existence of outstanding Awards shall not affect in any manner the
right or power of the Company or its partners to make or authorize any or all
adjustments, recapitalization, reorganizations or other changes in the
ownership of the Company or its business or any merger or consolidation of the
Company, or any issue of bonds, debentures, preferred or prior preference
stock (whether or not such issue is prior to, on a parity with or junior to
the Common Stock) or other obligations, or the dissolution or liquidation of
the Company, or any sale or transfer of all or any part of its assets or
business, or any other Company act or proceeding of any kind, whether or not
of a character similar to that of the acts or proceedings enumerated above.
 
  (b) In the event of any Common Stock distribution or split,
recapitalization, extraordinary distribution, merger, consolidation,
combination or exchange of shares of Common Stock or similar change or upon
the occurrence of any other event that the Committee, in its sole discretion,
deems appropriate, the (i) the number of shares of Common Stock reserved under
this Plan and covered by outstanding Awards and related Incentive Stock Option
award limitation; (ii) the Exercise Price in respect of such Awards; and (iii)
the appropriate Fair Market Value and other price determinations for such
Awards shall be adjusted as appropriate.
 
  (c) In the event of a corporate merger, consolidation, acquisition of
property or stock, separation, reorganization or liquidation (such event
hereinafter referred to as a "Transaction"), the Board shall be authorized (i)
to issue or assume Awards by means of substitution of new Awards, as
appropriate, for previously issued Awards or to assume previously issued
Awards as part of such adjustment, (ii) to make provision, prior to the
transaction, for the acceleration of the vesting and exercisability of, or
lapse of restrictions with respect to, Awards or (iii) in the event of a
Transaction of which the Company is not the surviving corporation, to (A)
cancel Awards that are Options or SARs and give the Participants who are the
holders of such Awards notice and opportunity to exercise for 30 days prior to
such cancellation or (B) settle an Award that is an Option or SAR by a cash
payment equal to the difference between the Fair Market Value per share of
Common Stock on the date of the Transaction and the Exercise Price of the
Award, multiplied by the number of shares subject to the Award.
 
  12. Purchase for Investment. Unless the Awards and shares of Common Stock
covered by this Plan have been registered under the Securities Act of 1933, as
amended, each person receiving shares of Common Stock pursuant to an Award
under this Plan may be required by the Company to give a representation in
writing in form and substance satisfactory to the Company to the effect that
he is acquiring such shares for his own account for investment and not with a
view to, or for sale in connection with, the distribution of such shares or
any part thereof.
 
  13. Tax Withholding. The Company shall have the right to deduct applicable
taxes from any Award payment and withhold, at the time of delivery or vesting
of cash or shares of Common Stock under this Plan, an appropriate amount of
cash or number of shares of Common Stock or a combination thereof for payment
of taxes required by law or to take such other action as may be necessary in
the opinion of the Company to satisfy all obligations for withholding of such
taxes. The Committee may also permit withholding to be satisfied by the
transfer to the Company of shares of Common Stock theretofore owned by the
holder of the Award with respect to which withholding is required. If shares
of Common Stock are used to satisfy tax withholding, such shares shall be
valued based on the Fair Market Value when the tax withholding is required to
be made.
 
  14. Amendments or Termination. The Committee may amend, alter or discontinue
this Plan, except that no amendment or alteration that would impair the rights
of any Participant under any Award that he has been granted shall be made
without his consent, and no amendment or alteration shall be effective prior
to approval by the Company's shareholders to the extent such approval is
determined by the Committee to be required by applicable laws, regulations or
exchange requirements. No Awards shall be granted more than ten years after
the Effective Date.
 
  15. Restrictions. No shares of Common Stock or other form of payment shall
be issued with respect to any Award unless the Company shall be satisfied
based on the advice of its counsel that such issuance will be in
 
                                      A-6
<PAGE>
 
compliance with applicable federal and state securities laws. The Award
Agreement may include provisions for the repurchase by the Company of Common
Stock acquired pursuant to an Award and repurchase of the Participant's Option
rights.
 
  16. Unfunded Plan. Insofar as it provides for Awards of cash, Common Stock
or rights thereto, this Plan shall be unfunded. Although bookkeeping accounts
may be established with respect to Participants who are entitled to cash,
Common Stock or rights thereto under this Plan, any such accounts shall be
used merely as a bookkeeping convenience. The Company shall not be required to
segregate any assets that may at any time be represented by cash, Common Stock
or rights thereto, nor shall this Plan be construed as providing for such
segregation, nor shall the Company, the Board or the Committee be deemed to be
a trustee of any cash, Common Stock or rights thereto to be granted under this
Plan. Any liability or obligation of the Company to any Participant with
respect to a grant of cash, Common Stock or rights thereto under this Plan
shall be based solely upon any contractual obligations that may be created by
this Plan and any Award Agreement, and no such liability or obligation of the
Company shall be deemed to be secured by any pledge or other encumbrance on
any property of the Company. None of the Company, the Board or the Committee
shall be required to give any security or bond for the performance of any
obligation that may be created by this Plan.
 
  17. Miscellaneous. The granting of any Award shall not impose upon the
Company any obligation to maintain any Participant as an Employee and shall
not diminish the power of the Company to discharge any Participant at any
time.
 
  18. Governing Law. This Plan and all determinations made and actions taken
pursuant hereto, to the extent not otherwise governed by mandatory provisions
of the Code or the securities laws of the United States, shall be governed by
and construed in accordance with the laws of the State of Texas.
 
  19. Effective Date of Plan; Shareholder Approval. This Plan shall be
effective as of the Effective Date; however, the adoption of this Plan is
expressly conditioned upon the approval of the holders of a majority of the
outstanding shares of Common Stock present, or represented, and entitled to
vote at the annual meeting of shareholders in 1999 and upon shareholder
approval at that annual meeting that satisfies the applicable exchange
requirements for shareholder approval. If the shareholders of the Company
should fail so to approve this Plan at such annual meeting, this Plan shall
terminate and cease to be of any further force or effect and all grants of
Awards hereunder shall be null and void.
 
                                          Attested to by the Secretary of
                                          Lyondell Chemical Company, as
                                          effective on the 11th day of
                                          December, 1998.
 
                                          /s/ Robert Millstone
                                          -------------------------------------
                                          Robert Millstone
 
                                      A-7
<PAGE>
 
[Logo of Lyondell appears here]





                                           [Logo of recycled paper appears here]
                                                           Recycled Paper
<PAGE>
 
[LYONDELL LOGO]


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

March 31, 1999

Dear Stockholder:

        You are cordially invited to join us at the 1999 Annual Meeting of 
Stockholders on Thursday, May 6, 1999, beginning at 10:00 a.m. in the Highland 
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 proxy card.

        The enclosed 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.

Sincerely yours,

/s/ Dan F. Smith
Dan F. Smith
President and Chief Executive Officer


<TABLE> 
<CAPTION> 
                                                   Please Detach Proxy Card Here
                                                   .                           .
- ------------------------------------------------------------------------------------------------------------------------------------
<S>                        <C>                                                                                          |
        [______]                                                                                                         
 1. ELECTION OF DIRECTORS  FOR all nominees       WITHHOLD AUTHORITY to vote             *EXCEPTIONS                    |
                           listed below      [_]  for all nominees listed below   [_]               [_]                  
                                                                                                                        |
    Nominees: Carol A. Anderson, William T. Butler, Travis Engen, Stephen F. Hinchliffe, Jr., Dudley C. Mecum II,         
    Frank Savage, 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 appointment of PricewaterhouseCoopers, LLP,      3. Proposal to adopt the Lyondell Chemical    
   Independent auditors, as the Company's auditors for the year 1999.         Company 1999 Long-Term Incentive Plan.    |
                                                                                                                         
   FOR [_]        AGAINST   [_]          ABSTAIN    [_]                       FOR  [_]  AGAINST [_]  ABSTAIN  [_]       |
                                                                                                                         
                                                                     IN THEIR DISCRETION, THE PROXIES ARE AUTHORIZED TO |
                                                                     VOTE UPON SUCH OTHER BUSINESS AS MAY PROPERLY COME  
                                                                     BEFORE THE MEETING AND ANY POSTPONEMENTS OR        |
                                                                     ADJOURNMENTS THEREOF.                               
                                                                                                                        |
                                                                     I/we will attend            Address Change          
                                                                     the meeting.     [_]        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:__________________________________, 1999       
                                                                                                                        |
                                                                     _____________________________________________       
                                                                                         Signature                      |
                                                                                                                         
                                                                     _____________________________________________      |
                                                                                Signature if held jointly                
                                                                                                                        |
PLEASE SIGN, DATE AND RETURN THE PROXY PROMPTLY USING                Votes MUST be indicated                             
THE ENCLOSED ENVELOPE.                                               (x) in Black or Blue ink.   [X}                    |
                                                                                                                         
                                                                                                                        |
                                                                                                           . Please Detach Here .
                                                                                                       You Must Detach This Portion 
                                                                                                       of the Proxy Card Before
                                                                                                       Returning It in the Enclosed
                                                                                                       Envelope
</TABLE> 

<PAGE>
 
                                [LYONDELL LOGO]

                              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 Robert J. 
Millstone, Jeffrey R. Pendergraft and Edward W. Rich and each of them, lawful 
attorney and proxies of the undersigned, with full power of substitution, for
and in the name, place and stead of the undersigned to attend the Annual Meeting
of Stockholders of Lyondell Chemical Company (herein the "Company") in the
Highland Room at the Four Seasons Hotel, 1300 Lamar, in Houston, Texas, on
Thursday, May 6, 1999 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, and with discretionary authority to vote on all other matters that may
properly come before the meeting.

        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 through 3.

        This card also constitutes your voting instructions for shares held in 
the Lyondell Chemical 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, the LYONDELL-CITGO Refining 
Company Ltd. 401(k) and Savings Plan for 
Represented Employees, the ARCO Chemical 
Company Capital Accumulation Plan and the 
ARCO Chemical Company Savings Plan and 
the undersigned hereby authorizes State              LYONDELL CHEMICAL COMPANY
Street Bank, as Trustee of such plans,               P.O. BOX 11244
to vote the shares held in the                       NEW YORK, N.Y. 10203-0244
undersigned's accounts.

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

<PAGE>
                   [LOGO OF LYONDELL
                   APPEARS HERE]
                                   LYONDELL

                              One Houston Center
                           1221 McKinney, Suite 1600
                             Houston, Texas 77010
P 
         THIS PROXY IS SOLICITED ON BEHALF OF THE BOARD OF DIRECTORS
R
          The undersigned hereby makes, constitutes and appoints Robert J. 
O    Millstone, Jeffrey R. Pendergraft and Edward W. Rich and each of them,
     lawful attorney and proxies of the undersigned, with full power of
X    substitution, for and in name, place and stead of the undersigned to attend
     the Annual Meeting of Stockholders of Lyondell Chemical Company (herein the
Y    "Company") in the Highland Room at the Four Seasons Hotel 1300 Lamar, in
     Houston, Texas on Thursday, May 6, 1999 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, and with discretionary authority to
     vote on all other matters that may properly come before the meeting.

          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 THROUGH 3.

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

          LYONDELL CHEMICAL COMPANY                                _____________
          P.O. BOX 11244                                           |SEE REVERSE|
          NEW YORK, NY 10203-0244                                  |   SIDE    |
                                                                   _____________
           (Continued, and to be signed and dated, on reverse side.)

                             FOLD AND DETACH HERE
<PAGE>
 
<TABLE> 
<CAPTION> 
[X]  PLEASE MARK YOUR                                                                                 |  6187
     VOTE AS IN THIS                                                                                  ---
     EXAMPLE.

     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 THROUGH 3.
- ------------------------------------------------------------------------------------------------------------------------------------
<S>             <C>            <C>                                            <C>                               <C>  
                 FOR  WITHHELD                                                                                   FOR AGAINST ABSTAIN
1. Election of   [_]    [_]    Nominees: Carol A. Anderson, William T. Butler, 2. Proposal to ratify the         [_]    [_]    [_]
   Directors                   Travis Engen, Stephen F. Hinchliffe, Jr.,          appointment of 
                               Dudley C. Mecum II, Frank Savage, Dan F. Smith     PricewaterhouseCoopers, LLP
FOR EXCEPT VOTES WITHHELD      Paul R. Staley.                                    independent auditors
FROM THE FOLLOWING NOMINEE(S)                                                     as the Company's auditors for
                                                                                  the year 1999.
___________________________________
                                                                               3. Proposal to adopt the Lyondell  [_]   [_]    [_]
                                                                                  Chemical Company 1999 Long-Term
________________________________________________________________                  Plan.
                                                                                  
                                                                                  IN THEIR DISCRETION, THE PROXIES ARE AUTHORIZED TO
                                                                                  VOTE UPON SUCH OTHER BUSINESS AS MAY PROPERLY COME
                                                                                  BEFORE THE MEETING AND ANY POSTPONEMENTS OR
                                                                                  ADJOURNMENTS THEREOF.
                                                                                  __________________________________________________
                                                                                      I will attend the meeting [_]   Address  [_]
                                                                                                                      Change
                                                                                                                      Mark
                                                                                                                      Here

                                                                                  Please sign exactly as name appears hereon. Joint
                                                                                  owners should each sign. When signing as attorney,
                                                                                  executor, administrator, trustee or guardian,
                                                                                  please give full title as such.    

                                                                                  __________________________________________________

                                                                                  __________________________________________________
                                                                                   SIGNATURE(S)                             DATE
- ------------------------------------------------------------------------------------------------------------------------------------
                                                       FOLD AND DETACH HERE
</TABLE> 

[LYONDELL LOGO
APPEARS HERE]

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

March 31, 1999

Dear Stockholder:

You are cordially invited to join us at the 1999 Annual Meeting of Stockholders 
on Thursday, May 6, 1999, beginning at 10:00 a.m. in the Highland 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,

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


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