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                                                                Exhibit (10)(bb)

                            THE LUBRIZOL CORPORATION
                            ANNUAL INCENTIVE PAY PLAN

                                  INTRODUCTION

      The Lubrizol Corporation (hereinafter referred to as the "Corporation")
hereby establishes, effective as of January 1, 2005, The Lubrizol Corporation
Annual Incentive Pay Plan (hereinafter referred to as the "Plan") in order to
provide an award for employees which reflects the pursuit of superior
performance, increased customer satisfaction and enhancement of shareholder
value. Awards for participating employees under the Plan shall depend upon
corporate performance measures as determined by the Committee for the Plan Year.

      Except as otherwise provided, the Plan shall be administered by the
Organization and Compensation Committee (hereinafter referred to as the
"Committee") of the Board of Directors of the Corporation. The Committee shall
have conclusive authority to construe and interpret the Plan and any agreements
entered into under the Plan and to establish, amend, and rescind rules and
regulations for its administration. The Committee shall also have any additional
authority as the Board may from time to time determine to be necessary or
desirable.

                                    ARTICLE I
                                   DEFINITIONS

      1.01 Definitions. The following terms shall have the indicated meanings
for purposes of the Plan:

      (a)   "Board" shall mean the Board of Directors of the Corporation.

      (b)   "Chief Executive Officer" shall mean the chief executive officer of
            the Corporation.

      (c)   "Committee" shall mean the Organization and Compensation Committee
            of the Board, or other designated committee of the Board, consisting
            of persons who are not Employees or Foreign Employees.

      (d)   "Corporation" shall mean The Lubrizol Corporation, a corporation
            organized under the laws of the State of Ohio.

      (e)   "Director" shall mean a member of the Board.

      (f)   "Employee" shall mean any person other than an Officer, who is
            employed for a wage or salary by the Corporation or a domestic
            Subsidiary.

      (g)   "Foreign Employee" shall mean any person who is employed for a wage
            or salary by an international Subsidiary of the Corporation.

      (h)   "Foreign Participant" shall mean any Foreign Employee who has been
            selected by the Committee pursuant to Article VI of the Plan, and
            who has not for any reason become ineligible to participate in the
            Plan.

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      (i)   "Individual Award" shall mean the amount paid (or to be paid) to a
            Participant or Foreign Participant, as the case may be, by the
            Corporation pursuant to the Plan.

      (j)   "Individual Performance Shares" shall have the definition, and shall
            be determined, as set forth in Section 3.02 herein.

      (k)   "Officer shall mean an employee of the Corporation or a Subsidiary
            who is a member of the Executive Council of the Corporation.

      (l)   "Participant" shall mean all Officers, and any Employee who has been
            selected by the Committee pursuant to Article II herein to
            participate in the Plan, and have not for any reason become
            ineligible to participate in the Plan.

      (m)   "Pay" shall be determined at the time of calculating the Individual
            Performance Shares and shall be the Participant's base pay.

      (n)   "Plan" shall mean The Lubrizol Corporation Annual Incentive Pay
            Plan, effective January 1, 2005.

      (o)   "Plan Year" shall mean each twelve-month period commencing January 1
            and ending December 31.

      (p)   "Subsidiary" shall mean any corporation, foreign or domestic, that
            is wholly or partially (but not less than 50%) owned directly or
            indirectly by the Corporation.

      1.02 Construction. Where necessary or appropriate to the meaning of a
word, the singular shall be deemed to include the plural, the plural to include
the singular, the masculine to include the feminine, and the feminine to include
the masculine.

                                   ARTICLE II
                          ELIGIBILITY AND PARTICIPATION

      2.01 Eligibility. All Employees and Officers shall be eligible to
participate in the Plan.

      2.02 Participation. All Officers shall participate in the Plan. In
addition, the Committee shall determine which Employees shall participate in the
Plan for each Plan Year. The Committee may also determine which Employees hired
during the Plan Year shall participate in the Plan for such Plan Year. The
Committee's selection of Participants shall be after considering recommendations
presented to it by the Chief Executive Officer.

                                   ARTICLE III
                          INDIVIDUAL PERFORMANCE SHARES

      3.01 In General. At the time the Committee selects Participants for any
Plan Year, the Committee shall, after consideration of the recommendations of
the Chief Executive Officer, establish, for each Plan Year, Individual
Performance Shares for each Participant.

      3.02 Calculation of Individual Performance Shares. Individual Performance
Shares shall be calculated in the following manner:

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      (a)   The Pay of each Participant shall be multiplied by a designated
            percentage which shall take into account the Participant's position
            in the Corporation. Such designated percentage shall be determined
            by the Committee.

      (b)   The product for each Participant, determined pursuant to the
            calculation in paragraph (a) above, shall be divided by the sum of
            all such amounts produced for all Participants calculated in
            accordance with paragraph (a) above.

      (c)   The quotient determined for each Participant, calculated pursuant to
            paragraph (b) above, shall be multiplied by 100 and rounded, up or
            down, to the nearer whole number to produce the number of each
            Participant's Individual Performance Shares.

      Individual Performance Shares may be either increased or decreased, at any
time, or from time to time, during a Plan Year, for any Participant at the sole
discretion of the Committee in order to reflect any change in the individual
contribution under the formula set forth in this Section 3.02.

                                   ARTICLE IV
                              DETERMINATION OF FUND

      4.01 Fund. A fund shall be accrued on a monthly basis during each Plan
Year, based upon a fixed percentage of the Corporation's monthly consolidated
net income during such Plan Year (the "Fund"), as established by the Committee,
which percentage may be increased or decreased at any time, and from time to
time, prior to the end of the Plan Year at the discretion of the Committee. The
Fund shall consist of bookkeeping accruals on the books of the Corporation and
no cash or other property shall be set aside by the Corporation for these
purposes.

      4.02 Post-Plan Year Fund Adjustment. At the beginning of each Plan Year,
corporate initiatives for the Plan Year will be categorized into corporate
performance measures and shall be presented to the Committee by the Chief
Executive Officer. In February following the Plan Year, the Chief Executive
Officer shall evaluate the outcome of the performance measures for the Plan Year
just concluded and shall present his evaluation to the Committee which the
Committee may, at its discretion, increase or decrease the amount of the Fund.

                                    ARTICLE V
                                INDIVIDUAL AWARDS

      5.01 Allocation. Each Participant's Individual Award for a Plan Year shall
be calculated in January following the close of the Plan Year and shall be an
amount determined as follows:

      (a)   Divide the total Fund, as finally approved by the Committee, by the
            total Individual Performance Shares of all Participants;

      (b)   For each Participant, multiply the amount determined in paragraph
            (a) by such Participant's Individual Performance Shares; and

      (c)   The product determined in paragraph (b) shall be the tentative
            amount of the Participant's Individual Award which may be increased
            or decreased in the sole discretion of the Committee.

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      The Committee may also in its sole and unrestricted discretion determine
Individual Awards for Participants who were hired during the Plan Year. No
Participant shall have any vested interest in, or be entitled to, any Individual
Award unless and until payment is authorized by the Committee.

      5.02 Time and Method of Payment of Individual Awards. In the event the
Committee determines that a Participant is entitled to an Individual Award, the
Corporation shall pay such Individual Award to that Participant as soon after
the close of the Plan Year as may be feasible, but in no event later than thirty
30 days after the date that the Corporation releases its public announcement of
the Corporation's earnings for such Plan Year. A Participant, who leaves the
Corporation's employ after the Plan Year but prior to the payment of an
Individual Award, except in the case of retirement under the provisions of a
qualified defined benefit plan maintained by the Corporation, disability or
death, will not be eligible to receive any payment under this Plan. However, an
Individual Award may be made to such a Participant in those instances where
recommendation for such a payment has been made by the Chief Executive Officer
and approved by the Committee.

      In the event a Participant dies after the Plan Year but prior to the
payment of any Individual Award with respect to the Plan Year, any Individual
Award determined to be payable by the Committee shall be paid by the Corporation
to the Participant's estate.

      5.03 Conditions. Anything contained herein to the contrary
notwithstanding, the payment of Individual Awards to Participants with respect
to any Plan Year is conditioned upon the availability of adequate corporate
profits for the Corporation's fiscal year coinciding with any Plan Year. The
determination of whether adequate corporate profits exist shall be made by the
Board in its sole and unrestricted judgment and discretion and such
determination shall be conclusive and binding.

                                   ARTICLE VI
                          AWARDS FOR FOREIGN EMPLOYEES

      6.01 Participation. The Committee shall determine which Foreign Employees
shall participate in the Plan for each Plan Year. The Committee's selection of
Foreign Participants shall be made after considering recommendations presented
to it by the Chief Executive Officer.

      6.02 Individual Awards. At the time the Individual Awards are determined
for Participants, the Committee shall, in its discretion, after consideration of
the recommendations of the Chief Executive Officer, establish for each Plan Year
Individual Awards for each Foreign Participant.

      6.03 Payment of Awards. Individual Awards to each Foreign Participant
shall be paid by the international Subsidiary that is the employer of such
Foreign Participant at the same time as payment is made to Participants under
Section 5.02. All payments shall be converted from the U.S. dollar measurement
under the Plan to the currency of the country of such Subsidiary at the currency
exchange rate in effect at the time the Individual Award is determined. All
applicable withholding taxes shall be withheld from the distribution and
remitted by the international subsidiary to the appropriate taxing authority.

      6.04 Conditions.

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      (a)   A Foreign Employee who leaves the international Subsidiary's employ
            after the end of the Plan Year but prior to the payment of an
            Individual Award, except in the case of retirement in accordance
            with the customary practice of such Subsidiary, disability or death,
            will not be eligible to receive any payment under this Plan.
            However, an Individual Award may be made to such a Foreign
            Participant in those instances where recommendation for such a
            payment has been made by the Chief Executive Officer and approved by
            the Committee.

      (b)   In the event a Foreign Participant dies after the Plan year but
            prior to the payment of any Individual Award with respect to the
            Plan Year, any Individual Award determined by the Committee to be
            payable, shall be paid by the international Subsidiary to the
            Foreign Participant's estate or in accordance with local laws.

                                   ARTICLE VII
                                CHANGE OF CONTROL

      7.01 Effect of Change in Control. In the event a Change in Control of the
Corporation (as defined in Section 7.02) occurs prior to final determination by
the Committee of the amounts of Individual Awards to be paid under the Plan with
respect to any Plan Year, the Committee shall calculate such Individual Awards
as soon as practicable after such Change in Control. The Fund from which
Individual Awards are to be made shall be based upon accruals by the Corporation
up to the time of such Change in Control and Individual Awards shall be
calculated in accordance with Sections 5.01 and 6.02 herein. Payment of such
Individual Awards shall be made within thirty (30) days of the date on which the
determination is made to compute the payments according to the terms of this
Section 7.01.

      7.02 For all purposes of the Plan, a "Change in Control of the
Corporation" shall have occurred if any of the following events shall occur:

      (a)   The Corporation is merged, consolidated or reorganized into or with
            another corporation or other legal person, and, as a result of such
            merger, consolidation or reorganization, less than a majority of the
            combined voting power of the then-outstanding securities of such
            surviving corporation or person entitled to vote, immediately after
            such transaction, is held in the aggregate by the holders of Voting
            Stock (as hereinafter defined) of the Corporation immediately prior
            to such transaction;

      (b)   The Corporation sells all or substantially all of its assets to any
            other corporation or other legal person, and less than a majority of
            the combined voting power of the then-outstanding securities of such
            corporation or person, immediately after such sale, is held in the
            aggregate by the holders of Voting Stock of the Corporation
            immediately prior to such sale;

      (c)   There is a report filed on Schedule 13D or Schedule 14D-1 (or any
            successor schedule, form or report), each as promulgated pursuant to
            the Securities Exchange Act of 1934, as amended (the "Exchange
            Act"), disclosing that any person (as the term "person" is used in
            Section 13(d)(3) or Section 14(d)(2) of the Exchange Act) has become
            the beneficial owner (as the term "beneficial owner" is defined
            under Rule 13(d)(3) or any successor rule or regulation promulgated
            under the Exchange Act) of securities representing 20% or more of

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            the combined voting power of the then-outstanding securities
            entitled to vote generally in the election of directors of the
            Corporation ("Voting Stock");

      (d)   The Corporation files a report or proxy statement with the
            Securities and Exchange Commission pursuant to the Exchange Act
            disclosing in response to Form 8-K or Schedule 14A (or any successor
            schedule, form or report or item therein) that a change in control
            of the Corporation has or may have occurred or will or may occur in
            the future pursuant to any then-existing contract or transaction; or

      (e)   If during any period of two consecutive years, individuals who, at
            the beginning of any such period constitute the Directors of the
            Corporation, cease for any reason to constitute at least a majority
            thereof, unless the election, or the nomination for election by the
            Corporation's stockholders, of each Director of the Corporation
            first elected during such period was approved by a vote of at least
            two-thirds of the Directors of the Corporation then still in office
            who were Directors of the Corporation at the beginning of any such
            period.

      Notwithstanding the foregoing provisions, a "Change in Control" shall not
be deemed to have occurred for purposes of the Plan solely because (i) the
Corporation, (ii) an entity in which the Corporation directly or indirectly
beneficially owns 50% or more of the voting securities or (iii) any
Corporation-sponsored employee stock ownership plan or any other employee
benefit plan of the Corporation, either files or becomes obligated to file a
report or a proxy statement under or in response to Schedule 13D, Schedule
14D-1, Form 8-K or Schedule 14A (or any successor schedule, form or report or
item therein) under the Exchange Act, disclosing beneficial ownership by it of
shares of Voting Stock, whether in excess of 20% or otherwise, or because the
Corporation reports that a change in control of the Corporation has or may have
occurred or will or may occur in the future by reason of such beneficial
ownership.

                                  ARTICLE VIII
                                 ADMINISTRATION

      8.01 Plan Administrator. The Committee shall be the Plan administrator.

      8.02 Duties of Plan Administrator.

      (a)   The Committee shall administer the Plan in accordance with its terms
            and shall have all powers necessary to carry out the provisions of
            the Plan including, but not limited to, the following:

            (1)   Determination of Employees and Foreign Employees who are
                  eligible for Plan participation;

            (2)   Determination of the amount of the Fund to be distributed to
                  Participants and Foreign Participants for each Plan Year; and

            (3)   Determination of each Officer's actual Individual Award.

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      (b)   The Committee shall interpret the Plan and shall resolve all
            questions arising in the administration, interpretation, and
            application of the Plan. Any such determination of the Committee
            shall be conclusive and binding on all persons.

      (c)   The Committee shall establish such procedures and keep such records
            or other data as the Committee in its discretion determines
            necessary or proper for the administration of the Plan.

      (d)   The Committee may delegate administrative responsibilities to such
            person or persons as the Committee deems necessary or desirable in
            connection with the administration of the Plan.

                                   ARTICLE IX
                                  MISCELLANEOUS

      9.01 Unfunded Plan. The Corporation shall be under no obligation to
segregate or reserve any funds or other assets for purposes relating to this
Plan and no Participant or Foreign Participant shall have any rights whatsoever
in or with respect to any funds or assets of the Corporation.

      9.02 Non-Alienation. Since a Participant or Foreign Participant does not
have any rights to any Individual Award under the Plan until the time that
payment of such Individual Award is made, no anticipated payment of any
Individual Award shall be subject in any manner to alienation, sale, transfer,
assignment, pledge, attachment, garnishment or encumbrance of any kind. If a
Participant or Foreign Participant attempts to alienate, sell, transfer, assign,
pledge or otherwise encumber any such anticipated Individual Award, or if he has
filed or will be filing for bankruptcy, the Committee in its discretion may
cause such amounts as would otherwise become payable to such Participant or
Foreign Participant at such time or times to be paid to or applied for the
benefit of such one or more of the following as the Committee in its sole and
unrestricted judgment and discretion may designate: the Participant or Foreign
Participant, his spouse, child or children, or other dependents.

      9.03 Unclaimed Payments. Should the whereabouts of any Participant or
Foreign Participant entitled to receive any Individual Award be unknown to the
Corporation, and unascertainable after reasonable inquiry by the Corporation,
for a period of two years from the date of scheduled payment of the Individual
Award, the right of such person to receive payments hereunder shall be
terminated, and the amounts which would otherwise have been payable to such
person shall be forfeited.

      9.04 Actions or Decisions with Respect to the Plan. Any decision or action
of the Corporation, the Board, or the Committee, arising out of or in connection
with the administration and operation of this Plan, may be made or taken in
their sole and unrestricted judgment and discretion, and such decision or action
shall be conclusive and binding upon all Participants and Foreign Participants.

      9.05 No Employment Rights. Nothing herein contained shall be construed as
a commitment or agreement upon the part of any Participant, Foreign Participant,
Employee or Foreign Employee hereunder to continue his employment with the
Corporation or a Subsidiary, and nothing herein contained shall be construed as
a commitment on the part of the Corporation or any Subsidiary to continue the
employment or rate of compensation of any Participant or Foreign Participant
hereunder or any Employee or Foreign Employee for any period.

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      9.06 Amendment of the Plan. The Corporation reserves the right, to be
exercised by instruction from the Committee, to modify or amend this Plan at any
time.

      9.07 Duration and Termination of the Plan. The Corporation also reserves
the right, to be exercised by action of the Board, to discontinue or terminate
the Plan; provided that, and subject to all the provisions of this plan, any
termination shall be effective only for all Plan Years following December 31 of
the Plan Year in which the decision to terminate occurs.

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                            The Lubrizol Corporation
                        Annual Incentive Pay Grant Letter

Dear _______________,

For our 2005 plan we have set the following targets:

-     The size of the pool used to fund performance pay will be tied to the
      attainment of our 2005 plan and can vary significantly based on overall
      performance.

-     To reach a "targeted pay-out" we must meet the plan for the following
      metrics with the following weighting factors:

                          [INSERT METRICS AND WEIGHTS]

-     Meeting all plan objectives will result in the "targeted pay-out".

-     Exceeding objectives can increase the "targeted pay-out". Missing those
      objectives can also significantly decrease it.

-     Your individual "targeted pay-out" is a function of your level of
      responsibility within the corporation and your individual performance.

-     The plan has a "circuit breaker" provision. If the company is below its
      _____________ target but at or above _____________ in 2005, there will be
      a reduced pay out. Below _____________, there will be no annual incentive
      pay awards for anyone regardless of plan performance in other areas.

-     The Organization & Compensation Committee of the Board of Directors
      reserves the right during the year, and when determining pay-out, to alter
      any of the provisions up or down. Our plan does not provide for guaranteed
      payments.

What does this mean to you for 2005? Depending on the degree to which targeted
performance is achieved, and provided your personal performance remains at a
high level, your annual incentive pay would be in the range shown below:

<TABLE>
<CAPTION>
<S>                                      <C>                                  <C>
_________ Barely Exceeds                 Meets ______ Targets and             Exceeds _________ Targets by
Circuit Breaker and Less Than            Meets Plan in All Other              ____% and Exceeds Plan in All
Plan in All Areas                        Areas                                Other Areas
-----------------------------            ------------------------             -----------------------------
$______     to      $________            $______    to    $______             $_______     to     $________
</TABLE>

If we do not achieve ____________, your performance pay will be ZERO. As a
leader, we trust that you'll treat the above information as EXTREMELY
CONFIDENTIAL.

Regards,

James L. Hambrick
President and CEO

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