<PAGE>
 
                                                                   EXHIBIT 10.33


                                                 EXHIBIT A TO FIRST AMENDMENT TO
                                                    MASTER TRANSACTION AGREEMENT


                              LIMITED PARTNERSHIP

                                   AGREEMENT

                                       OF

                             EQUISTAR CHEMICALS, LP


        --------------------------------------------------------------
                          ORGANIZED UNDER THE DELAWARE
                    REVISED UNIFORM LIMITED PARTNERSHIP ACT
        --------------------------------------------------------------
<PAGE>
 
                               TABLE OF CONTENTS
<TABLE>
<CAPTION>
                                                                                          PAGE
                                                                                          ----
<C>              <S>                                                                      <C>
SECTION 1        ORGANIZATION MATTERS.................................................     1
            1.1  Formation of Partnership.............................................     1
            1.2  Name.................................................................     2
            1.3  Business Offices.....................................................     2
            1.4  Purpose and Business.................................................     2
            1.5  Filings..............................................................     2
            1.6  Power of Attorney....................................................     2
            1.7  Term.................................................................     3

SECTION 2        CAPITAL CONTRIBUTIONS................................................     3
            2.1  Acquisition of Units.................................................     3
            2.2  Transaction Costs....................................................     4
            2.3  Property Contributions...............................................     4
            2.4  Other Contributions..................................................     4
            2.5  Capital Accounts.....................................................     5
            2.6  No Return of or on Capital...........................................     5
            2.7  Partner Loans........................................................     5
            2.8  Administration and Investment of Funds...............................     5

SECTION 3        DISTRIBUTIONS........................................................     5
            3.1  Operating Distributions..............................................     5
            3.2  Liquidating Distributions............................................     6
            3.3  Withholding..........................................................     6
            3.4  Offset...............................................................     6

SECTION 4        BOOK AND TAX ALLOCATIONS.............................................     7
            4.1  General Book Allocations.............................................     7
            4.2  Change in Partner's Units............................................     7
            4.3  Deficit Capital Account and Nonrecourse Debt Rules...................     7
            4.4  Federal Tax Allocations..............................................     8
            4.5  Other Tax Allocations................................................     9

SECTION 5        ACCOUNTING, FINANCIAL REPORTING AND TAX MATTERS......................     9
            5.1  Fiscal Year..........................................................     9
            5.2  Method of Accounting for Financial Reporting Purposes................     9
            5.3  Books and Records; Right of Partners to Audit........................     9
            5.4  Reports and Financial Statements.....................................    10
            5.5  Method of Accounting for Book and Tax Purposes.......................    10
            5.6  Taxation.............................................................    10
            5.7  Delegation...........................................................    12
</TABLE> 
<PAGE>
 
<TABLE>
<CAPTION>
<C>              <S>                                                                      <C>
SECTION 6        MANAGEMENT...........................................................    12
            6.1  Partnership Governance Committee.....................................    12
            6.2  Limitations on Authority of General Partners.........................    13
            6.3  Lack of Authority of Persons Other Than General Partners
                   and Officers.......................................................    13
            6.4  Composition of Partnership Governance Committee......................    14
            6.5  Partnership Governance Committee Meetings............................    15
            6.6  Partnership Governance Committee Quorum and General Voting
                   Requirement........................................................    16
            6.7  Partnership Governance Committee Unanimous Voting Requirements.......    16
            6.8  Control of Interested Partner Issues.................................    19
            6.9  Auxiliary Committees.................................................    19
            6.10  Certain Limitations on Partner Representatives......................    20

SECTION 7        OFFICERS AND EMPLOYEES...............................................    20
            7.1  Partnership Officers.................................................    20
            7.2  Selection and Term of Executive Officers.............................    21
            7.3  Removal of Executive Officers........................................    21
            7.4  Duties...............................................................    22
            7.5  CEO..................................................................    22
            7.6  Other Officers.......................................................    23
            7.7  Secretary............................................................    23
            7.8  Salaries.............................................................    23
            7.9  Delegation...........................................................    23
            7.10  Employee Hirings....................................................    23
            7.11  General Authority...................................................    24

SECTION 8        STRATEGIC PLANS, ANNUAL BUDGETS AND LOANS............................    24
            8.1  Strategic Plan.......................................................    24
            8.2  Annual Budget........................................................    25
            8.3  Funding of Partnership Expenses......................................    25
            8.4  Implementation of Budgets and Discretionary Expenditures by CEO......    26
            8.5  Strategic Plan Deadlock..............................................    26
            8.6  Loans................................................................    27

SECTION 9        RIGHTS OF PARTNERS...................................................    28
            9.1  Delegation and Contracts with Related Parties........................    28
            9.2  General Authority....................................................    28
            9.3  Limitation on Fiduciary Duty; Non-Competition........................    29
            9.4  Limited Partners.....................................................    31
            9.5  Partner Covenants....................................................    31
            9.6  Special Purpose Entities.............................................    31

SECTION 10       TRANSFERS AND PLEDGES................................................    32
           10.1  Restrictions on Transfer and Prohibition on Pledge...................    32
           10.2  Right of First Option................................................    32
           10.3  Inclusion of General or Limited Partner Units........................    34
</TABLE>

                                      ii
<PAGE>
 
<TABLE>
<CAPTION>
<C>              <S>                                                                      <C>
           10.4  Rights of Transferee.................................................    34
           10.5  Effective Date of Transfer...........................................    34
           10.6  Transfer to Wholly Owned Affiliate...................................    34
           10.7  Invalid Transfer.....................................................    35

SECTION 11       DEFAULT..............................................................    35
           11.1  Default..............................................................    35
           11.2  Remedies for Default.................................................    35
           11.3  Purchase of Defaulting Partners' Units...............................    36
           11.4  Liquidation..........................................................    37
           11.5  Certain Consequences of Default......................................    37

SECTION 12       DISSOLUTION, LIQUIDATION AND TERMINATION.............................    37
           12.1  Dissolution and Termination..........................................    37
           12.2  Procedures Upon Dissolution..........................................    38
           12.3  Termination of the Partnership.......................................    39
           12.4  Asset and Liability Statement........................................    39

SECTION 13       MISCELLANEOUS........................................................    39
           13.1  Confidentiality and Use of Information...............................    39
           13.2  Indemnification......................................................    41
           13.3  Third Party Claim Reimbursement......................................    43
           13.4  Dispute Resolution...................................................    44
           13.5  EXTENT OF LIMITATION OF LIABILITY, INDEMNIFICATION, ETC..............    44
           13.6  Further Assurances...................................................    44
           13.7  Successors and Assigns...............................................    44
           13.8  Benefits of Agreement Restricted to the Parties......................    44
           13.9  Notices..............................................................    44
           13.10  [Reserved]..........................................................    46
           13.11  Severability........................................................    46
           13.12  Construction........................................................    46
           13.13  Counterparts........................................................    46
           13.14  Waiver of Right to Partition........................................    46
           13.15  Governing Law.......................................................    46
           13.16  Jurisdiction; Consent to Service of Process; Waiver.................    46
           13.17  Expenses............................................................    47
           13.18  Waiver of Jury Trial................................................    47
           13.19  Payment Terms and Interest Calculations.............................    47
           13.20  Usury Savings Clause................................................    47
           13.21  Other Waivers.......................................................    48
           13.22  Special Joinder by Millennium America...............................    48
           13.23  Amendment...........................................................    48

</TABLE>

                                      iii
<PAGE>
 
     APPENDICES

            APPENDIX A - Defined Terms
            APPENDIX B - Partnership Financial Statements and Reports
            APPENDIX C - Initial Executive Officers
            APPENDIX D - Dispute Resolution Procedures
            APPENDIX E - Division of Partnership Business

                                      iv
<PAGE>
 
                         LIMITED PARTNERSHIP AGREEMENT
                                       OF
                             EQUISTAR CHEMICALS, LP


     This Limited Partnership Agreement of Equistar Chemicals, LP dated October
__, 1997 is entered into by and among Lyondell Petrochemical G.P. Inc.
("Lyondell GP"), Lyondell Petrochemical L.P. Inc. ("Lyondell LP"), Millennium
Petrochemicals GP LLC ("Millennium GP") and Millennium Petrochemicals LP LLC
("Millennium LP").

     The definitions of capitalized terms used in this Agreement, including the
appendices hereto, are set forth in Appendix A hereto.

     WHEREAS, as contemplated by the Master Transaction Agreement, Lyondell
Petrochemical Company ("Lyondell"), the ultimate parent entity of each of
Lyondell GP and Lyondell LP, and Millennium Chemicals Inc. ("Millennium"), the
ultimate parent entity of each of Millennium GP and Millennium LP, desire to
establish a joint venture in the form of a limited partnership to engage in the
olefins, polyolefins and related petrochemicals businesses in the United States
and internationally;

     WHEREAS, in furtherance of the foregoing, Lyondell GP, Lyondell LP,
Millennium GP and Millennium LP wish to form the Partnership to acquire, own and
operate the Contributed Businesses, Initial Assets and such other assets and
businesses as are consistent with the purposes of the Partnership.

     WHEREAS, on the Closing Date, the Related Agreements relating to the
Partnership and the Contributed Businesses also will be entered into, all as set
forth in the Master Transaction Agreement; and

     NOW, THEREFORE, in consideration of the premises and the mutual covenants
of the parties hereto, it is hereby agreed as follows:


                                   SECTION 1
                              ORGANIZATION MATTERS

1.1         Formation of Partnership. The Certificate of Limited Partnership
of the Partnership has heretofore been or is on the date hereof being filed with
the Secretary of State of the State of Delaware. The Partners desire to enter
into this Agreement which constitutes the limited partnership agreement of the
Partnership as of the date hereof. Except as expressly provided herein to the
contrary, the rights and obligations of the Partners and the administration and
termination of the Partnership shall be governed by the Act. Without the need
for the consent of any other Person, upon their execution of this Agreement, (i)
each of Lyondell GP and Millennium GP is hereby admitted to the Partnership as a
general partner of the Partnership and (ii) each of Lyondell LP and Millennium
LP is hereby admitted to the Partnership as a limited partner of the
Partnership. Subject
<PAGE>
 
to the restrictions set forth in this Agreement, the Partnership shall have the
power to exercise all the powers and privileges granted by this Agreement and by
the Act, together with any powers incidental thereto, so far as such powers and
privileges are necessary, appropriate, convenient or incidental for the conduct,
promotion or attainment of the purposes of the Partnership.

1.2         Name. The name of the Partnership is "Equistar Chemicals, LP" The
Partnership's business may be conducted under such name or any other name or
names deemed advisable by the Partnership Governance Committee. The General
Partners will comply or cause the Partnership to comply with all applicable laws
and other requirements relating to fictitious or assumed names.

1.3         Business Offices. The principal place of business of the
Partnership shall be 1221 McKinney Street, Houston, Texas 77010, or such other
place as the General Partners may from time to time determine. The registered
agent of the Partnership in the State of Delaware is The Corporation Trust
Company, 1209 Orange Street, Wilmington, Delaware 19801.

1.4         Purpose and Business. The business of the Partnership shall be to,
directly or indirectly, (i) engage in the Specified Petrochemicals Businesses,
in the United States and internationally, including research and development,
purchasing, processing and disposing of feedstocks, and manufacturing, marketing
and distributing products, (ii) acquire and dispose of properties and assets
used or useful in connection with the foregoing and (iii) do all things
necessary, appropriate, convenient or incidental in connection with the
ownership, operation or financing of such business and activities, or otherwise
in connection with the foregoing, as are permitted under the Act, including the
acquisition and operation of the Contributed Businesses.

1.5         Filings. The General Partners shall, or shall cause the Partnership
to, execute, swear to, acknowledge, deliver, file or record in public offices
and publish all such certificates, notices, statements or other instruments, and
take all such other actions, as may be required by law for the formation,
reformation, qualification, registration, operation or continuation of the
Partnership in any jurisdiction, to maintain the limited liability of the
Limited Partners, to preserve the Partnership's status as a partnership for tax
purposes or otherwise to comply with applicable law. Upon request of the General
Partners, the Limited Partners shall execute all such certificates and other
documents as may be necessary, in the sole judgment of the General Partners, in
order for the General Partners to accomplish all such executions, swearings,
acknowledgments, deliveries, filings, recordings in public offices, publishings
and other acts. Each General Partner hereby agrees and covenants that it will
execute any appropriate amendment to the Certificate of Limited Partnership of
the Partnership pursuant to Section 17-204 of the Act to reflect any admission
of a Substitute General Partner in accordance with this Agreement.

1.6         Power of Attorney.  Each Limited Partner hereby irrevocably makes,
constitutes and appoints its Affiliated General Partner and any successor
thereto permitted as provided herein, with full power of substitution and
resubstitution, as the true and lawful agent and attorney-in-fact of such
Limited Partner, with full power and authority in the name, place and stead of
such Limited Partner to execute, swear, acknowledge, deliver, file or record in
public offices and publish:  (i) all certificates and other instruments
(including counterparts thereof) which such General Partner deems 

                                       2
<PAGE>
 
appropriate to reflect any amendment, change or modification of or supplement to
this Agreement in accordance with the terms of this Agreement; (ii) all
certificates and other instruments and all amendments thereto which such General
Partner deems appropriate or necessary to form, qualify or continue the
Partnership in any jurisdiction, to maintain the limited liability of such
Limited Partner, to preserve the Partnership's status as a partnership for tax
purposes or otherwise to comply with applicable law; and (iii) all conveyances
and other instruments or documents which such General Partner deems appropriate
or necessary to reflect the transfers or assignments of interests in, to or
under, this Agreement, including the Units, the dissolution, liquidation and
termination of the Partnership, and the distribution of assets of the
Partnership in connection therewith, pursuant to the terms of this Agreement.

     Each Limited Partner hereby agrees to execute and deliver to its Affiliated
General Partner within five Business Days after receipt of a written request
therefore such other further statements of interest and holdings, designations,
powers of attorney and other instruments as such General Partner deems
necessary.  The power of attorney granted herein is hereby declared irrevocable
and a power coupled with an interest, shall survive the bankruptcy, dissolution
or termination of such Limited Partner and shall extend to and be binding upon
such Limited Partner's successors and permitted assigns.  Each Limited Partner
hereby (i) agrees to be bound by any representations made by the agent and
attorney-in-fact acting in good faith pursuant to such power of attorney; and
(ii) waives any and all defenses which may be available to contest, negate, or
disaffirm any action of the agent and attorney-in-fact taken in accordance with
such power of attorney.

1.7         Term.  The term for which the Partnership is to exist as a limited
partnership is from the date of first filing of the Partnership's Certificate of
Limited Partnership with the office of the Secretary of State of the State of
Delaware through the dissolution of the Partnership in accordance with the
provisions of Section 12.


                                   SECTION 2
                             CAPITAL CONTRIBUTIONS

2.1         Acquisition of Units.  On the date hereof, each Partner has
contributed cash to the Partnership in exchange for Units as shown below:

<TABLE>
<CAPTION>
    Partner                  Cash            Units 
<S>                       <C>                <C>   
Lyondell GP               $   11,400            114
Millennium GP             $    8,600             86
Lyondell LP               $  558,600          5,586
Millennium LP             $  421,400          4,214
TOTAL                     $1,000,000         10,000 
</TABLE>

                                       3
<PAGE>
 
The Units shall entitle the holder to the distributions set forth in Section 3
and to the allocation of Profits, Losses and other items as set forth in Section
4.  Units shall not be represented by certificates.

2.2         Transaction Costs.  If the Partnership is entitled to deductions
with respect to costs described in Section 6.10 of the Master Transaction
Agreement to which a Partner is not entitled to reimbursement, the incurrence of
such costs shall not increase the Capital Account of such a Partner, and such
Partner shall be entitled to any deductions attributable to such costs.

2.3         Property Contributions.  On the Closing Date, the Limited Partners
shall make the following additional contributions:

(a)  Lyondell LP.  Pursuant to its Asset Contribution Agreement, Lyondell LP
     will contribute or cause to be contributed to the Partnership, the Initial
     Assets contemplated thereby subject to the Assumed Liabilities contemplated
     thereby.  Thereupon, its Capital Account will be credited with the amount
     set forth on Schedule 2.3.  In addition, on the Closing Date, Lyondell LP
     will execute and deliver to the Partnership the Lyondell Note.  Thereafter,
     its Capital Account will be increased as and to the extent principal
     payments are made on the Lyondell Note.

(b)  Millennium LP.  Pursuant to its Asset Contribution Agreement, Millennium LP
     will contribute or cause to be contributed to the Partnership, the Initial
     Assets contemplated thereby subject to the Assumed Liabilities contemplated
     thereby.  Contemporaneously with such contribution, the Partnership will
     borrow $750 million as contemplated by Section 8.6 and use the proceeds of
     such borrowing to satisfy the Millennium Debt in full.  Thereupon,
     Millennium LP's Capital Account will be credited with the amount set forth
     on Schedule 2.3.

(c)  The Partners intend that the contribution of assets subject to liabilities
     provided for in Sections 2.3(a) and (b) will qualify as a tax-free
     contribution under Section 721 of the Code in which no Partner will
     recognize gain or loss.  The Partners agree that the Partnership will so
     file its tax return, and each Partner agrees to file its tax return on the
     same basis and to maintain such position consistently at all times
     thereafter.

2.4         Other Contributions.  From time to time and subject to the
limitations of Section 6.7, if applicable, the Partnership Governance Committee
(or the CEO acting pursuant to Section 8.3), on behalf of the Partnership, may
issue a written notice ("Funding Notice") to the Limited Partners calling for an
additional capital contribution to the Partnership.  Any Funding Notice will set
forth:

(a)  the use of funds therefor;

(b)  the aggregate amount of the capital contribution required, which amount
     shall be apportioned among the Limited Partners Pro Rata; and

(c)  the date by which the capital contribution must be received by the
     Partnership, which date will not be earlier than seven Business Days from
     the date the Funding Notice is issued.

                                       4
<PAGE>
 
Each Limited Partner shall timely wire transfer its Pro Rata share of the amount
set forth in the Funding Notice to the Partnership's bank account.  Except as
expressly set forth in this Agreement,  no Partner shall be permitted or
required to make any additional capital contribution to the Partnership.

2.5         Capital Accounts.  Each Partner's Capital Account shall be
determined and maintained in accordance with Regulation (S)1.704-1(b)(2)(iv) as
reasonably interpreted by the Tax Matters Partner.  The Tax Matters Partner
shall have the discretion, after consultation with the other General Partner, to
make those determinations, valuations, adjustments and allocations with respect
to each Partner's Capital Account as it deems appropriate so that the
allocations made pursuant to this Agreement will have substantial economic
effect as such term is used in Regulation (S)1.704-1(b).  If any Partner
transfers all or a portion of its Units in accordance with the terms of this
Agreement, the transferee shall succeed to the Capital Account of the transferor
to the extent such Capital Account relates to the transferred Units.

2.6         No Return of or on Capital.  Except as provided in Sections 3 and 4,
no Partner shall receive any interest or other return on its capital
contributions or on the balance in its Capital Account and no return of its
capital contributions.

2.7         Partner Loans.  A Partner or its Affiliates may loan funds to the
Partnership on such terms and conditions as may be approved by the Partnership
Governance Committee, and, subject to other applicable law, have the same rights
and obligations with respect thereto as a Person who is neither a Partner nor an
Affiliate of a Partner.  The existence of such a relationship and acting in such
a capacity will not result in a Limited Partner being deemed to be participating
in the control of the business of the Partnership or otherwise affect the
limited liability of a Partner.  If a Partner or any Affiliate thereof is a
lender, in exercising its rights as a lender, including making its decision
whether to foreclose on property of the Partnership, such lender will have no
duty to consider (i) its status as a Partner or an Affiliate of a Partner, (ii)
the interests of the Partnership, or (iii) any duty it may have to any other
Partner or the Partnership.

2.8         Administration and Investment of Funds.  The administration and
investment of  Partnership funds shall be in accordance with the procedures and
guidelines as shall be adopted by the Partnership Governance Committee.  The
Partnership may delegate to a third party (which may be an Affiliate of one of
the Partners) the responsibility for administering and investing Partnership
funds pursuant to such guidelines.


                                   SECTION 3
                                 DISTRIBUTIONS

3.1         Operating Distributions.  Subject to Section 17-607 of the Act and
other applicable law, Available Net Operating Cash shall be distributed as soon
as practicable following the end of each month to the Partners as follows:

                                       5
<PAGE>
 
(a)  General.  On a cumulative basis, (i) distributions are to be made to the
     Partners Pro Rata to the extent of cumulative Profits, and (ii) the
     remaining distributions are to be made to the Limited Partners Pro Rata.
     For simplicity, however, in the absence of extraordinary transactions, the
     Partnership may make monthly distributions to the Partners Pro Rata,
     subject to subsequent adjustments as provided below in this Section 3.1.

(b)  Return of Excess Distributions.  Within 90 days after the end of each year,
     each General Partner shall return to the Partnership any amount it receives
     for such year that is in excess of its share of the sum of the cumulative
     undistributed Profits as of the end of the preceding year and the Profits
     for such year.

(c)  Effect of Operating Losses.  For any year in which  a General Partner's
     share of a Loss is sustained that exceeds its previously undistributed
     Profits, no distributions shall be made to such General Partner in any
     subsequent year until such excess Loss is recouped, and for subsequent
     years only Profits in excess of such  recoupment shall be treated as Profit
     for purpose of this Section 3.1.

(d)  Makeup Distributions.  If for any reason the Partnership does not make a
     monthly distribution to all Partners Pro Rata, each General Partner shall
     be entitled at the end of the year to receive the amount necessary to make
     its aggregate distributions for the year equal the amount it was entitled
     to receive and keep pursuant to the preceding criteria.

3.2         Liquidating Distributions.  Distributions to the Partners of cash or
property arising from a liquidation of the Partnership shall be made in
accordance with the Capital Account balances of the Partners as provided in
Section 12.2(d).

3.3         Withholding.  The Partnership is authorized to withhold from
distributions to a Partner and to pay over to a foreign, federal, state or local
government, any amounts required to be withheld pursuant to the Code or any
provisions of any other foreign, federal, state or local law.  Any amounts so
withheld shall be treated as distributed to such Partner pursuant to this
Section 3 for all purposes of this Agreement, and shall be offset against any
amounts otherwise distributable to such Partner.

3.4         Offset.  Any amount otherwise distributable to a Partner pursuant to
this Section 3 shall, unless otherwise agreed by two Representatives of the
Nonconflicted General Partner pursuant to Section 6.8, be applied by the
Partnership to satisfy any of the following obligations that are owed by such
Partner or its Affiliate to the Partnership and that are not paid when due:

(a)  Lyondell Note and Other Notes.  In the case of Lyondell LP, the failure to
     pay any interest or principal when due on the Lyondell Note or, in the case
     of any Partner, the failure to pay any interest or principal when due on
     any indebtedness for borrowed money of such Partner or any Affiliate of
     such Partner to the Partnership.

                                       6
<PAGE>
 
(b)  Asset Contribution Agreement. In the case of any Partner, the failure of
     such Partner or any Affiliate of such Partner to make any payment pursuant
     to Section 6 of its Asset Contribution Agreement that has been Finally
     Determined to be due.

(c)  Contribution.  In the case of any Partner, the failure to make any capital
     contribution required pursuant to this Agreement (other than pursuant to
     its Asset Contribution Agreement).


                                   SECTION 4
                            BOOK AND TAX ALLOCATIONS

4.1         General Book Allocations.  Except as otherwise provided in Sections
4.2 and 4.3, Profits or Losses each year shall be allocated among the Partners
Pro Rata for book purposes.  As used herein, "book" means the allocations used
to determine debits and credits to the Capital Accounts of the Partners and to
determine the amounts distributable to the Partners pursuant to Section 3 and
Section 12.2(d).  It does not refer to the method in which books are maintained
for financial reporting purposes pursuant to Section 5.2.

4.2         Change in Partner's Units.  If during a year Units are transferred
or new Units issued, allocations among the Partners shall be made in accordance
with their interests in the Partnership from time to time during such year in
accordance with Section 706 of the Code, using the closing-of-the-books method,
except that depreciation and other amortization with respect to each Partnership
asset shall be deemed to accrue ratably on a daily basis over the entire period
during such year that the asset is owned and in service by the Partnership.

4.3         Deficit Capital Account and Nonrecourse Debt Rules.  The special
rules in this Section 4.3 apply in the following order to take into account the
possibility of the Partners' having deficit Capital Account balances for which
they are not economically responsible and the effect of the Partnership's
incurring nonrecourse debt, directly or indirectly.

(a)  Partnership Minimum Gain Chargeback.  If there is a net decrease in
     "partnership minimum gain" during any year, determined in accordance with
     the tiered partnership rules of Regulation (S)1.704-2(k), each Partner
     shall be allocated items of income and gain for such year equal to such
     Partner's share of the net decrease in partnership minimum gain within the
     meaning of Regulation (S)1.704-2(g)(2), except to the extent not required
     by Regulation (S)1.704-2(f).  To the extent that this subsection (a) is
     inconsistent with Regulation (S)1.704-2(f) or (S)1.704-2(k) or incomplete
     with respect to such regulations, the minimum gain chargeback provided for
     herein shall be applied and interpreted in accordance with such
     regulations.

(b)  Partner Minimum Gain Chargeback.  If there is a net decrease in "partner
     nonrecourse debt minimum gain" during any year, within the meaning of
     Regulation (S) 1.704-2(i)(2), each Partner who has a share of such gain,
     determined in accordance with Regulation (S) 1.704-2(i)(5), shall be
     allocated items of income and gain for such year (and, if necessary,
     subsequent years) equal to such Partner's share of the net decrease in
     partner nonrecourse debt minimum gain.  To the extent that this 

                                       7
<PAGE>
 
     subsection (b) is inconsistent with Regulation (S) 1.704-2(i) or 1.704-2(k)
     or incomplete with respect to such regulations, the partner nonrecourse
     debt minimum gain chargeback provided for herein shall be applied and
     interpreted in accordance with such regulations.

(c)  Deficit Account Chargeback and Qualified Income.  If any Partner has an
     Adjusted Capital Account Deficit at the end of any year, including an
     Adjusted Capital Account Deficit for such Partner caused or increased by an
     adjustment, allocation or distribution described in Regulation (S)1.704-
     1(b)(2)(ii)(d)(4), (5) or (6), such Partner shall be allocated items of
     income and gain (consisting of a pro rata portion of each item of
     Partnership income, including gross income and gain) in an amount and
     manner sufficient to eliminate such Adjusted Capital Account Deficit as
     quickly as possible.  This subsection (c) is intended to constitute a
     "qualified income offset" pursuant to Regulation (S)1.704-1(b)(2)(ii)(d)
     and shall be interpreted consistently therewith.

(d)  Partner Nonrecourse Deductions.  Any partner nonrecourse deductions for any
     year or other period shall be allocated to the Partner who bears the
     economic risk of loss with respect to the partner nonrecourse debt to which
     such partner nonrecourse deductions are attributable in accordance with
     Regulation (S)1.704-2(i) or (S)1.704-2(k).

(e)  Curative Allocations.  The Allocations provided by this Section 4.3 may not
     be consistent with the manner in which the Partners intend to divide
     Profits, Losses and similar items.  Accordingly, Profits, Losses and other
     items will be reallocated among the Partners (in the same year and to the
     extent necessary, in subsequent years) in a manner consistent with
     Regulation (S)1.704-1(b) and 1.704-2 so as to prevent such allocations from
     distorting the manner in which Profits, Losses and other items are intended
     to be allocated among the Partners pursuant to Sections 4.1 and 4.2.

(f)  Nonrecourse Debt Sharing.  For purposes of this Agreement, nonrecourse
     deductions, within the meaning of Regulation (S)1.704-2, shall be deemed to
     be allocated among the Partners Pro Rata.  Solely for purposes of
     determining a Partner's proportionate share of the "excess nonrecourse
     liabilities" of the Partnership within the meaning of Regulation (S)1.752-
     3(a)(3), Partnership Profits are allocated to the Partners Pro Rata.

4.4         Federal Tax Allocations.

(a)  General Rule.  Except as otherwise provided in the following paragraphs of
     this Section 4.4, allocations for federal income tax purposes of items of
     income, gain, loss and deduction, and credits and basis therefor, shall be
     made in the same manner as book allocations are made.

(b)  Elimination of Book/Tax Disparities.  Taxable income and tax deductions
     shall be shared among the Partners so as to take into account the variation
     between the Book Value and the adjusted tax basis of each property at the
     time it is contributed to the Partnership and at each time it is revalued
     when any other cash or property is contributed to the Partnership.

(i)  To account for such variation with respect to the Initial Assets , the
     Partnership shall elect in accordance with Regulations 1.704-3(b) and (c)
     such 

                                       8
<PAGE>
 
     reasonable combination of the traditional method and, to the minimum extent
     required, the traditional method with curative allocations that will as
     closely as possible, in the opinion of the General Partners, cause the
     total depreciation deductions plus curatives with respect to the Initial
     Assets to be allocated each year among the Partners Pro Rata. The election
     shall be made on the first taxable return filed by the Partnership.

(ii) The choice of allocation methods to be used by the Partnership with respect
     to assets other than the Initial Assets shall be made by the General
     Partners at the time such assets are contributed to the Partnership or
     assets are revalued.
(c)  Allocation of Items Among Partners.  Each item of income, gain, loss,
     deduction and credit and all other items governed by Section 702(a) of the
     Code shall be allocated among the Partners in proportion to the allocation
     of Profits, Losses and other items to such Partners hereunder, provided
     that any gain treated as ordinary income because it is attributable to the
     recapture of any depreciation or amortization shall be allocated among the
     Partners in accordance with Prop. Treas. Reg. (S)(S) 1.1245-1(e)(2) and
     1.1250-1(f), or, upon promulgation of final regulations with respect to the
     matters covered therein, such final regulations.

(d)  Section 754 Election Allocations.  Income and deductions of the Partnership
     that are attributable to the Section 754 election shall be allocated to the
     Partners entitled thereto.

4.5         Other Tax Allocations.  Items of income, gain, loss, deduction,
credit and tax preference for state, local and foreign income tax purposes shall
be allocated among the Partners in a manner consistent with the allocation of
such items for federal income tax purposes in accordance with the foregoing
provisions of this Section.


                                   SECTION 5
                ACCOUNTING, FINANCIAL REPORTING AND TAX MATTERS

5.1         Fiscal Year.  The fiscal year of the Partnership shall be the
calendar year.

5.2         Method of Accounting for Financial Reporting Purposes.  For
financial reporting purposes, the Partnership shall adopt a standard set of
accounting policies and shall maintain separate books of account, all in
accordance with GAAP.  The Partnership's financial reports shall comply with
requirements of the SEC to the extent applicable to the Partnership and any
Partner or any controlling Person of such Partner, to the extent such
information is necessary, in conjunction with the financial reporting
obligations of such Person under applicable SEC requirements.

5.3         Books and Records; Right of Partners to Audit.

(a)  Proper and complete records and books of account of the Partnership's
     business, including all such transactions and other matters as are usually
     entered into records and books of 

                                       9
<PAGE>
 
     account maintained by businesses of like character or as are required by
     law, shall be kept by the Partnership at the Partnership's principal place
     of business. None of the Partnership's funds shall be commingled with the
     funds of any Partner.

(b)  Each Partner and its internal and independent auditors, at the expense of
     such Partner, shall have full and complete access to the internal and
     independent auditors of the Partnership and shall have the right to inspect
     such books and records and the physical properties of the Partnership
     during normal business hours and, at its own expense, to cause an
     independent audit thereof.  The Partnership shall make all books and
     records of the Partnership available to such Partner and its internal and
     independent auditors in connection with such audit and shall cooperate with
     such Partner and auditors and to provide any assistance reasonably
     necessary in connection with such audit.

5.4         Reports and Financial Statements.  The Partnership shall prepare and
deliver to the Partners the Partnership financial statements and reports
described on Appendix B as soon as reasonably practicable and in any event on or
prior to the due date indicated on Appendix B.

5.5         Method of Accounting for Book and Tax Purposes.  For purposes of
making allocations and distributions hereunder (including distributions in
liquidation of the Partnership in accordance with Capital Account balances as
required by Section 12.3), Capital Accounts and Profits, Losses and other items
described in Section 4.1 shall be determined in accordance with federal income
tax accounting principles utilizing the accrual method of accounting, with the
adjustments required by Regulation (S)1.704-1(b) to properly maintain Capital
Accounts.

5.6         Taxation.

(a)  Status of the Partnership.  The Partners acknowledge that the Partnership
     is a partnership for federal, foreign and state income tax purposes, and
     hereby agree not to elect to be excluded from the application of Subchapter
     K of Chapter 1 of Subtitle A of the Code or any similar state statute.

(b)         Tax Elections and Reporting.

(i)  Generally.  The Partnership shall make the following elections under the
     Code and the Regulations and any similar state statutes:

            (A) Adopt the calendar year as the annual accounting period;

            (B) Adopt the accrual method of accounting;

            (C) Elect to deduct organization costs ratably over a 60-month
          period as provided in Section 709 of the Code;

            (D) Adopt the LIFO method of accounting for inventory; and

                                      10
<PAGE>
 
            (E) Make any other elections available under the Code that the
          Partnership Governance Committee determine are appropriate, with the
          determination of whether an election is appropriate to be made
          pursuant to the principle that each Partner shall be treated equally
          (i.e., no Partner will receive preferential tax treatment to the
          disadvantage of another Partner).

(ii) Section 754 Election.  The Partnership shall, upon the written request of
     any Partner benefitted thereby, cause the Partnership to file an election
     under Section 754 of the Code and the Regulations thereunder to adjust the
     basis of the Partnership assets under Section 734(b) or 743(b) of the Code,
     and a corresponding election under the applicable sections of state and
     local law.

(c)  Tax Returns.  The Tax Matters Partner, on behalf of the Partnership, shall
     prepare and file the necessary tax and information returns.  Each Partner
     shall timely provide such information, if any, as may be needed by the
     Partnership for purposes of preparing such tax and information returns.  At
     least 75 days before the due date (as extended) for the Partnership's
     federal income tax return, the Tax Matters Partner shall deliver a draft of
     such return to each Partner.  Each Partner shall have 15 Business Days
     after receipt of the draft in which to furnish any objections or comments
     on the draft to the Tax Matters Partner.  A Partner may not report its
     share of any Partnership tax item in a manner inconsistent with the
     Partnership's reporting of such item unless the Partner has timely
     furnished its objection to the Tax Matters Partner as provided in the
     immediately preceding sentence.  If a Partner reports its share of any
     Partnership tax item in a manner inconsistent with the Partnership's
     reporting of such item, such Partner shall promptly notify the Partnership
     in writing at least 20 Business Days prior to the filing of any statement
     with the IRS in which such inconsistent position is reported.  The
     Partnership shall promptly deliver to each Partner a copy of the federal
     income tax return for the Partnership as filed with the appropriate taxing
     authorities and a copy of any material state and local income tax return as
     filed.

(d)         Tax Audits.

(i)  Federal Tax Matters.  The Partnership is authorized to make such filings
     with the IRS as may be required to designate Lyondell GP as the Tax Matters
     Partner.  The Tax Matters Partner, as an authorized representative of the
     Partnership, shall direct the defense of any claims made by the IRS to the
     extent that such claims relate to the adjustment of Partnership items at
     the Partnership level.  The Tax Matters Partner shall promptly deliver to
     each Partner a copy of all notices, communications, reports or writings of
     any kind (including, without limitation, any notice of beginning of
     administrative proceedings or any report explaining the reasons for a
     proposed adjustment) received from the IRS relating to or potentially
     resulting in an adjustment of Partnership items, as well as any other
     information requested by a Partner that is commercially reasonable to
     request.  The Tax Matters Partner shall, diligently and in good faith
     contest any proposed adjustment of a Partnership item which principally
     affects the Partners at the administrative and judicial levels, including,
     if appropriate, appealing any adverse judicial decision.  The Tax Matters
     Partner shall keep each Partner advised of all material developments with
     respect to any 

                                      11
<PAGE>
 
     proposed adjustment which comes to its attention. All costs incurred by the
     Tax Matters Partner in performing under this subsection (d) shall be paid
     by the Partnership. Without first obtaining the written consent of all
     Partners, the Tax Matters Partner shall not, with respect to any proposed
     adjustment of a Partnership item which materially and adversely affects any
     Partner, (i) enter into a settlement agreement which purports to bind
     Partners other than the Tax Matters Partner (including, without limitation,
     any stipulation consenting to an entry of decision by the Tax Court), or
     (ii) enter into an agreement or stipulation extending the statute of
     limitations; provided, however, that if any Partner declines to give its
     written consent, then the dispute shall be resolved by the Partnership
     Governance Committee, which may direct the Tax Matters Partner to enter
     into such agreements notwithstanding the objection of an individual
     Partner.

(ii) State and Local Tax Matters.  The Partnership shall promptly deliver to
     each Partner a copy of all notices, communications, reports or writings of
     any kind with respect to income or similar taxes received from any state or
     local taxing authority relating to the Partnership which might, in the
     judgment of the Tax Matters Partner, materially and adversely affect any
     Partner, and shall keep each Partner advised of all material developments
     with respect to any proposed adjustment of Partnership items which come to
     its attention.

(iii)       Continuation of Rights.  Each Partner shall continue to have the
rights described in this subsection (d) with respect to tax matters relating to
any period during which it was a Partner, whether or not it is a Partner at the
time of the tax audit or contest.

(e)  Tax Rulings.  No Person other than the Tax Matters Partner shall request an
     administrative ruling (or similar administrative procedures) from any
     taxing authority with respect to any tax issue relating to the Partnership
     or affecting the taxation of any other Partner unless such Person shall
     have received written authorization from the Tax Matters Partner and any
     such other Partner to make such request.

5.7         Delegation.  The Partners agree that all of the tasks to be
performed under this Section (other than serving as Tax Matters Partner) may be
delegated to employees and consultants of the Partnership.


                                   SECTION 6
                                   MANAGEMENT

6.1         Partnership Governance Committee.

(a)  The General Partners hereby establish a committee (the "Partnership
     Governance Committee") to manage and control the business, property and
     affairs of the Partnership, including the determination and implementation
     of the Partnership's strategic direction.  The Partnership Governance
     Committee (on behalf of the Partners) shall have (i) the full authority of
     the General 

                                      12
<PAGE>
 
     Partners to exercise all of the powers of the Partnership and
     (ii) full control over the business, property and affairs of the
     Partnership.  Except to the extent set forth in this Agreement, the
     Partnership Governance Committee shall have full, exclusive and complete
     discretion to manage and control the business, property and affairs of the
     Partnership, to make all decisions affecting the business, property and
     affairs of the Partnership and to take all such actions as it deems
     necessary, appropriate, convenient or incidental to accomplish the purpose
     of the Partnership as set forth in Section 1.4 (as such purpose may be
     expanded in accordance with Section 6.7(i)).

(b)  The Partnership Governance Committee shall act exclusively by means of
     Partnership Governance Committee Action.  As used in this Agreement,
     "Partnership Governance Committee Action" means any action which the
     Partnership Governance Committee is authorized and empowered to take in
     accordance with this Agreement and the Act and which is taken by the
     Partnership Governance Committee either (i) by action taken at a meeting of
     the Partnership Governance Committee duly called and held in accordance
     with this Agreement or (ii) by a formal written consent complying with the
     requirements of Section 6.5(f).  In no event shall the Partnership
     Governance Committee be authorized to act other than by Partnership
     Governance Committee Action, and any action or purported action by the
     Partnership Governance Committee (including any authorization, consent,
     approval, waiver, decision or vote) not constituting a Partnership
     Governance Committee Action shall be null and void and of no force and
     effect.  Each Partnership Governance Committee Action shall be binding on
     the Partnership.

(c)  The Partnership Governance Committee shall adopt policies and procedures,
     not inconsistent with this Agreement (including Section 6.7) or  the Act,
     governing financial controls and legal compliance, including delegations of
     authority (and limitations thereon) to the officers of the Partnership as
     permitted hereby.  Such policies and procedures may be revised or revoked
     (in a manner consistent with this Agreement and the Act) from time to time
     as determined by the Partnership Governance Committee.  To the extent any
     authority is not delegated to officers of the Partnership in this Agreement
     or in accordance with Partnership Governance Committee Action, it shall
     remain with the Partnership Governance Committee.

6.2         Limitations on Authority of General Partners.  Except as expressly
set forth in this Agreement, each General Partner agrees to exercise its
authority to manage and control the Partnership only through Partnership
Governance Committee Action.  No General Partner has the authority (and each
General Partner agrees not to exercise, or purport or attempt to exercise any
authority) (i) to act for or incur, create or assume any obligation, liability
or responsibility on behalf of the Partnership or any other Partner, (ii) to
execute any documents on behalf of, or otherwise bind, or purport or attempt to
bind, the Partnership or (iii) to otherwise transact any business in the
Partnership's name, in each case except pursuant to Partnership Governance
Committee Action.

6.3         Lack of Authority of Persons Other Than General Partners and
Officers.  Except as expressly set forth in this Agreement, no Person or Persons
other than (i) the General Partners, acting through the Partnership Governance
Committee, and (ii) the officers of the Partnership appointed in accordance with
this Agreement and acting as agents or employees, as applicable, of the
Partnership in conformity with this Agreement and any applicable Partnership
Governance 

                                      13
<PAGE>
 
Committee Action, shall be authorized (a) to exercise the powers of
the Partnership, (b) to manage the business, property and affairs of the
Partnership or (c) to contract for, or incur on behalf of, the Partnership any
debts, liabilities or other obligations.

6.4         Composition of Partnership Governance Committee.

(a)  The Partnership Governance Committee shall consist of six Representatives
     and each General Partner shall designate three Representatives (each a
     "Representative").  All the Representatives of both General Partners shall
     together constitute the Partnership Governance Committee.

(b)  Each General Partner may designate one or more individuals (each an
     "Alternate") who (i) shall be authorized, in the event a Representative is
     absent from any meeting of the Partnership Governance Committee (and in the
     order of succession designated by the General Partner so designating the
     Alternates), to attend such meeting in the place of, and as substitute for,
     such Representative and (ii) shall be vested with all the powers to take
     action on behalf of such General Partner which the absent Representative
     could have exercised at such meeting.  The term "Representative," when used
     herein with reference to any Representative who is absent from a meeting of
     the Partnership Governance Committee, shall mean and refer to any Alternate
     attending such meeting in place of such absent Representative.

(c)  On or before the date hereof, each General Partner shall have delivered to
     the other General Partner a written notice (i) designating the three
     persons to serve as such General Partner's initial Representatives and (ii)
     designating the person or persons, if any, who are to serve as initial
     Alternates and their order of succession.

(d)  Each General Partner may, in its sole discretion and by written notice
     delivered to the other General Partner and the Partnership at any time or
     from time to time, remove or replace one or more of its Representatives or
     change one or more of its Alternates.  If a Representative or Alternate
     dies, resigns or becomes disabled or incapacitated, the General Partner
     that designated such Representative or Alternate, as the case may be, shall
     promptly designate a replacement.  Each Representative and each Alternate
     shall serve until replaced by the General Partner that designated such
     Representative or Alternate, as the case may be.

(e)  Copies of all written notices designating Representatives and Alternates
     shall be delivered to the Secretary and shall be placed in the Partnership
     minute books, but the failure to deliver a copy of any such notice to the
     Secretary shall not affect the validity or effectiveness of such notice or
     the designation described therein.

(f)  Each Representative, in his capacity as such, shall be the agent of the
     General Partner that designated such Representative.  Accordingly, (i) each
     Representative, as such, shall act (or refrain from acting) with respect to
     the business, property and affairs of the Partnership solely in accordance
     with the wishes of the General Partner that designated such Representative
     and (ii) no Representative, as such, shall owe (or be deemed to owe) any
     duty (fiduciary or otherwise) to the 

                                      14
<PAGE>
 
     Partnership or to any General Partner other than the General Partner that
     designated such Representative; provided, however, that nothing in this
     Agreement is intended to or shall relieve or discharge any Representative
     or General Partner from liability to the Partnership or the Partners on
     account of any fraudulent or intentional misconduct of such Representative.
     Nothing in this Section 6.4(f) shall limit the duty owed to the Partnership
     by any person acting in his capacity as an officer of the Partnership
     (including any such officer who is also a Representative).

(g)  Representatives shall not receive from the Partnership any compensation for
     their service or any reimbursement of expenses for attendance at meetings
     of the Partnership Governance Committee.

6.5         Partnership Governance Committee Meetings.

(a)  Regular meetings of the Partnership Governance Committee shall be held at
     such times and at such places as shall from time to time be determined in
     advance and committed to a written schedule by the Partnership Governance
     Committee.  The first regular meeting of the Partnership Governance
     Committee during January of each fiscal year shall be deemed to be the
     "Annual Meeting."  The Secretary shall deliver by commercial courier
     service or other hand delivery or transmit by facsimile transmission (with
     proof of confirmation from the transmitting machine), an agenda for each
     regular meeting to the Representatives at least five Business Days prior to
     such meeting.  Each agenda for a regular meeting shall specify, to a
     reasonable degree, the business to be transacted at such meeting.  Subject
     to Section 6.6, at any regular meeting of the Partnership Governance
     Committee at which a quorum is present, any and all business of the
     Partnership may be transacted.

(b)  Special meetings of the Partnership Governance Committee may be called by
     any Representative by delivering by commercial courier service or other
     hand delivery or transmitting by facsimile transmission (with proof of
     confirmation from the transmitting machine), written notice of a special
     meeting to each of the other Representatives at least two Business Days
     before such meeting.  Each notice of a special meeting shall specify, to a
     reasonable degree, the business to be transacted at, or the purpose of,
     such meeting.  Notice of any special meeting may be waived before or after
     the meeting by a written waiver of notice signed by the Representative
     entitled to notice.  A Representative's attendance at a special meeting
     shall constitute a waiver of notice unless the Representative states at the
     beginning of the meeting his objection to the transaction of business
     because the meeting was not lawfully called or convened.  Special meetings
     of the Partnership Governance Committee shall be held at the Partnership's
     offices (or at such other place or in such other manner as the
     Representatives shall agree) at such time as may be stated in the notice of
     such meeting.

(c)  One Representative of each General Partner shall serve as a co-chair of
     each meeting (regular and special) of the Partnership Governance Committee.
     Either co-chair may instruct the Secretary to include one or more items on
     a meeting agenda and neither co-chair nor the Secretary may delete or
     exclude an agenda item proposed by the other.

                                      15
<PAGE>
 
(d)  Following each meeting of the Partnership Governance Committee, the
     Secretary shall promptly draft and distribute minutes of such meeting to
     the Representatives for approval at the next meeting, and after such
     approval shall retain the minutes in the Partnership minute books.

(e)  Representatives, at their discretion, may participate in or hold regular or
     special meetings of the Partnership Governance Committee by means of a
     telephone conference or any comparable device or technology by which all
     individuals participating in the meeting may hear each other, and
     participation in such a meeting shall constitute presence in person at such
     meeting.

(f)  Any action required or permitted to be taken at a meeting of the
     Partnership Governance Committee may be taken without a meeting if a
     consent in writing, setting forth the action so taken, shall be signed by
     at least two Representatives of each General Partner, and such consent
     shall have the same force and effect as a duly conducted vote of the
     Partnership Governance Committee.  A counterpart of each such consent to
     action shall be delivered promptly to each of the Representatives and to
     the Secretary for placement in the minute books of the Partnership, but the
     failure to deliver a counterpart of any such consent to action to the
     Secretary shall not affect the validity or effectiveness of such consent to
     action.

6.6         Partnership Governance Committee Quorum and General Voting
Requirement.

(a)  The presence of at least two Representatives (including any duly present
     Alternates) of Lyondell GP shall constitute a quorum of the Partnership
     Governance Committee for the transaction of business and the taking of
     appropriate Partnership Governance Committee Actions at any meeting;
     provided, however, that the presence at such meeting of at least two
     Representatives (including any duly present Alternates) from each General
     Partner shall be necessary for the taking of any action described in
     Section 6.7; and provided, further, that no Partnership Governance
     Committee Actions can be taken at any meeting with respect to any matter
     that was not reflected on an agenda for such meeting that was delivered in
     accordance with Section 6.5 unless at least one Representative of each
     General Partner is present.  No Partnership Governance Committee Action may
     be taken at any meeting at which a quorum is not present.

(b)  Except as otherwise provided in Section 6.7 or elsewhere in this Agreement,
     the approval of two or more Representatives acting for Lyondell GP will be
     sufficient for the Partnership Governance Committee to take any Partnership
     Governance Committee Action and in such case the Partnership shall be
     authorized to take such action without the consent of any other Person.

6.7         Partnership Governance Committee Unanimous Voting Requirements.
Unless and until two or more Representatives of Lyondell GP and two or more
Representatives of Millennium GP have given their approval (in which event a
Partnership Governance Committee Action is hereby authorized without the need
for the consent of any other Person), no Partnership Governance Committee Action
will be deemed for any purpose to have been taken at any Partnership Governance
Committee meeting that would cause or permit the Partnership or any subsidiary
thereof (or any Person acting in the name or on behalf of any of them) directly
or indirectly to take (or commit to take), and neither the Partnership or any
subsidiary thereof nor any person acting in the name or on 

                                      16
<PAGE>
 
behalf of any of them directly or indirectly may take or commit to take, any of
the actions described below in this subsection (whether in a single transaction
or series of related transactions):

(i)  to cause the Partnership, directly or indirectly, to engage, participate or
     invest in any business outside the scope of its business as described in
     Section 1.4;

(ii) to approve any Strategic Plan, as well as any amendments or updates thereto
     (including the annual updates provided for in Section 8.1);

(iii) to authorize any disposition of assets having a fair market value
      exceeding $30 million in any one transaction or a series of related
      transactions not contemplated in an approved Strategic Plan;

(iv) to authorize any acquisition of assets or any capital expenditure exceeding
     $30 million that is not contemplated in an approved Strategic Plan;

(v)  to require capital contributions to the Partnership (other than
     contributions contemplated by the Asset Contribution Agreements or an
     approved Strategic Plan or to achieve or maintain compliance with any HSE
     Law) within any fiscal year if the total of such contributions required
     from the Partners within that year would exceed $100 million or the total
     of such contributions required from the Partners within that year and the
     immediately preceding four years would exceed $300 million;

(vi) to authorize the incurrence of debt for borrowed money unless (x) such debt
     is contemplated by clause (vii) below, (y) after giving effect to the
     incurrence of such debt (and any related transactions) the Partnership
     would be expected to have an "investment grade" debt rating by Moody's
     Investor Services Inc. and Standard & Poor's Corporation or (z) such debt
     is incurred to refinance the public or bank debt assumed or incurred by the
     Partnership as contemplated by the Master Transaction Agreement or to
     refinance any such refinancing debt, and in the case of each of (y) and
     (z), the agreement relating to such debt does not provide that the Transfer
     by a Partner of its Units (or a change of control with respect to any
     Partner or any of its Affiliates) would constitute a default thereunder,
     otherwise accelerate the maturity thereof or give the lender or holder any
     "put rights" or similar rights with respect thereto; provided, however,
     that notwithstanding the foregoing, the provisions of Section 6.7(xxi), if
     applicable, must be satisfied with respect to any refinancing;

(vii) to make borrowings under the Partnership's bank credit facility and/or its
      uncommitted lines of credit at any time if the aggregate principal amount
      of such borrowings outstanding at such time would exceed $1.25 billion;

(viii) to enter into interest rate protection or other hedging agreements (other
       than hydrocarbon hedging agreements in the ordinary course);

                                      17
<PAGE>
 
(ix) to enter into any capitalized lease or similar off-balance sheet financing
     arrangements involving payments (individually or in the aggregate) by it in
     excess of $30 million in any fiscal year;

(x)  to cause the Partnership or any subsidiary of the Partnership to issue,
     sell, redeem or acquire any Units or other equity securities (or any rights
     to acquire, or any securities convertible into or exchangeable for, Units
     or other equity securities);

(xi) to make Partnership cash distributions in excess of Available Net Operating
     Cash or to make non-cash distributions (except as contemplated by Section
     12);

(xii)  to appoint or discharge Executive Officers (other than the CEO),
       based on the recommendation of the CEO;

(xiii) to approve material compensation and benefit plans and
       policies, material employee policies and material collective bargaining
       agreements for the Partnership's employees;

(xiv)  to initiate or settle any litigation or governmental proceedings if the
       effect thereof would be material to the financial condition of the
       Partnership;

(xv) to initially select or to change the independent accountants for the
     Partnership;

(xvi)  to change the Partnership's method of accounting as adopted pursuant to
       Section 5.2 or to change the Partnership's method of accounting as
       provided in Section 5.5 or to make the elections referred to in Section
       5.6(b)(i)(E);

(xvii)  to create or change the authority of any Auxiliary Committee;

(xviii)  to merge, consolidate or convert the Partnership or any subsidiary
         thereof with or into any other entity (other than a Wholly Owned
         Subsidiary of the Partnership);

(xix)    to file a petition in bankruptcy or seeking any reorganization,
         liquidation or similar relief on behalf of the Partnership or any
         subsidiary; or to consent to the filing of a petition in bankruptcy
         against the Partnership or any subsidiary; or to consent to the
         appointment of a receiver, custodian, liquidator or trustee for the
         Partnership or any subsidiary or for all or any substantial portion of
         their property;

(xx) to exercise any power or right described in Section 6.8(a)(i) or (ii) with
     respect to a Conflict Circumstance involving (a) LYONDELL-CITGO Refining
     Company Ltd., its successors or assigns, (b) Lyondell Methanol Company,
     L.P., its successors or assigns or (c) any other Affiliate of either of
     Lyondell GP or Millennium GP if such Affiliate's actions with respect to
     such Conflict Circumstance are not controlled by Lyondell or Millennium,
     respectively; and

                                      18
<PAGE>
 
            (xxi)  (a) prior to the seventh anniversary of the Closing Date, to
     repay any Millennium America Guaranteed Debt, other than through
     refinancing or (b) to refinance any Millennium America Guaranteed Debt
     prior to the seventh anniversary of the Closing Date if any of the
     principal of the debt refinancing such Millennium America Guaranteed Debt
     would be due and payable after the seventh anniversary of the Closing Date.

6.8         Control of Interested Partner Issues.

(a)  Notwithstanding anything to the contrary contained in this Agreement, with
     respect to any Conflict Circumstance (other than a Conflict Circumstance
     described in Section 6.7(xx), which shall be governed by Section 6.7), the
     Nonconflicted General Partner (through its Representatives) shall, subject
     to Section 6.8(b), have the sole and exclusive power and right for and on
     behalf, and at the sole expense, of the Partnership (i) to control all
     decisions, elections, notifications, actions, exercises or nonexercises and
     waivers of all rights, privileges and remedies provided to, or possessed
     by, the Partnership with respect to a Conflict Circumstance and (ii) in the
     event of any potential, threatened or asserted claim, dispute or action
     with respect to a Conflict Circumstance, to retain and direct legal counsel
     and to control, assert, enforce, defend, litigate, mediate, arbitrate,
     settle, compromise or waive any and all such claims, disputes and actions.
     Accordingly, Partnership Governance Committee Action with respect to a
     Conflict Circumstance (other than a Conflict Circumstance described in
     Section 6.7(xx), which shall be governed by Section 6.7) shall require the
     approval of two Representatives of the Nonconflicted General Partner.  Each
     General Partner shall, and shall cause its Affiliates to, take all such
     actions, execute all such documents and enter into all such agreements as
     may be necessary or appropriate to facilitate or further assure the
     accomplishment of this Section.

(b)  The Nonconflicted General Partner, in exercising its control, power and
     rights pursuant to this Section, shall act in good faith and in a manner it
     believes to be in the best interests of the Partnership.  The Nonconflicted
     General Partner shall act through its Representatives, and the approval of
     two Representatives acting for the Nonconflicted General Partner will be
     sufficient for the Nonconflicted General Partner (and therefore the
     Partnership Governance Committee on behalf of the Partnership) to take any
     action in respect of the relevant Conflict Circumstance.  The Conflicted
     General Partner (or its Affiliates) shall have the right to deal with the
     Partnership and with the Nonconflicted General Partner on an arm's-length
     basis and in a manner it believes to be in its own best interests, but in
     any event must deal with them in good faith.

6.9         Auxiliary Committees.

(a)  From time to time, the Partnership Governance Committee may, by Partnership
     Governance Committee Action, designate one or more committees ("Auxiliary
     Committees") or disband any Auxiliary Committee.  Each Auxiliary Committee
     shall (i) operate under the specific authority delegated to it by the
     Partnership Governance Committee (consistent with Section 6.7) for the
     purpose of assisting the Partnership Governance Committee in managing (on
     behalf of the General Partners) the business, property and affairs of the
     Partnership and (ii) report to the Partnership Governance Committee.

                                      19
<PAGE>
 
(b)  Each General Partner shall have the right to appoint an equal number of
     members on each Auxiliary Committee.  Auxiliary Committee members may (but
     need not) be members of the Partnership Governance Committee.  No Auxiliary
     Committee member shall be compensated or reimbursed by the Partnership for
     service as a member of such Auxiliary Committee.

(c)  Each Partnership Governance Committee Action designating an Auxiliary
     Committee shall be in writing and shall set forth  (i) the name of such
     Auxiliary Committee, (ii) the number of members and (iii) in such detail as
     the Partnership Governance Committee deems appropriate, the purposes,
     powers and authorities (consistent with Section 6.7) of such Auxiliary
     Committee; provided, however, that in no event shall any Auxiliary
     Committee have any powers or authority in reference to amending this
     Agreement, adopting an agreement of merger, consolidation or conversion of
     the Partnership, authorizing the sale, lease or exchange of all or
     substantially all of the property and assets of the Partnership,
     authorizing a dissolution of the Partnership or declaring a distribution.
     Each Auxiliary Committee shall keep regular minutes of its meetings and
     promptly deliver the same to the Partnership Governance Committee.

6.10        Certain Limitations on Partner Representatives.  No Representative
or Alternate of a Partner who, as an officer, director or employee of such
Partner or any of its Affiliates, participates in material operational decisions
by such Partner or Affiliate regarding a business or operation of such Partner
or Affiliate that competes with a business or operation of the Partnership or of
the other Partner or its Affiliates, or that competes with a Business
Opportunity offered pursuant to Section 9.3(c) or (d), shall receive or have
access to any competitively sensitive information regarding the competing
business of the Partnership or of the other Partner or its Affiliates or such
Business Opportunity, nor shall such Representative or Affiliate participate in
any decision of the Partnership Governance Committee relating to such business
or operation of the Partnership or the other Partner or its Affiliates or such
Business Opportunity.


                                   SECTION 7
                             OFFICERS AND EMPLOYEES

7.1         Partnership Officers.

(a)  The Partnership Governance Committee may select natural persons who are (or
     upon becoming an officer will be) agents or employees of the Partnership to
     be designated as officers of the Partnership, with such titles as the
     Partnership Governance Committee shall determine.

(b)  The executive officers of the Partnership shall consist of a Chief
     Executive Officer ("CEO"), and others as determined from time to time by
     Partnership Governance Committee (collectively, the "Executive Officers").

(c)  The Partnership Governance Committee also shall appoint a Secretary and may
     appoint such other officers and assistant officers and agents as may be
     deemed necessary or desirable 

                                      20
<PAGE>
 
     and such persons shall perform such duties in the management of the
     Partnership as may be provided in this Agreement or as may be determined by
     Partnership Governance Committee Action.

(d)  The Partnership Governance Committee may leave unfilled any offices except
     those of CEO and Secretary.  Two or more offices may be held by the same
     person except that the same person may not hold the offices of CEO and
     Secretary.

7.2         Selection and Term of Executive Officers.

(a)  The initial Executive Officers are listed on Appendix C.

(b)  The CEO shall hold office for a five-year term, subject to the CEO's
     earlier death, resignation or removal.  Upon the expiration of such term or
     earlier vacancy, Lyondell GP shall designate the CEO, provided that such
     person shall be reasonably acceptable to Millennium GP.  The CEO shall not
     be required to be an employee of the Partnership.

(c)  Each Executive Officer (other than the CEO) shall hold office until his or
     her death, resignation or removal.  Upon the death, resignation or removal
     of an Executive Officer, or the creation of a new Executive Officer
     position, the CEO may nominate a person to fill the vacancy, which shall be
     subject to Partnership Governance Committee approval.  Executive Officers
     shall not be required to be employees of the Partnership.  Any Executive
     Officer also may serve as an officer or employee of any Partner or
     Affiliate of a Partner.

7.3         Removal of Executive Officers.
     (a) The CEO may be removed, at any time, by Partnership Governance
Committee Action taken pursuant to Section 6.6, with or without cause, whenever
in the judgment of the Partnership Governance Committee the best interests of
the Partnership would be served thereby.

     (b) Any Executive Officer (other than the CEO), or any other officer or
agent may be removed, at any time, by Partnership Governance Committee Action
taken pursuant to Section 6.7(xii), with or without cause, upon the
recommendation of the CEO, whenever in the judgment of the Partnership
Governance Committee the best interests of the Partnership would be served
thereby.

     (c) Notwithstanding anything to the contrary in Sections 7.3(a) and 7.3(b),
either General Partner may, by action of two or more of its Representatives,
remove from office any Executive Officer who takes or causes the Partnership to
take any action described in Section 6.7 that has not been approved by two or
more Representatives of Lyondell GP and two or more Representatives of
Millennium GP as contemplated by Section 6.7.  Any such removal shall be
effected by delivery by such Representatives of written notice of such removal
to such Executive Officer and to the Representatives of the other General
Partner; provided that such removal shall not be effective if such action is
rescinded or cured (to the reasonable satisfaction of the General Partner who
has delivered such notice) promptly after such notice is delivered.

                                      21
<PAGE>
 
7.4         Duties.

(a)  Each officer or employee of the Partnership shall owe to the Partnership,
     but not to any Partner, all such duties (fiduciary or otherwise) as are
     imposed upon such an officer or employee of a Delaware corporation.
     Without limitation of the foregoing, each officer and employee in any
     dealings with a Partner shall have a duty to act in good faith and to deal
     fairly; provided, that, no officer shall be liable to the Partnership or to
     any Partner for his or her good faith reliance on the provisions of this
     Agreement.  Notwithstanding the foregoing, it is understood that any
     officer or employee of the Partnership who is also a Representative of a
     General Partner shall, in his capacity as a Representative, owe no duty
     (fiduciary or otherwise) to any Person other than such General Partner.

(b)  The policies and procedures of the Partnership adopted by the Partnership
     Governance Committee may set forth the powers and duties of the officers of
     the Partnership to the extent not set forth in or inconsistent with this
     Agreement.  The officers of the Partnership shall have such powers and
     duties, except as modified by the Partnership Governance Committee, as
     generally pertain to their respective offices in the case of a publicly
     held Delaware corporation, as well as other such powers and duties as from
     time to time may be conferred by the Partnership Governance Committee and
     by this Agreement.  The CEO and the other officers and employees of the
     Partnership shall develop and implement management and other policies and
     procedures consistent with this Agreement and the general policies and
     procedures established by the Partnership Governance Committee.

(c)  Notwithstanding any other provision of this Agreement, no Partner,
     Representative, officer, employee or agent of the Partnership shall have
     the power or authority, without specific authorization from the Partnership
     Governance Committee, to undertake any of the following:

          (i)  to do any act which contravenes (or otherwise is inconsistent
               with) this Agreement or which would make it impracticable or
               impossible to carry on the Partnership's business;

          (ii) to confess a judgment against the Partnership;

          (iii)  to possess Partnership property other than in the ordinary
               conduct of the Partnership's business; or

          (iv) to take, or cause to be taken, any of the actions described in
               Section 6.7.

7.5       CEO.  Subject to the terms of this Agreement, the CEO shall have
general authority and discretion comparable to that of a chief executive officer
of a publicly held Delaware corporation of similar size to direct and control
the business and affairs of the Partnership, including without limitation its
day-to-day operations in a manner consistent with the Annual Budget and the most
recently approved Strategic Plan.  The CEO shall take steps to implement all
orders and resolutions of the Partnership Governance Committee or, as
applicable, any Auxiliary Committee.  The CEO 

                                      22
<PAGE>
 
shall be authorized to execute and deliver, in the name and on behalf of the
Partnership, (i) contracts or other instruments authorized by Partnership
Governance Committee Action and (ii) contracts or instruments in the usual and
regular course of business (not otherwise requiring Partnership Governance
Committee Action), except in cases when the execution and delivery thereof shall
be expressly delegated by the Partnership Governance Committee to some other
officer or agent of the Partnership, and, in general, shall perform all duties
incident to the office of CEO as well as such other duties as from time to time
may be assigned to him or her by the Partnership Governance Committee or as are
prescribed by this Agreement.

7.6       Other Officers.  The President (if any) and the Vice Presidents shall
perform such duties as may, from time to time, be assigned to them by the
Partnership Governance Committee or by the CEO.  In addition, at the request of
the CEO, or in the absence or disability of the CEO, the President (if any) or
any Vice President, in any order determined by the Partnership Governance
Committee, temporarily shall perform all (or if limited through the scope of the
delegation, some of) the duties of the CEO, and, when so acting, shall have all
the powers of, and be subject to all restrictions upon, the CEO.

7.7       Secretary.  The Secretary shall keep the minutes of all meetings (and
copies of written records of action taken without a meeting) of the Partnership
Governance Committee in minute books provided for such purpose and shall see
that all notices are duly given in accordance with the provisions of this
Agreement.  The Secretary shall be the custodian of the records and of the seal,
if any.  The Secretary shall have general charge of books and papers of the
Partnership as the Partnership Governance Committee may direct and, in general,
shall perform all duties and exercise all powers incident to the office of
Secretary and such other duties and powers as the Partnership Governance
Committee or the CEO from time to time may assign to or confer upon the
Secretary.

7.8       Salaries.  Salaries or other compensation of the other Executive
Officers of the Partnership shall be established by the CEO consistent with
plans approved by the Partnership Governance Committee.  Except as approved by
the Partnership Governance Committee, all fees and compensation of the officers
and employees of the Partnership other than the CEO with respect to their
services as such officers and employees shall be payable solely by the
Partnership and no Partner or its Affiliates shall pay (or offer to pay) any
such fees or compensation to any officer or employee, except to the extent that
the Partnership shall have agreed with a Partner or one of its Affiliates
pursuant to a separate agreement that a portion of the compensation of such
officer or employee shall be paid by such Partner or Affiliate.

7.9       Delegation.  The Partnership Governance Committee may delegate
temporarily the powers and duties of any officer of the Partnership, in case of
absence or for any other reason, to any other officer of the Partnership, and
may authorize the delegation by any officer of the Partnership of any of such
officer's powers and duties to any other officer or employee of the Partnership,
subject to the general supervision of such officer.

7.10      Employee Hirings.  With the prior approval of the other General
Partner, which approval shall not be unreasonably withheld, a General Partner
(or its Affiliates) shall be entitled to 

                                      23
<PAGE>
 
hire specific employees of the Partnership and specific individuals who had been
employed by the Partnership within the previous year. With the prior approval of
the relevant General Partner, which approval shall not be unreasonably withheld,
the Partnership shall be entitled to hire specific employees of either General
Partner (or its Affiliates) and specific individuals who had been employed by
either General Partner (or its Affiliates) within the previous year. Without
such approval, (i) the General Partners (and their Affiliates) will not hire
employees of the Partnership or individuals who had been employed by the
Partnership within the previous year and (ii) the Partnership will not hire
employees of either General Partner (or its Affiliates) or individuals who had
been employed by either General Partner (or its Affiliates) within the previous
year.

7.11      General Authority.  Persons dealing with the Partnership are entitled
to rely conclusively on the power and authority of each of the officers as set
forth in this Agreement.  In no event shall any Person dealing with any officer
with respect to any business or property of the Partnership be obligated to
ascertain that the terms of this Agreement have been complied with, or be
obligated to inquire into the necessity or expedience of any act or action of
the officer; and every contract, agreement, deed, mortgage, security agreement,
promissory note or other instrument or document executed by the officer with
respect to any business or property of the Partnership shall be conclusive
evidence in favor of any and every Person relying thereon or claiming thereunder
that (i) at the time of the execution and/or delivery thereof, this Agreement
was in full force and effect, (ii) the instrument or document was duly executed
in accordance with the terms and provisions of this Agreement and is binding
upon the Partnership, and (iii) the officer was duly authorized and empowered to
execute and deliver any and every such instrument or document for and on behalf
of the Partnership.


                                   SECTION 8
                   STRATEGIC PLANS, ANNUAL BUDGETS AND LOANS

8.1       Strategic Plan.

(a)  The Partnership shall be managed in accordance with a five-year strategic
     business plan (the "Strategic Plan") which shall be updated annually under
     the direction of the CEO and presented for approval by the Partnership
     Governance Committee pursuant to Section 6.7 no later than 90 days prior to
     the start of the first fiscal year covered by the updated plan.

(b)  The Strategic Plan shall establish the strategic direction of the
     Partnership, including plans relating to capital maintenance and
     enhancement, geographic expansion, acquisitions and dispositions, new
     product lines, technology, long-term supply and customer arrangements,
     internal and external financing, environmental and legal compliance, and
     plans, programs and policies relating to compensation and industrial
     relations.  The Strategic Plan shall include projected income statements,
     balance sheets and cash flow statements, including the expected timing and
     amounts of capital contributions and cash distributions.  The format and
     level of detail of each Strategic Plan shall be consistent with that of the
     initial Strategic Plan agreed to by the Partners on or prior to the Closing
     Date or the Strategic Plan most recently approved pursuant to Section 6.7.

                                      24
<PAGE>
 
8.2       Annual Budget.

(a)  The Executive Officers of the Partnership shall prepare an Annual Budget
     (each, an "Annual Budget") for each fiscal year, including an Operating
     Budget and Capital Expenditure Budget; provided that each Annual Budget
     shall be consistent with the information for such fiscal year included in
     the Strategic Plan most recently approved pursuant to Section 6.7; and
     provided, further, that unless provided otherwise in the most recently
     approved Strategic Plan, the Annual Budget (including any Annual Budget
     prepared under Section 8.2(b)) shall utilize a format and provide a level
     of detail consistent with the Partnership's initial Annual Budget.  The
     Annual Budget for each year shall be submitted to the Partnership
     Governance Committee for approval at least 60 days prior to the start of
     the fiscal year covered by such budget.  Each Annual Budget shall
     incorporate (i) a projected income statement, balance sheet and a cash flow
     statement, (ii) the amount of any corresponding cash deficiency or surplus
     and (iii) the estimated amount, if any, and expected timing for all
     required capital contributions.  Each proposed Annual Budget shall be
     prepared on a basis consistent with the Partnership's financial statements.

(b)  If for any fiscal year the Partnership Governance Committee has failed to
     approve an updated Strategic Plan, then, subject to Section 8.5, for such
     year and each subsequent year prior to approval of an updated Strategic
     Plan, the Executive Officers of the Partnership shall prepare (and promptly
     furnish to the Partnership Governance Committee) the Annual Budget
     consistent with the projections and other information for that year
     included in the Strategic Plan most recently approved pursuant to Section
     6.7; provided, however, that the CEO, acting in good faith, shall be
     entitled to modify any such Annual Budget in order to satisfy current
     contractual and compliance obligations and to account for other changes in
     circumstances resulting from the passage of time or the occurrence of
     events beyond the control of the Partnership; provided, further, that the
     CEO shall not be authorized to cause the Partnership to proceed with
     capital expenditures to accomplish capital enhancement projects except to
     the extent that such expenditures would enable the Partnership to continue
     or complete any such capital project reflected in the last Strategic Plan
     that was approved by the Partnership Governance Committee pursuant to
     Section 6.7.

(c)  Each "Operating Budget" shall constitute an estimate for each applicable
     period of all operating income, which shall include expenses required to
     maintain, repair and restore to good and usable condition the Partnership's
     assets.

(d)  Each "Capital Expenditure Budget" shall constitute an estimate for the
     applicable period of the capital expenditures required to (i) accomplish
     capital enhancement projects included in the most recently approved
     Strategic Plan, (ii) maintain and preserve the Partnership's assets in good
     operating condition and repair and (iii) achieve or maintain compliance
     with any HSE Law.

8.3       Funding of Partnership Expenses.  All Partnership expenses (both
operating and capital expenses), regardless of whether included in any Strategic
Plan or Annual Budget, shall be funded from operating cash flows or authorized
borrowings under available lines of credit, unless otherwise agreed by the
Partnership Governance Committee.  Subject to the limitations of Section 6.7(v),
if applicable, to the extent that the CEO determines at any time that funds are
needed 

                                      25
<PAGE>
 
to fund Partnership operations, the CEO may issue a Funding Notice to the
Limited Partners calling for an additional capital contribution.  The Limited
Partners will take all steps necessary to cause compliance with such Funding
Notice.

8.4       Implementation of Budgets and Discretionary Expenditures by CEO.

(a)  After a Strategic Plan and an Annual Budget have been approved by the
     Partnership Governance Committee (or an Annual Budget has been developed in
     accordance with Section 8.2(b)), the CEO will be authorized, without
     further action by the Partnership Governance Committee, to cause the
     Partnership to make expenditures consistent with such Strategic Plan and
     Annual Budget; provided, however, that all internal control policies and
     procedures, including those regarding the required authority for certain
     expenditures, shall have been followed.

(b)  In any emergency, the CEO or the CEO's designee shall be authorized to take
     such actions and to make such expenditures as may be reasonably necessary
     to react to the emergency, regardless of whether such expenditures have
     been included in an approved Strategic Plan or Annual Budget.  Promptly
     after learning of an emergency, the CEO or such designee shall notify the
     Representatives of the nature of the emergency and the response that has
     been made, or is committed or proposed to be made, with respect to the
     emergency.

8.5       Strategic Plan Deadlock.  If the Partnership Governance Committee has
not agreed upon and approved an updated Strategic Plan, as contemplated by
Sections 6.7 and 8.1, by such date as is 12 months after the beginning of the
first fiscal year that would have been covered by such plan, then the General
Partners shall submit their disagreements to mediation by a Neutral.  If the
General Partners are unable to agree upon a mutually acceptable Neutral within
30 days after a nomination of a Neutral is made by one General Partner to the
other, then such Neutral shall upon the application of either General Partner be
appointed within 70 days of such nomination by the Center for Public Resources,
or if such appointment is not so made promptly then promptly thereafter by the
American Arbitration Association in Philadelphia, Pennsylvania, or if such
appointment is not so made promptly then promptly thereafter by the senior
United States District Court judge sitting in Wilmington, Delaware.  The fees of
the Neutral shall be paid equally by the General Partners.  Within 20 days of
selection of the Neutral, two persons having decision-making authority on behalf
of each General Partner shall meet with the Neutral and agree upon procedures
and a schedule for attempting to resolve the differences between the General
Partners.  They shall continue to meet thereafter on a regular basis until (i)
agreement is reached by the General Partners (acting through their
Representatives) on an updated Strategic Plan or (ii) at least 24 months have
elapsed since the beginning of the first fiscal year that was to be covered by
the first updated plan for which agreement was not reached and one General
Partner shall determine and notify the other General Partner and the Neutral in
writing (a "Deadlock Notice") that no agreement resolving the dispute is likely
to be reached.

                                      26
<PAGE>
 
8.6       Loans.

(a)  Initial Facilities.  On or prior to the Closing Date, the Partnership shall
     enter into the Bank Credit Agreement providing for (i) loans of an
     aggregate principal amount of $1.0 billion and (ii) a working capital
     facility in an aggregate principal amount of $250 million, all as more
     specifically provided for in the Master Transaction Agreement, and may also
     arrange for uncommitted lines of credit in an aggregate principal amount of
     up to $250 million; provided, however, that the total amount outstanding
     pursuant to such working capital facility and such uncommitted lines of
     credit, if any, in the aggregate, shall not at any time exceed $250 million
     unless authorized by Partnership Governance Committee Action pursuant to
     Section 6.7.  On the Closing Date, the Partnership shall borrow an amount
     equal to the principal amount of the Millennium Debt pursuant to the loans
     referred to in clause  (i) above and apply such amount to repay the
     Millennium Debt.

(b)  Other Loans.  The Partnership Governance Committee may by Partnership
     Governance Committee Action authorize the CEO to cause the Partnership to
     borrow funds from third party lenders.  Neither General Partner shall be
     required, and the Partnership Governance Committee shall not be authorized
     to require any Partner, to guarantee or to provide other credit or
     financial support for any loan.  Any Partner may, at its sole discretion,
     guarantee or provide other credit or financial support for all or any
     portion of any debt, including any refinancing of debt contemplated by
     Section 8.6(a), for such period of time and on such other terms as the
     Partner shall determine.

(c)  Millennium Guarantee.   On or before the Closing Date, Millennium America,
     an Affiliate of Millennium GP and Millennium LP, shall issue a full and
     unconditional guarantee (the "Millennium America Guarantee") in respect of
     $750 million of principal and interest owed by the Partnership pursuant to
     the Bank Credit Agreement in such form and on such terms as may be mutually
     agreed by Millennium America, the Partnership and the lenders under the
     Bank Credit Agreement.  Millennium America (or its successors or assigns)
     shall maintain the Millennium America Guarantee in full force and effect in
     respect of $750 million of  principal and interest under the Bank Credit
     Agreement or any refinancings thereof (including, without limitation, any
     further refinancings of such refinancings) indefinitely; provided, however,
     that Millennium America may terminate the Millennium America Guarantee at
     any time on or after the seventh anniversary of the Closing Date if, and
     only if:  (i) the Partnership's ratio of Total Indebtedness to Total
     Capitalization is, as of the end of the most recently completed fiscal
     quarter of the Partnership lower than such ratio as of December 31, 1998,
     (ii) the Partnership's ratio of EBITDA to Net Interest for the most recent
     12 month period is at least 105% of such ratio for the 12 month period
     ending December 31, 1998, (iii) the Partnership is not then in default in
     the payment of principal of, or interest on, any indebtedness for borrowed
     money in excess of $15 million and (iv) the Partnership is not then in
     default in respect of any covenants relating to any indebtedness for
     borrowed money if the effect of any such default shall be to accelerate, or
     to permit the holder or obligee of such indebtedness (or any trustee on
     behalf of such holder or obligee) to accelerate (with or without the giving
     of notice or lapse of time or both), such indebtedness in an aggregate
     amount in excess of $50 million; provided, further, that if Millennium GP
     and Millennium LP sell all of their respective interests in 

                                      27
<PAGE>
 
     the Partnership, or if Millennium Petrochemicals Inc. sells all of its
     equity interests in both Millennium GP and Millennium LP, in each case to
     an unaffiliated third party (or parties) at any time in accordance with the
     terms of this Agreement, Millennium America may terminate the Millennium
     America Guarantee if, at the time of such sale or at the time of such
     termination, (A) the Partnership has an "investment grade" credit rating
     issued by Moody's Investor Service Inc. or Standard & Poor's Corporation
     (or, if the Partnership has no rated indebtedness outstanding at such time,
     Millennium America demonstrates to the reasonable satisfaction of the
     Partnership that the Partnership could obtain such an "investment grade"
     credit rating), or (B) the fair market value of the Partnership's assets is
     at least 140% of the gross amount of its liabilities. For purposes of this
     paragraph (c), "EBITDA" means, with respect to any period, operating income
     before interest, taxes, depreciation and amortization, as determined in
     accordance with GAAP; "Net Interest" means, with respect to any period, (i)
     the amount which, in conformity with GAAP, would be set forth opposite the
     caption "interest expense" (or any like caption) on a consolidated income
     statement of the Partnership and all other Persons with which the
     Partnership's financial statements are to be consolidated in accordance
     with GAAP for the relevant period ended on such date less (ii) the amount
     which, in conformity with GAAP, would be set forth opposite the caption
     "interest income" (or any like caption) on such consolidated income
     statement; "Total Indebtedness" means at the time of determination all
     indebtedness of the Partnership and its subsidiaries on a consolidated
     basis, as determined in accordance with GAAP; "Total Capitalization" means,
     at the time of determination, the sum of Total Indebtedness plus the
     partner's equity reflected on a balance sheet of the Partnership prepared
     in accordance with GAAP.

                                   SECTION 9
                               RIGHTS OF PARTNERS

9.1       Delegation and Contracts with Related Parties.

(a)  The Partners acknowledge that the General Partners (acting through the
     Partnership Governance Committee) are permitted to delegate responsibility
     for day-to-day operations of the Partnership to officers and employees of
     the Partnership.

(b)  Upon receipt of any required approval by the Partnership Governance
     Committee (including, as applicable, any approval required by Section 6.8),
     all contracts and transactions between the Partnership and a Partner or its
     Affiliates shall be deemed to be entered into on an arm's-length basis and
     to be subject to ordinary contract and commercial law, without any other
     duties or rights being implied by reason of a Partner being a Partner or by
     reason of any provision of this Agreement or the existence of the
     Partnership.

9.2       General Authority.  Persons dealing with the Partnership are entitled
to rely conclusively on the power and authority of each of the General Partners
as set forth in this Agreement.  In no event shall any Person dealing with
either General Partner or such General Partner's representatives with respect to
any business or property of the Partnership be obligated to ascertain that the
terms of this Agreement have been complied with, or be obligated to inquire into
the necessity or expedience of any act or action of the General Partner or the
General Partner's 

                                      28
<PAGE>
 
representatives; and every contract, agreement, deed, mortgage, security
agreement, promissory note or other instrument or document executed by the
General Partner or the General Partner's representatives with respect to any
business or property of the Partnership shall be conclusive evidence in favor of
any and every Person relying thereon or claiming thereunder that (i) at the time
of the execution and/or delivery thereof, this Agreement was in full force and
effect, (ii) the instrument or document was duly executed in accordance with the
terms and provisions of this Agreement and is binding upon the Partnership, and
(iii) the General Partner or the General Partner's representative was duly
authorized and empowered to execute and deliver any and every such instrument or
document for and on behalf of the Partnership. Nothing in this Section 9.2 shall
be deemed to be a waiver or release of either General Partner's obligations to
the other Partners as set forth elsewhere in this Agreement.

9.3       Limitation on Fiduciary Duty; Non-Competition.

(a)  Each Partner (directly or through its Affiliates) is a sophisticated party
     possessing extensive knowledge of and experience relating to, and is
     actively engaged in, significant businesses in addition to its Contributed
     Businesses, has been represented by legal counsel, is capable of evaluating
     and has thoroughly considered the merits, risks and consequences of the
     provisions of this Section 9.3 and is agreeing to such provision knowingly
     and advisedly.  The liability of each of the General Partners (including
     any liability of its Affiliates or its and their respective officers,
     directors, agents and employees) or of any Limited Partner (including any
     liability of its Affiliates or its and their respective officers, agents,
     directors and employees), either to the Partnership or to any other
     Partner, for any act or omission by such Partner in its capacity as a
     partner of the Partnership that is imposed by such Partner's status as a
     "general partner" or "limited partner" (as such terms are used in the Act)
     of a limited partnership is hereby eliminated, waived and limited to the
     fullest extent permitted by law; provided, however, that each General
     Partner shall at all times owe to the other General Partner a fiduciary
     duty in observing the requirement described in Section 6.7 that two or more
     Representatives of Lyondell GP and two or more Representatives of
     Millennium GP shall be required to give their approval before the
     Partnership may undertake any of the actions listed in Section 6.7.
     Nothing in this subsection shall relieve any Partner from liability for any
     breach of this Agreement and each General Partner shall at all times owe to
     the other General Partner a duty to act in good faith with respect to all
     matters involving the Partnership.

(b)  Except as set forth in Section 9.3(c), each Partner's Affiliates shall be
     free to engage in or possess an interest in any other business of any type,
     including any business in direct competition with the Partnership, and to
     avail itself of any business opportunity available to it without having to
     offer the Partnership or any Partner the opportunity to participate in such
     business.  Except as set forth in Section 9.3(c), it is expressly agreed
     that the legal doctrine of "corporate or business opportunities" sometimes
     applied to a Person deemed to be subject to fiduciary or other similar
     duties so as to prevent such Persons from engaging in or enjoying the
     benefits of certain additional business opportunities shall not be applied
     in the case of any investment, acquisition, business, activity or operation
     of any Partner's Affiliates.

                                      29
<PAGE>
 
(c) (i)  If a Partner's Affiliate desires to initiate or pursue an opportunity
     to undertake, engage in, acquire or invest in a business, activity or
     operation within the scope of Section 1.4 ("Related Business") by investing
     in or acquiring a Person whose business is a Related Business, acquiring
     assets of a Related Business, or otherwise engaging in or undertaking a
     Related Business (a "Business Opportunity"), such Partner or its Affiliate
     (such Partner, together with its Affiliates, being called the "Proposing
     Partner") shall offer the Partnership the Business Opportunity on the terms
     set forth in Section 9.3(c)(ii).

(ii) When a Proposing Partner offers a Business Opportunity to the Partnership,
     the Partnership shall elect to do one of the following:

          (A)  acquire or undertake the Business Opportunity for the benefit of
               the Partnership as a whole, at the cost, expense and benefit of
               the Partnership; provided, however, that, if the Partnership
               ceases to actively pursue such opportunity for any reason, then
               the Proposing Partner will be entitled to proceed under clause
               (B) below; or

          (B)  permit the Proposing Partner to acquire or undertake the Business
               Opportunity for its own benefit and account without any duty to
               the Partnership or the other Partners with respect thereto;
               provided, however, that if the Business Opportunity is in direct
               competition with the then existing business of the Partnership (a
               "Competing Opportunity"), then the Proposing Partner and the
               Partnership shall, if either so elects, seek to negotiate and
               implement an arrangement whereby the Partnership would either (i)
               acquire or undertake the Competing Opportunity at the sole cost,
               expense and benefit of the Proposing Partner under a mutually
               acceptable arrangement whereby the Competing Opportunity is
               treated as a separate business within the Partnership with the
               costs, expenses and benefits related thereto being borne and
               enjoyed solely by the Proposing Partner, or (ii) enter into a
               management agreement with the Proposing Partner to manage the
               Competing Opportunity on behalf of the Proposing Partner on terms
               and conditions mutually acceptable to the Proposing Partner and
               the Partnership.  If the Partnership and the Proposing Partner do
               not reach agreement as to such arrangement, the Proposing Partner
               may acquire or undertake the Competing Opportunity for its own
               benefit and account without any duty to the Partnership or the
               other Partners with respect thereto.

(d)  Notwithstanding the provisions of Section 9.3(c)(ii), if the Business
     Opportunity constitutes less than 25% (based on annual revenues for the
     most recently completed fiscal year) of an acquisition of or investment in
     assets, activities, operations or businesses that is not otherwise a
     Related Business, then a Proposing Partner may acquire or invest in such
     Business Opportunity without first offering it to the Partnership;
     provided, that, after completion of the acquisition or investment thereof,
     such Proposing Partner must offer the Business Opportunity to the
     Partnership pursuant to the terms of Section 9.3(c)(ii).  If the
     Partnership elects option (A) of Section 9.3(c)(ii) 

                                      30
<PAGE>
 
     with respect thereto, the Business Opportunity shall be acquired by the
     Partnership at its Fair Market Value as of the date of such acquisition.

(e)  Notwithstanding the provisions of Section 9.3(c), any direct or indirect
     expansion by LYONDELL-CITGO Refining Company Ltd. of its aromatics business
     shall not be deemed to constitute a Business Opportunity for purposes of
     Section 9.3(c).

(f)  If (i) the Partnership is presented with an opportunity to acquire or
     undertake a Business Opportunity that it determines not to acquire or
     undertake and (ii) the Representatives of one General Partner, but not the
     other General Partner, desired that the Partnership acquire or undertake
     such Business Opportunity, then the Partnership shall permit such first
     General Partner and its Affiliates to acquire or undertake such Business
     Opportunity and Section 9.3(c)(ii)(B) shall be deemed to be applicable
     thereto to the same extent as if such General Partner and its Affiliates
     were a Proposing Partner with respect to such Business Opportunity.

9.4       Limited Partners.

(a)  No Limited Partner shall take part in the management or control of the
     Partnership's business, transact any business in the Partnership's name or
     have the power to sign documents for or otherwise to bind the Partnership.

(b)  Each Limited Partner shall have the rights with respect to the
     Partnership's books and records as set forth in Section 5.3.

9.5       Partner Covenants.  Each Partner covenants and agrees with the
Partnership and with the other Partners as follows:

(i)  It shall not exercise, or purport or attempt to exercise, its authority to
     withdraw, retire, resign, or assert that it has been expelled from the
     Partnership;

(ii) It shall not do any act that would make it impossible or impracticable to
     carry on the Partnership's business; and

(iii)     It shall not act or purport or attempt to act in a manner inconsistent
with any act of a General Partner acting pursuant to the Partnership Governance
Committee or in a manner contrary to the agreements of the Partners set forth in
this Agreement;

provided, that, nothing in this Section 9.5 shall be deemed to waive its rights
under Sections 10, 11 or 12.

9.6       Special Purpose Entities.  Each Partner covenants and agrees that (i)
its business shall be restricted solely to the holding of its Units and the
doing of things necessary or incidental in connection therewith (including,
without limitation, the exercise of its rights and powers under this 

                                      31
<PAGE>
 
Agreement), and (ii) it shall not own any assets, incur any liabilities or
engage, participate or invest in any business outside the scope of such
business; provided, however, that this Section 9.6 shall not be binding upon 
(a) Millennium Petrochemicals Inc., a Virginia corporation, or its successors by
operation of law to the extent that any Units shall be Transferred to it in 
accordance with Section 10.6 or (b) at its option, any Wholly Owned Affiliate of
any Partner to whom Units shall be Transferred pursuant to Section 10.6 if, at 
the date of such Transfer, such Wholly Owned Affiliate shall have a consolidated
net worth, as determined in accordance with GAAP, of at least $50 million.

                                  SECTION 10
                             TRANSFERS AND PLEDGES

10.1      Restrictions on Transfer and Prohibition on Pledge.  Except pursuant
to Section 11 or the procedures described below in this Section, a Partner shall
not, in any transaction or series of transactions, directly or indirectly
Transfer all or any part of its Units.  A Partner shall not, in any transaction
or series of transactions, directly or indirectly Pledge all or any part of its
Units or its interest in the Partnership.  Neither the term "Transfer" nor the
term "Pledge," however, shall include an assignment by a Partner of such
Partner's right to receive distributions from the Partnership so long as such
assignment does not purport to assign any right of such Partner to participate
in or manage the affairs of the Partnership, to receive any information or
accounting of the affairs of the Partnership, or to inspect the books or records
of the Partnership or any other right of a Partner pursuant to this Agreement or
the Act.  Any attempt by a Partner to Transfer or Pledge all or a portion of its
Units in violation of this Agreement shall be void ab initio and shall not be
effective to Transfer or Pledge such Units or any portion thereof.   Subject to
any applicable restrictions imposed by the Parent Agreement, nothing in this
Agreement shall prevent the Transfer or Pledge by the owner thereof of any
capital stock, equity ownership interests or other security of a Partner or any
Affiliate of a Partner.

10.2      Right of First Option.

(a)  Without the consent of the Partnership Governance Committee, no Partner may
     Transfer less than all of its Units.  Any Limited Partner and its
     Affiliated General Partner desiring to Transfer (pursuant to a cash sale)
     all of their Units (together, the "Selling Partners") shall give written
     notice (the "Initial Notice") to the Partnership and the other Partners
     (the "Offeree Partners") stating that the Selling Partners desire to
     Transfer their Units and stating the cash purchase price and all other
     terms on which they are willing to sell (the "Offer Terms").  Delivery of
     an Initial Notice shall constitute the irrevocable offer of the Selling
     Partners to sell their Units to the Offeree Partners hereunder.

(b)  The Offeree Partners shall have the option, exercisable by delivering
     written notice (the "Acceptance Notice") of such exercise to the Selling
     Partners within 45 days of the date of the Initial Notice, to elect to
     purchase all of the Units of the Selling Partners on the Offer Terms
     described in the Initial Notice.  The Acceptance Notice shall set a date
     for closing the purchase, such date to be not less than 30 nor more than 90
     days after delivery of the Acceptance Notice; provided that such time
     period shall be subject to extension as reasonably necessary (up to a
     maximum of an additional 120 days after such 90 day period) in order to
     comply with any applicable filing and waiting period requirements under the
     Hart-Scott-Rodino Antitrust Improvements Act.  The closing shall be held at
     the Partnership's offices.  The purchase price for the Selling Partners'
     Units shall be paid in cash delivered at the closing.  The purchase shall
     be consummated by appropriate and 

                                      32
<PAGE>
 
     customary documentation (including the giving of representations and
     warranties substantially similar to those set forth in Sections 2.1 through
     2.3 of the Master Transaction Agreement).

(c)  If the Offeree Partners do not elect to purchase the Selling Partners'
     Units within 45 days after the receipt of the Initial Notice, the Selling
     Partners shall have a further 180 days during which they may, subject to
     Sections 10.2(d) and (e), consummate the sale of their Units to a third
     party purchaser at a purchase price and on such other terms that are no
     more favorable to such purchaser than the Offer Terms.  If the sale is not
     completed within such further 180-day period, the Initial Notice shall be
     deemed to have expired and a new notice and offer shall be required before
     the Selling Partners may make any Transfer of their Units.

(d)  Before the Selling Partners may consummate a Transfer of their Units to a
     third party in accordance with this Agreement, the Selling Partners shall
     demonstrate to the Partnership that the Person willing to serve as the
     proposed purchaser's guarantor under the agreement contemplated by Section
     10.2(e)(vi) has outstanding indebtedness that is rated investment grade by
     Moody's Investors Service, Inc. and Standard & Poor's Corporation, or if
     such Person has no rated indebtedness outstanding, such Person shall
     provide an opinion from a nationally recognized investment banking firm
     that such Person could be reasonably expected to obtain such ratings.

(e)  Notwithstanding the foregoing provisions of this Section 10.2, a Partner
     may Transfer its Units (other than pursuant to Section 10.6) only if all of
     the following occur:

(i)  The Transfer is accomplished in a non-public offering in compliance with,
     and exempt from, the registration and qualification requirements of all
     federal and state securities laws and regulations.

(ii) The Transfer does not cause a default under any material contract to which
     the Partnership is a party or by which the Partnership or any of  its
     properties is bound.

(iii)     The transferee executes an appropriate agreement to be bound by this
Agreement.

(iv) The transferor and/or transferee bears all reasonable costs incurred by the
     Partnership in connection with the Transfer.

(v)  The business and activities of the transferee comply with Section 9.6.

(vi) The guarantor of the transferee satisfies the criteria set forth in Section
     10.2(d) and delivers an agreement to the ultimate parent entity of the
     Offeree Partners and to the Partnership, substantially in the form of the
     Parent Agreement.

(vii)     The proposed transferor is not in default in the timely performance of
any of its material obligations to the Partnership.

                                      33
<PAGE>
 
(viii)         The provisions of Section 10.3 are satisfied.

10.3      Inclusion of General or Limited Partner Units.  No Limited Partner may
Transfer its Units to any Person (other than in accordance with Section 10.6)
unless the General Partner Units of its General Partner Affiliate are
simultaneously transferred to such Person or a Wholly Owned Affiliate of such
Person.  No General Partner may transfer its Units to any Person (other than a
Wholly Owned Affiliate of such Partner) unless the Limited Partner Units of the
Affiliated Limited Partner are simultaneously transferred to such Person or a
Wholly Owned Subsidiary of such Person.

10.4      Rights of Transferee.  Upon consummation of a Transfer in accordance
with Section 10.2, the transferee or transferees shall immediately, and without
any further action of any Person, become (i) a Substitute Limited Partner if and
to the extent Limited Partner Units are transferred and (ii) a Substitute
General Partner, if and to the extent General Partner Units are transferred.

10.5      Effective Date of Transfer.  Each Transfer shall become effective as
of the first day of the calendar month following the calendar month during which
the Partnership Governance Committee approves such Transfer and receives a copy
of the instrument of assignment and all such certificates and documents of the
character described in Section 10.2, which the Partnership Governance Committee
may reasonably request.

10.6      Transfer to Wholly Owned Affiliate.  Without the need for the consent
of any Person (subject to the provisions contained in this Section 10.6):

     (a) any Partner may Transfer its Units to any Wholly Owned Affiliate of
such Partner (other than the Partner that is its Affiliate), provided the
transferee executes an instrument reasonably satisfactory to the Partnership
Governance Committee accepting the terms and provisions of this Agreement
(except as may be provided in Section 9.6). Upon consummation of a Transfer in
accordance with this Section 10.6(a), the transferee shall immediately, and
without any further action of any Person, become (i) a Substitute Limited
Partner if and to the extent Limited Partner Units are transferred and (ii) a
Substitute General Partner, if and to the extent General Partner Units are
transferred; and

     (b) any Limited Partner may, at its option and at any time, Transfer up to
99% of its Limited Partner Units to its Affiliated General Partner, whereupon
such Limited Partner Units shall, without any further action, become General
Partner Units.  Promptly following any Transfer of Limited Partner Units in
accordance with this Section 10.6(b), each Partner shall take such actions and
execute such instruments or documents (including, without limitation, amendments
to this Agreement or supplemental agreements hereto) as may be reasonably
necessary to ensure that each Affiliated Partner Group shall, taken as a whole
and following such Transfer, maintain all of its rights under this Agreement as
in effect immediately prior to such Transfer (including, without limitation, the
portion of Available Net Operating Cash distributable to such Affiliated Partner
Group).

                                      34
<PAGE>
 
10.7      Invalid Transfer.  No Transfer of Units which is in violation of this
Section 10 shall be valid or effective, and the Partnership shall not recognize
the same for the purposes of making any allocation or distribution.


                                  SECTION 11
                                    DEFAULT

11.1      Default.

(a)  Each of the following events shall constitute a "Default" and create the
     rights provided for in this Section 11 in favor of the Partnership and the
     Non-Defaulting Partners against the Defaulting Partners:

(i)  the failure by a Partner to make any contribution to the Partnership as
     required pursuant to this Agreement (other than pursuant to the Asset
     Contribution Agreement), which failure continues for at least five Business
     Days from the date that the Partner is notified such contribution is
     overdue;

(ii) in the case of each of Lyondell GP and Lyondell LP, the failure to pay
     principal, when due, on the Lyondell Note, which failure continues for at
     least five Business Days from the date such payment is due; or

(iii)     the withdrawal, retirement, resignation or dissolution of a Partner
(other than in connection with a Transfer of all of a Partner's Units in
accordance with this Agreement);  or the Bankruptcy of a Partner or its
Guarantor.

(b)  The day upon which the Default commences or occurs (or if the Default is
     subject to a cure period and is not timely cured, then the day following
     the end of the applicable cure period) shall be the "Default Date."
     Without prejudice to a Partner's (or any of its Affiliates') rights to seek
     temporary or preliminary judicial relief, prior to any such Default Date
     all rights and obligations of the Partners under this Agreement shall
     remain in full force and effect.

11.2      Remedies for Default.  Provided that there shall be no duplication of
remedies, without prejudice to any right to pursue independently and at any
time, including simultaneously, any other remedy it may have under law,
including the right to seek to recover Damages, or equity, the Non-Defaulting
Partners in their sole discretion may elect to pursue the following remedies:

(a)  At any time prior to the expiration of 60 days from the Default Date, the
     Non-Defaulting Partners may elect to purchase all, but not less than all,
     the Units of the Defaulting Partners as described in Section 11.3;
     provided, however, that within 10 days after the determination of the Fair
     Market Value, the Non-Defaulting Partners may elect not to proceed with a
     purchase of the Units of the Defaulting Partners, in which case the Non-
     Defaulting Partners shall have an 

                                      35
<PAGE>
 
     additional 30 days from their determination not to proceed to elect an
     alternative remedy under Section 11.2(b) below; and

(b)  At any time prior to the expiration of 60 days from the Default Date (or if
     the Non-Defaulting Partners initially elected to pursue their remedy under
     Section 11.2(a) above, then at any time prior to the expiration of the 30-
     day extension period), the Non-Defaulting Partners may elect to effect a
     liquidation of the Partnership under Section 11.4 and thereby cause the
     Partnership to dissolve under Section 12.1(iv).

11.3      Purchase of Defaulting Partners' Units.

(a)  Upon any election pursuant to Section 11.2(a), the purchase price that the
     Non-Defaulting Partners shall pay to the Defaulting Partners for their
     Units shall be an amount equal to (i) the amount that the Defaulting
     Partners would receive in a liquidation (assuming that any sale under
     Section 12.2 were for an amount equal to the Fair Market Value, without
     giving effect to any Damages) reduced by (ii) the unrecovered Damages
     attributable to the Default by the Defaulting Partners.

(b)  If the Non-Defaulting Partners have a right to purchase the Units of the
     Defaulting Partners, they may first seek a determination of Fair Market
     Value by delivering notice in writing to the Defaulting Partners. The Non-
     Defaulting Partners shall have 10 days from the final determination of Fair
     Market Value to elect to purchase the Defaulting Partner Units by
     delivering notice of such election in writing, and the purchase shall be
     consummated prior to the expiration of 60 days from the date such notice is
     delivered; provided that, such time period shall be subject to extension as
     reasonably necessary (up to a maximum of an additional 120 days after such
     60 day period) in order to comply with any applicable filing and waiting
     period requirements under the Hart-Scott-Rodino Antitrust Improvements Act.

(c)  The purchase price so determined shall be payable in cash at a closing held
     at the Partnership's offices.  The purchase shall be consummated by
     appropriate and customary documentation (including the giving of
     representations and warranties substantially similar to those set forth in
     Sections 2.1 through 2.3 of the Master Transaction Agreement) as soon as
     practicable and in any event within the applicable time period specified in
     subsection (b).

(d)  The Non-Defaulting Partners may assign, in whole or in part, their right to
     purchase the Units of the Defaulting Partners to one or more third parties.

(e)  If Units are transferred in accordance with this Section 11.3, whether to
     the Non-Defaulting Partners or a third party (under subsection (d) above),
     upon the consummation of such  Transfer, each such transferee shall
     immediately, and without any further action on the part of any Person,
     become (i) a Substitute Limited Partner if and to the extent that Limited
     Partner Units were transferred to such Person and (ii) a Substitute General
     Partner if and to the extent that General Partner Units were transferred to
     such Person.

                                      36
<PAGE>
 
11.4      Liquidation.  Upon any election pursuant to Section 11.2(b), the Non-
Defaulting Partners shall have the right to elect to dissolve and liquidate the
Partnership pursuant to the procedures in Section 12.1(iv) (such procedures
constituting a "Liquidation"); provided, however, that any amount payable to the
Defaulting Partners in such Liquidation pursuant to Section 12.2 shall be
reduced by, without duplication, any unrecovered Damages incurred by the Non-
Defaulting Partner and the Non-Defaulting Partners' Percentage Interest of any
unrecovered Damages incurred by the Partnership in connection with the Default.
The Non-Defaulting Partners shall deliver notice of such election to dissolve
and liquidate in writing to the Partnership and the Defaulting Partners.

11.5      Certain Consequences of Default.  Notwithstanding any other provision
of this Agreement, commencing on the Default Date and (i) prior to the Non-
Defaulting Partners' collection of Damages through the exercise of its legal
remedies or otherwise, or (ii) while the Non-Defaulting Partners are pursuing
their remedies under Section 11.2(a) or (b), the Representatives of the
Defaulting General Partner shall not have any voting or decisional rights with
respect to matters requiring Partnership Governance Committee Action, and such
matters shall be determined solely by the Representatives of the Non-Defaulting
General Partner; provided, however, that the foregoing loss of voting and
decisional rights shall not occur as a result of a Default caused solely by the
Bankruptcy of  a Partner or a Guarantor described in Section 11.1(a)(iii); and
provided further, that in the case of a Default under Section 11.1(a)(i) or
(ii), the foregoing loss of voting and decisional rights shall not apply to
those voting and decisional rights contained in Sections 6.7(i), (x), (xvi) or
(xviii) of this Agreement, which rights shall continue in full force and effect
at all times.


                                  SECTION 12
                    DISSOLUTION, LIQUIDATION AND TERMINATION

12.1      Dissolution and Termination.  As long as there is at least one other
General Partner (who is hereby authorized in such event to conduct the business
of the Partnership without dissolution), the withdrawal, retirement,
resignation, dissolution or Bankruptcy of a General Partner shall not dissolve
the Partnership, but rather shall be a Default covered by Section 11.  The
Partnership shall be dissolved upon the happening of any one of the following
events:

(i)  the written determination of both General Partners to dissolve the
     Partnership;

(ii) the entry of a judicial decree of dissolution;

(iii)     any other act or event which results in the dissolution of a limited
partnership under the Act (except as provided in the first sentence of this
Section 12.1);

(iv) the election of the Non-Defaulting Partners to effect a dissolution of the
     Partnership under Section 11.4; or

(v)            after the delivery of a Deadlock Notice by a General Partner
pursuant to   Section 8.5, the written determination by either General Partner
to dissolve the Partnership.

                                      37
<PAGE>
 
12.2      Procedures Upon Dissolution.

(a)  General.  If the Partnership dissolves, it shall commence winding up
     pursuant to the appropriate provisions of the Act and the procedures set
     forth in this Section 12.  Notwithstanding the dissolution of the
     Partnership, prior to the termination of the Partnership, the business of
     the Partnership and the affairs of the Partners, as such, shall continue to
     be governed by this Agreement.

(b)  Control of Winding Up.  The winding up of the Partnership shall be
     conducted under the direction of the Partnership Governance Committee;
     provided, however, that if the dissolution is caused by entry of a decree
     of judicial dissolution, the winding up shall be carried out in accordance
     with such decree.

(c)  Manner of Winding Up.  Unless the provisions of Section 12.2(e) apply, the
     Partnership shall attempt to sell all property and apply the proceeds
     therefrom in accordance with this Section 12.2(c) and Section 12.2(d)
     below.  Upon dissolution of the Partnership, the Partnership Governance
     Committee shall determine the time, manner and terms of any sale or sales
     of Partnership property pursuant to such winding up, consistent with its
     duties and having due regard to the activity and condition of the relevant
     market and general financial and economic conditions.  Except as otherwise
     agreed by the Partners, no distributions will be made in kind to any
     Partner without the consent of each Partner.

(d)  Application of Assets.  In the case of a dissolution and winding-up of the
     Partnership, the Partnership's assets shall be applied as follows:

(i)  First, to satisfaction of the liabilities of the Partnership owing to third
     parties and then to Partners (including Affiliates of the Partners),
     whether by payment or reasonable provision for payment.  Any reserves
     created to make any such provision for payment may be paid over by the
     Partnership to an independent escrow holder or trustee, to be held in
     escrow or trust for the purpose of paying any such contingent, conditional
     or unmatured liabilities or obligations, and, at the expiration of such
     period as the Partnership Governance Committee may deem advisable, such
     reserves shall be distributed to the Partners or their assigns in the
     manner set forth in subsection (d)(ii) below.

(ii) Second, after all allocations of Profits or Losses and other items pursuant
     to Section 4, to the Partners in accordance with the balances in their
     Capital Accounts.  Any Partner that then has a deficit in its Capital
     Account shall contribute cash in the amount necessary to eliminate  such
     deficit.  Such contributions shall be made within 90 days after the date in
     which all undistributed assets of the Partnership have been converted to
     cash.

(iii)  Notwithstanding the foregoing, if any Partner shall be indebted to the
       Partnership, then until payment in full of the principal of and accrued
       but unpaid interest on such indebtedness, regardless of the stated
       maturity or maturities thereof, the Partnership shall retain such
       Partner's distributive share of Partnership property and apply such sums
       to 

                                      38
<PAGE>
 
       the liquidation of such indebtedness and the cost of operation of such
       Partnership property during the period of such liquidation.

(e)       Division of Assets upon Deadlock.  If dissolution occurs pursuant to
Section 12.1(v), then the provisions of this Section 12.2(e) shall, if elected
by any Partner, apply in lieu of the provisions of Section 12.2(c), but subject
to the provisions of Section 12.2(d)(ii).  In such event, the Partnership
properties shall be divided and distributed in kind to the Partners in
accordance with the provisions of Appendix E.

12.3      Termination of the Partnership.  Upon the completion of the
liquidation of the Partnership and the distribution of all Partnership assets,
the Partnership's affairs shall terminate and the Partnership shall cause to be
executed and filed a Certificate of Cancellation of the Partnership's
Certificate of Limited Partnership pursuant to the Act, as well as any and all
other documents required to effectuate the termination of the Partnership.

12.4      Asset and Liability Statement.  Within a reasonable time following the
completion of the winding-up and liquidation of the Partnership's business, the
Partnership Governance Committee shall supply to each of the Partners a
statement (which may be unaudited) which shall set forth the assets and the
liabilities of the Partnership as of the date of complete liquidation, and each
Partner's pro rata portion of distributions pursuant to Section 12.2.


                                  SECTION 13
                                 MISCELLANEOUS

13.1      Confidentiality and Use of Information.

(a)  Except as provided in subsection (c) or (d) hereof, each Partner shall, and
     shall cause each of its Affiliates and its and their respective partners,
     shareholders, directors, officers, employees and agents (collectively,
     "Related Persons") to,  keep secret, retain in strictest confidence, and
     not distribute, disseminate or disclose any and all Confidential
     Information except to (i) the Partnership and its officers and employees,
     (ii) any lender to the Partnership or (iii) any Partner or any of their
     respective Affiliates or other Related Persons on a "need to know" basis in
     connection with the transactions leading up to and contemplated by this
     Agreement and the operation of the Partnership, and such Partner disclosing
     Confidential Information pursuant to this Section 13.1(a) shall use, and
     shall cause its Affiliates and other Related Persons to use, such
     Confidential Information only for the benefit of the Partnership in
     conducting the Partnership's business or for any other specific purposes
     for which it was disclosed to such party; provided that the disclosure of
     financial statements of, or other information relating to the Partnership
     shall not be deemed to be the disclosure of Confidential Information (y) to
     the extent that any Partner (or its ultimate parent entity) deems it
     necessary, appropriate or customary pursuant to law, regulation or stock
     exchange rule (in the reasonable good faith judgment of such parent entity)
     to disclose such information in or in connection with filings with the SEC,
     press releases disseminated to the financial community, presentations to
     lenders, presentations to ratings agencies or information disclosed to
     similar 

                                      39
<PAGE>
 
     audiences or (z) to the extent that in order to sustain a position
     taken for tax purposes, any Partner deems it necessary and appropriate to
     disclose such financial statements or other information.  All Confidential
     Information disclosed in connection with the Partnership or pursuant to
     this Agreement shall remain the property of the Person whose property it
     was prior to such disclosure unless such property has been transferred to
     the Partnership pursuant to an Asset Contribution Agreement.

          (b) No Confidential Information regarding the plans or operations of
any Partner or any Affiliate thereof received or acquired by or disclosed to any
unaffiliated Partner or Affiliate thereof in the course of the conduct of
Partnership business, or otherwise as a result of the existence of the
Partnership, may be used by such unaffiliated Partner or Affiliate thereof for
any purpose other than for the benefit of the Partnership in conducting the
Partnership Business.  The Partnership and each Partner shall have the
affirmative obligation to take all necessary steps to prevent the disclosure to
any Partner or Affiliate thereof of information regarding the plans or
operations of such Partner and its Affiliates in markets and areas unrelated to
the business of the Partnership in which any other Partner and their respective
Affiliates compete.

          (c) In the event that any Partner is legally required (by
interrogatories, discovery requests for information or documents, subpoena,
civil investigative demand or similar process) to disclose any Confidential
Information, it is agreed that such Partner prior to disclosure will provide the
Partnership Governance Committee with prompt notice of such request(s) so that
the Partnership Governance Committee may seek an appropriate protective order or
other appropriate remedy and/or waive the Partner's compliance with the
provisions of this Section.  In the event that such protective order or other
remedy is not obtained, or that the Partnership Governance Committee grants a
waiver hereunder, such Partner may furnish that portion (and only that portion)
of the Confidential Information which, in the opinion of the Partner's counsel,
the Partner is legally compelled to disclose, and the Partner will exercise its
commercially reasonable best efforts to obtain reliable assurance that
confidential treatment will be accorded any Confidential Information so
furnished.

          (d) Any Partner may disclose Confidential Information to a third party
who requires such Confidential Information for the purpose of evaluating a
possible purchase of such Partner's Units in accordance with Section 10;
provided, however, that such third party shall be informed by such Partner of
the confidential nature of the information and the existence of this Section
13.1 and prior to any disclosure shall execute a written confidentiality
agreement with such Partner substantially identical in scope to this Section and
providing that such confidentiality agreement is also made for the benefit of
the Partnership and each of the other Partners.

          (e) The Partners and their Affiliates shall consult with each other on
an ongoing basis with respect to disclosures regarding the Partnership and its
business and affairs permitted under Section 13.1(a)(y).

                                      40
<PAGE>
 
13.2      Indemnification.

(a)  Indemnification by Partnership.  The Partnership agrees, to the fullest
     extent permitted by applicable law, to indemnify, defend and hold harmless
     each Partner, its Affiliates and their respective officers, directors and
     employees from, against and in respect of any Liability which such
     Indemnified Person may sustain, incur or assume as a result of, or relative
     to, a Third Party Claim arising out of or in connection with the business,
     property or affairs of the Partnership, except to the extent that it is
     Finally Determined that such Third Party Claim arose out of or was related
     to actions or omissions of the indemnified Partner, its Affiliates or any
     of their respective officers, directors or employees (acting in their
     capacities as such) constituting a breach of this Agreement or any Related
     Agreement.  The Partnership shall periodically reimburse or advance to any
     Person entitled to indemnity under this subsection (a) its legal and other
     expenses incurred in connection with defending any claim with respect to
     such Liability if such Person shall agree to reimburse promptly the
     Partnership for such amounts if it is finally determined that such Person
     was not entitled to indemnity hereunder.  Nothing in this Section 13.2(a)
     is intended to, nor shall it, affect or take precedence over the indemnity
     provisions contained in any Related Agreement.

(b)  Partner's Right of Contribution.  Each Partner hereby agrees, to the
     fullest extent permitted by law, to indemnify, defend and hold harmless the
     other Partners, their Affiliates and their respective officers, directors
     and employees from and against the indemnifying Partner's Percentage
     Interest (calculated at the time any such Liability was incurred) of any
     Liability that such Indemnified Person may sustain, incur or assume as a
     result of or relating to any Third Party Claim arising out of or in
     connection with the business, property or affairs of the Partnership;
     provided, however, that such indemnified Partner, its Affiliates and their
     respective officers, directors and employees shall not be entitled to
     indemnity under this subsection (b) to the extent that it is Finally
     Determined that such Third Party Claim arose out of or was related to
     actions or omissions of the indemnified Partner, its Affiliates or any of
     their respective officers, directors or employees (acting in their
     capacities as such) constituting a breach of this Agreement or any Related
     Agreement; provided, further, that such indemnified Partner, its Affiliates
     and their respective officers, directors and employees shall not be
     entitled to indemnity under this subsection (b) unless (x) the indemnified
     Partner shall first make a written demand for indemnification from the
     Partnership in accordance with subsection (a) above and subsection (c)
     below and the Partnership shall fail to satisfy such demand in a manner
     reasonably satisfactory to the indemnified Partner within 60 days of such
     notice or (y) the Partnership is insolvent or otherwise unable to satisfy
     its obligations.  The indemnifying Partner shall periodically reimburse any
     Person entitled to indemnity under this subsection (b) for its legal and
     other expenses incurred in connection with defending any claim with respect
     to such Liability if such Person shall agree to reimburse promptly the
     indemnifying Partner for such amounts if it is Finally Determined that such
     Person was not entitled to indemnity hereunder.

(c)  Procedures.  Promptly after receipt by a Person entitled to indemnification
     under subsection (a) or (b) (an "Indemnified Party") of notice of any
     pending or threatened claim against it (a "Claim"), such Indemnified Party
     shall give prompt written notice (including copies of all papers served
     with respect to such claim) to the party to whom the Indemnified Party is
     entitled to look for indemnification (the "Indemnifying Party") of the
     commencement thereof, which notice 

                                      41
<PAGE>
 
     shall describe in reasonable detail the nature of the Third Party Claim, an
     estimate of the amount of damages attributable to the Third Party Claim to
     the extent feasible and the basis of the Indemnified Party's request for
     indemnification under this Agreement; provided that the failure to so
     notify the Indemnifying Party shall not relieve the Indemnifying Party of
     any liability that it may have to any Indemnified Party except to the
     extent the Indemnifying Party demonstrates that it is prejudiced thereby.
     In case any Claim that is subject to indemnification under subsection (a)
     shall be brought against an Indemnified Party and it shall give notice to
     the Indemnifying Party of the commencement thereof, the Indemnifying Party
     may, and at the request of the Indemnified Party shall, participate in and
     control the defense of the Third Party Claim with counsel of its choice
     reasonably satisfactory to the Indemnified Party. The Indemnified Party
     shall have the right to employ separate counsel in any such action and to
     participate in the defense thereof, but the fees and expenses of such
     counsel shall be at the expense of the Indemnified Party unless (i) the
     employment thereof has been specifically authorized in writing by the
     Indemnifying Party, (ii) the Indemnifying Party failed to assume the
     defense and employ counsel or failed to diligently prosecute or settle the
     Third Party Claim or (iii) there shall exist or develop a conflict that
     would ethically prohibit counsel to the Indemnifying Party from
     representing the Indemnified Party. If requested by the Indemnifying Party,
     the Indemnified Party agrees to cooperate with the Indemnifying Party and
     its counsel in contesting any Third Party Claim that the Indemnifying Party
     elects to contest, including, without limitation, by making any
     counterclaim against the Person asserting the Third Party Claim or any
     cross-complaint against any Person, in each case only if and to the extent
     that any such counterclaim or cross-complaint arises from the same actions
     or facts giving rise to the Third Party Claim. The Indemnifying Party shall
     be the sole judge of the acceptability of any compromise or settlement of
     any claim, litigation or proceeding in respect of which indemnity may be
     sought hereunder, provided that the Indemnifying Party will give the
     Indemnified Party reasonable prior written notice of any such proposed
     settlement or compromise and will not consent to the entry of any judgment
     or enter into any settlement with respect to any Third Party Claim without
     the prior written consent of the Indemnified Party, which shall not be
     unreasonably withheld. The Indemnifying Party (if the Indemnified Party is
     entitled to indemnification hereunder) shall reimburse the Indemnified
     Party for its reasonable out of pocket costs incurred with respect to such
     cooperation.

          If the Indemnifying Party fails to assume the defense of a Third Party
Claim within a reasonable period after receipt of written notice pursuant to the
first sentence of this subparagraph (c), or if the Indemnifying Party assumes
the defense of the Indemnified Party pursuant to this subparagraph (c) but fails
diligently to prosecute or settle the Third Party Claim, then the Indemnified
Party shall have the right to defend, at the sole cost and expense of the
Indemnifying Party (if the Indemnified Party is entitled to indemnification
hereunder), the Third Party Claim by all appropriate proceedings, which
proceedings shall be promptly and vigorously prosecuted by the Indemnified Party
to a final conclusion or settled.  The Indemnified Party shall have full control
of such defense and proceedings; provided that the Indemnified Party shall not
settle such Third Party Claim without the written consent of the Indemnifying
Party, which consent shall not be unreasonably withheld.  The Indemnifying Party
may participate in, but not control, any defense or settlement controlled by the
Indemnified Party pursuant to this Section, and the Indemnifying Party shall
bear its own costs and expenses with respect to such participation.

                                      42
<PAGE>
 
          Notwithstanding the other provisions of this Section 13.2, if the
Indemnifying Party disputes its potential liability to the Indemnified Party
under this Section 13.2 and if such dispute is resolved in favor of the
Indemnifying Party, the Indemnifying Party shall not be required to bear the
costs and expenses of the Indemnified Party's defense pursuant to this Section
13.2 or of the Indemnifying Party's participation therein at the Indemnified
Party's request, and the Indemnified Party shall reimburse the Indemnifying
Party in full for all costs and expenses of the litigation concerning such
dispute.  If a dispute over potential liability is resolved in favor of the
Indemnified Party, the Indemnifying Party shall reimburse the Indemnified Party
in full for all costs of the litigation concerning such dispute.

          After it has been determined, by acknowledgment, agreement, or ruling
of court of Legal Requirements, that an Indemnifying Party is liable to the
Indemnified Party under this Section 13.2(c), the Indemnifying Party shall pay
or cause to be paid to the Indemnified Party the amount of the Liability  within
ten business days of receipt by the Indemnifying Party of a notice reasonably
itemizing the amount of the Liability but only to the extent actually paid or
suffered by the Indemnified Party.

(d)  Survival.  The indemnities contained in this Section shall survive the
     termination and liquidation of the Partnership.

(e)  Subrogation.  In the event of any payment by or on behalf of an
     Indemnifying Party to an Indemnified Party in connection with any
     Liability, the Indemnifying Party (or any guarantor who made such payment)
     shall be subrogated to and shall stand in the place of the Indemnified
     Party as to any events or circumstances in respect of which the Indemnified
     Party may have any right or claim against any third party relating to such
     event or indemnification.  The Indemnified Party shall cooperate with the
     Indemnifying Party (or such guarantor) in any reasonable manner in
     prosecuting any subrogated claim.

13.3      Third Party Claim Reimbursement.

(a)  In the case of a Liability relating to a Third Party Claim and caused by
     the Fault of a General Partner, its Affiliates or any of their respective
     officers, directors or employees (acting in their capacities as such)
     against whom reimbursement is being sought, such General Partner hereby
     agrees to reimburse the Partnership for such Liability to the extent that:

(i)  the Liability relates to a Third Party Claim that has been finally resolved
     and that the Partnership has actually paid (an "Expense");

(ii) the Expense is not covered by insurance carried by the Partnership
     (excluding any amounts relating to insured claims to the extent that they
     fall within deductibles or self-insured retentions or are above applicable
     coverage limits); and

(iii)  the Expense is not offset by third party indemnification or otherwise.

                                      43
<PAGE>
 
provided, however, that such General Partner shall reimburse the Partnership for
the Expense only to the extent and in proportion to its Fault.

(b)  Any claim by the Partnership for reimbursement under this Section may be
     initiated by a General Partner upon written notice to the other General
     Partner, and the General Partners shall have a period of 60 days during
     which to reach unanimous agreement as to the terms on which any
     reimbursement shall be made.  If the General Partners are unable to agree
     or there are any disputes over Fault and reimbursement under this Section,
     such matters shall be resolved pursuant to the Dispute Procedures.

13.4      Dispute Resolution.  Except as otherwise provided for herein, all
controversies or disputes arising under this Agreement shall be resolved
pursuant to the provisions set forth on Appendix D (the "Dispute Procedures").

13.5      EXTENT OF LIMITATION OF LIABILITY, INDEMNIFICATION, ETC.  TO THE
FULLEST EXTENT PERMITTED BY LAW AND WITHOUT LIMITING OR ENLARGING THE SCOPE OF
THE LIMITATION OF LIABILITY, INDEMNIFICATION, RELEASE AND ASSUMPTION OBLIGATIONS
SET FORTH HEREIN, A PARTY SHALL BE ENTITLED TO INDEMNIFICATION OR RELEASE
HEREUNDER IN ACCORDANCE WITH THE TERMS HEREOF, REGARDLESS OF WHETHER THE LOSS
GIVING RISE TO ANY SUCH INDEMNIFICATION OR RELEASE IS THE RESULT OF THE SOLE,
GROSS, ACTIVE, PASSIVE, CONCURRENT OR COMPARATIVE NEGLIGENCE, STRICT LIABILITY
OR OTHER FAULT OR VIOLATION OF ANY LAW OF OR BY ANY SUCH PARTY.  THE PARTIES
AGREE THAT THIS STATEMENT CONSTITUTES A CONSPICUOUS LEGEND.

13.6      Further Assurances.  From time to time, each Partner agrees to execute
and deliver such additional documents, and will provide such additional
information and assistance, as the Partnership may reasonably require to carry
out the terms of this Agreement and to accomplish the Partnership's business.

13.7      Successors and Assigns.  Except as may be expressly provided herein,
this Agreement shall be binding upon and inure to the benefit of the successors
of the Partners, but no Partner may assign or delegate any of its rights or
obligations under this Agreement.  Except as expressly provided herein, any
purported assignment or delegation shall be void and ineffective.

13.8      Benefits of Agreement Restricted to the Parties.  This Agreement is
made solely for the benefit of the Partnership and the Partners, and no other
Person shall have any right, claim or cause of action under or by virtue of this
Agreement.

13.9      Notices.  All notices, requests and other communications that are
required or may be given under this Agreement shall, unless otherwise provided
for elsewhere in this Agreement, be in writing and shall be deemed to have been
duly given if and when (i) transmitted by telecopier facsimile with proof of
confirmation from the transmitting machine or (ii) delivered by commercial
courier or other hand delivery, as follows:

                                      44
<PAGE>
 
Lyondell Petrochemical Company             Millennium Chemicals Inc.      
1221 McKinney Street                       99 Wood Avenue South        
Houston, Texas 77010                       Iselin, New Jersey  08830      
Attention:  Jeffrey R. Pendergraft         Attention:  George H. Hempstead, III
Telecopy Number: (713) 652-4538            Telecopy Number: (908) 603-6857    

                                      45
<PAGE>
 
13.10          [Reserved]

13.11          Severability.  In the event that any provisions of this Agreement
shall be Finally Determined to be unenforceable, such provision shall, so long
as the economic and legal substance of the transactions contemplated hereby is
not affected in any materially adverse manner as to any Partner, be deemed
severed from this Agreement and every other provision of this Agreement shall
remain in full force and effect.

13.12          Construction.  In construing this Agreement, the following
principles shall be followed:  (i) no consideration shall be given to the
captions of the articles, sections, subsections or clauses, which are inserted
for convenience in locating the provisions of this Agreement and not as an aid
in construction; (ii) no consideration shall be given to the fact or presumption
that any Partner had a greater or lesser hand in drafting this Agreement; (iii)
examples shall not be construed to limit, expressly or by implication, the
matter they illustrate; (iv) the word "includes" and its syntactic variants mean
"includes, but is not limited to" and corresponding syntactic variant
expressions; (v) the plural shall be deemed to include the singular, and vice
versa; (vi) each gender shall be deemed to include the other gender; and (vii)
each appendix, exhibit, attachment and schedule to this Agreement is a part of
this Agreement.

13.13          Counterparts.  This Agreement may be executed in one or more
counterparts, each of which shall constitute an original, and all of which when
taken together shall constitute one and the same original document.

13.14          Waiver of Right to Partition.  Except as provided in Section
12.2(e), each Person who now or hereafter is a party hereto or who has any right
herein or hereunder irrevocably waives during the term of the Partnership any
right to maintain any action for partition with respect to Partnership property.

13.15          Governing Law.  The laws of the State of Delaware shall govern
the construction, interpretation and effect of this Agreement without giving
effect to any conflicts of law principles.

13.16          Jurisdiction; Consent to Service of Process; Waiver.  ANY
JUDICIAL PROCEEDING BROUGHT AGAINST ANY PARTY TO THIS AGREEMENT OR ANY DISPUTE
UNDER OR ARISING OUT OF OR IN CONNECTION WITH THIS AGREEMENT OR ANY MATTER
RELATED HERETO SHALL BE BROUGHT IN THE FEDERAL OR STATE COURTS OF THE STATE OF
DELAWARE, AND, BY EXECUTION AND DELIVERY OF THIS AGREEMENT, EACH OF THE PARTIES
TO THIS AGREEMENT ACCEPTS THE EXCLUSIVE JURISDICTION OF SUCH COURTS AND
IRREVOCABLY AGREES TO BE BOUND BY ANY JUDGMENT (AS FINALLY ADJUDICATED) RENDERED
THEREBY IN CONNECTION WITH THIS AGREEMENT.  EACH OF THE PARTIES TO THIS
AGREEMENT SHALL APPOINT THE CORPORATION TRUST COMPANY, THE PRENTICE-HALL
CORPORATION SYSTEM, INC. OR A SIMILAR ENTITY (THE "AGENT") AS AGENT TO RECEIVE
ON ITS BEHALF SERVICE OF PROCESS IN ANY PROCEEDING IN ANY SUCH COURT IN THE
STATE OF DELAWARE.  THE FOREGOING CONSENTS TO JURISDICTION 

                                      46
<PAGE>
 
AND APPOINTMENTS OF AGENT TO RECEIVE SERVICE OF PROCESS SHALL NOT CONSTITUTE
GENERAL CONSENTS TO SERVICE OF PROCESS IN THE STATE OF DELAWARE FOR ANY PURPOSE
EXCEPT AS PROVIDED ABOVE AND SHALL NOT BE DEEMED TO CONFER RIGHTS ON ANY PERSON
OTHER THAN THE PARTIES HERETO.

13.17          Expenses.  Except as otherwise provided herein or in the Master
Transaction Agreement, each party hereto shall be responsible for its own
expenses incurred in connection with this Agreement.

13.18          Waiver of Jury Trial.  EACH PARTY HEREBY KNOWINGLY AND
INTENTIONALLY, IRREVOCABLY AND UNCONDITIONALLY WAIVES TRIAL BY JURY IN ANY LEGAL
ACTION OR PROCEEDING RELATING TO THIS AGREEMENT AND FOR ANY COUNTERCLAIM
THEREIN.

13.19          Payment Terms and Interest Calculations.

     (a) If the payment due date for any payment hereunder (including capital
contributions and Damages) falls on a Saturday or a bank or federal holiday,
other than a Monday, the payment shall be due on the past preceding business
day.  If the payment due date falls on a Sunday or Monday bank or federal
holiday, the payment shall be due on the following business day.

     (b) Interest shall accrue on any unpaid and outstanding amount from the
time such amount is due and payable through the date upon which such amount,
together with accrued interest thereon, is paid in full.  Interest shall,
subject to the provisions of Section 13.20, accrue at a per annum rate equal to
the lesser of (i) the Agreed Rate plus 2%, compounded quarterly, to the extent
permitted by law or (ii) the Highest Lawful Rate.

     (c) A wire transfer or delivery of a check shall not operate to discharge
any payment under this Agreement and shall be accepted subject to collection.

13.20          Usury Savings Clause.  Notwithstanding any other provision of
this Agreement, it is the intention of the parties hereto to conform strictly to
Applicable Usury Laws, in each case to the extent they are applicable to this
Agreement.  Accordingly, if any payment made pursuant to this Agreement results
in any Person having paid any interest in excess of the Maximum Amount, or if
any transaction contemplated hereby would otherwise be usurious under any
Applicable Usury Laws, then, in that event, it is agreed as follows:  (i) the
provisions of this Section 13.20 shall govern and control; (ii) the aggregate of
all interest under Applicable Usury Laws that is contracted for, charged or
received under this Agreement shall under no circumstances exceed the Maximum
Amount, and any excess shall be promptly refunded to the payor by the recipient
hereof; (iii) no Person shall be obligated to pay the amount of such interest to
the extent that it is in excess of the Maximum Amount; and (iv) the effective
rate of any interest payable under this Agreement shall be ipso facto reduced to
the Highest Lawful Rate, as hereinafter defined, and the provisions of this
Agreement immediately shall be deemed reformed, without the necessity of the
execution of any new document or instrument, so as to comply with all Applicable
Usury Laws.  All sums paid, or 

                                      47
<PAGE>
 
agreed to be paid, to any person pursuant to this Agreement for the use,
forbearance or detention of any indebtedness arising hereunder shall, to the
fullest extent permitted by the Applicable Usury Laws, be amortized, pro rated,
allocated and spread throughout the full term of any such indebtedness so that
the actual rate of interest does not exceed the Highest Lawful Rate in effect at
any particular time during the full term thereof.

13.21          Other Waivers.  EACH PARTY HEREBY WAIVES ANY OBJECTION IT MAY
HAVE BASED UPON LACK OF PERSONAL JURISDICTION, IMPROPER VENUE OR FORUM NON-
CONVENIENS.

13.22          Special Joinder by Millennium America.  Millennium America is a
party to this Agreement for the sole purpose of evidencing its agreement to be
bound by the provisions set forth in Section 8.6(c) and is not a partner of the
Partnership and shall not have any rights under this Agreement or any other
obligations under this Agreement.

13.23          Amendment.  All waivers, modifications, amendments or alterations
of this Agreement shall require the written approval of each of the General
Partners and each of the Limited Partners.

                            [signature page follows]

                                      48
<PAGE>
 
     IN WITNESS WHEREOF, this Agreement has been executed on behalf of each of
the parties hereto, by their respective officers thereunto duly authorized,
effective as of the date first written above.

               GENERAL PARTNERS

               LYONDELL PETROCHEMICAL G.P. INC.

               By:
               Name:
               Title:

               MILLENNIUM PETROCHEMICALS GP LLC

               By:
               Name:
               Title:

               LIMITED PARTNERS

               LYONDELL PETROCHEMICAL L.P. INC.

               By:
               Name:
               Title:

               MILLENNIUM PETROCHEMICALS LP LLC

               By:
               Name:
               Title:

                                      49
<PAGE>
 
               SPECIAL JOINDER PURSUANT TO SECTION 13.22

               MILLENNIUM AMERICA INC.

               By:
               Name:
               Title:

                                      50
<PAGE>
 
                                   APPENDIX A
                        TO LIMITED PARTNERSHIP AGREEMENT

                                 DEFINED TERMS


     Acceptance Notice.  See Section 10.2(b).

     Act.  The Delaware Revised Uniform Limited Partnership Act, as amended and
in effect from time to time.

     Adjusted Capital Account Deficit.  With respect to any Partner, the deficit
balance, if any, in such Partner's Capital Account as of the end of the relevant
fiscal year, after giving effect to the following adjustments:

          (i) Such Capital Account shall be deemed to be increased by any
     amounts which such Partner is obligated to restore to the Partnership
     (pursuant to this Agreement or otherwise) or is deemed to be obligated to
     restore pursuant to the second to last sentence of Regulation (S)1.704-
     2(g)(1) and (S)1.704-2(i)(5) (relating to allocations attributable to
     nonrecourse debt).

          (ii) Such Capital Account shall be deemed to be decreased by the items
     described in Regulation (S)1.704-1(b)(2)(ii)(d)(4), (5) and (6).

The foregoing definition of Adjusted Capital Deficit is intended to comply with
the provisions of Regulation (S)1.704-1(b)(2)(ii)(d) and shall be interpreted
and applied consistently therewith.

     Affiliate.  As to any specified Person, any other Person that directly or
indirectly through one or more intermediaries, controls or is controlled by or
is under common control with the specified Person; provided, however, that for
purposes of this Agreement such term shall not include (i) the Partnership or
any entities controlled by it, (ii) in the case of each of Lyondell GP and
Lyondell LP, shall not include Atlantic Richfield Company and any entities
controlled by it and (iii) in the case of Millennium GP and Millennium LP shall
not include Suburban Propane Partners, L.P. and any entities controlled by it.
For purposes of this definition the term "control" shall have the meaning set
forth in 17 CFR 230.405, as in effect on the date hereof.

     Affiliated General Partner.  In the case of Lyondell LP, the "Affiliated
General Partner" shall mean Lyondell GP.  In the case of Millennium LP, the
"Affiliated General Partner" shall mean Millennium GP.

     Affiliated Limited Partner. In the case of Lyondell GP, the "Affiliated
Limited Partner" shall mean Lyondell LP.  In the case of Millennium GP, the
"Affiliated Limited Partner" shall mean Millennium LP.

     Affiliated Partner Group.  A General Partner and its Affiliated Limited
Partner.

                                 Appendix A-1
<PAGE>
 
     Agreed Rate.  The base commercial lending rate announced by Citibank, N.A.
(or its successor) at its principal office, in effect from time to time, such
interest rate to change automatically, effective as of the date of each change
in such base rate.

     Agreement.  This Limited Partnership Agreement of Equistar Chemicals, LP,
as amended from time to time.

     Alternate.  See Section 6.4(b).

     Annual Budget.  See Section 8.2.

     Applicable Usury Laws.  Laws regarding the use, forbearance or detention of
any indebtedness arising under this Agreement whether such laws are now or
hereafter in effect, including the laws of the United States of America or any
other jurisdiction whose laws are applicable, and including any subsequent
revisions to or judicial interpretations of those laws.

     Asset Contribution Agreement.  In the case of Lyondell LP and Lyondell GP,
the Asset Contribution Agreement shall mean the Asset Contribution Agreement to
be entered into between the Partnership and Lyondell.  In the case of Millennium
LP and Millennium GP, the Asset Contribution Agreement shall mean the Asset
Contribution Agreement to be entered into between the Partnership and Millennium
Petrochemicals.

     Asset Fair Market Value.  With respect to any asset, as of the date of
determination, the cash price at which a willing seller would sell, and a
willing buyer would buy, each being apprised of all relevant facts and neither
acting under compulsion, such as in an arm's-length negotiated transaction with
an unaffiliated third party without time constraints.

     Assumed Liabilities.  In the case of Lyondell LP and Lyondell GP, Assumed
Liabilities means the "Assumed Liabilities" as defined in the Asset Contribution
Agreement of Lyondell.  In the case of Millennium LP and Millennium GP, Assumed
Liabilities shall mean the "Assumed Liabilities" as defined in the Asset
Contribution Agreement of Millennium Petrochemicals.

     Auxiliary Committee.  See Section 6.9.

     Available Net Operating Cash.  At the time of determination, (a) all cash
and cash equivalents on hand in the Partnership as of the most recent month end,
plus the excess, if any, of the Partnership Target Debt over the Partnership's
actual indebtedness (as determined in accordance with GAAP) as of such month
end, less (b) the Projected Cash Requirements, if any, of the Partnership as of
such month end, as determined by the Executive Officers of the Partnership.  For
purposes of this definition, "Projected Cash Requirements" means, for the 12-
month period following any such month end, the excess, if any, of the sum of (a)
forecast capital expenditures, plus (b) forecast cash payments for Taxes, debt
service including principal and interest requirements and other non-cash credits
to income, plus (c) forecast cash reserves for future operations or other
requirements, over the sum of (1) forecast net income of the Partnership, plus
(2) the sum of forecast depreciation, amortization, other non-cash charges to
income, interest expenses, and Tax expenses, 

                                 Appendix A-2
<PAGE>
 
in each case to the extent deducted in determining net income, plus or minus (3)
forecast decreases or increases, respectively, in working capital, plus (4) the
forecast cash proceeds of dispositions of assets (net of expenses) plus (5) an
amount equal to the forecast net proceeds of debt financings, contributions and
payments of the Lyondell Note. For purposes of this definition, "Partnership
Target Debt" means for such month end, the level of indebtedness (as determined
in accordance with GAAP) projected for the Partnership in the most recently
approved Strategic Plan (initially $1.75 billion), except to the extent the
Executive Officers of the Partnership determine that changes in the financial
condition, results of operations, assets, business or prospects of the
Partnership make a change advisable, in which case the Partnership shall advise
the General Partners promptly regarding the basis for the change. Projected Cash
Requirements shall be calculated consistent with the most recently approved
Strategic Plan, except to the extent the Executive Officers of the Partnership
determine that changes in the financial condition, results of operations,
assets, business or prospects of the Partnership make a change advisable, in
which case the Partnership shall advise the General Partners promptly regarding
the basis for the change.

     Bank Credit Agreement.  The bank credit agreement or agreements to be
entered into by the Partnership on or prior to the Closing Date as provided for
by Section 8.6.

     Bankruptcy.  The occurrence of any of the following:  (i) a Partner or its
Guarantor shall file a voluntary petition in bankruptcy or shall be adjudicated
a bankrupt or insolvent, or shall file any petition or answer or consent seeking
any reorganization, arrangement, composition, readjustment, liquidation,
dissolution or similar relief for itself under any present or future applicable
federal, state or other statute or law relating to bankruptcy, insolvency, or
other relief for debtors, or shall seek or consent to or acquiesce in the
appointment of any trustee, receiver, conservator or liquidator of such Partner
or its Guarantor or of all or any substantial part of its properties or its
Units (the term "acquiesce," as used in this definition, includes the failure to
file a petition or motion to vacate or discharge any order, judgment or decree
within ten Business Days after entry of such order, judgment or decree); (ii) a
court of competent jurisdiction shall enter an order, judgment or decree
approving a petition filed against any Partner or its Guarantor seeking a
reorganization, arrangement, composition, readjustment, liquidation, dissolution
or similar relief under the present or any future federal bankruptcy act, or any
other present or future applicable federal, state or other statute or law
relating to bankruptcy, insolvency, or other relief for debtors, and such
Partner or its Guarantor shall acquiesce in the entry of such order, judgment or
decree or such other order, judgment or decree shall remain unvacated and
unstayed for an aggregate of 60 days (whether or not consecutive) from the date
of entry thereof, or any trustee, receiver, conservator or liquidator of such
Partner or its Guarantor or of all or any substantial part of its property or
its Units shall be appointed without the consent or acquiescence of such Partner
or its Guarantor and such appointment shall remain unvacated and unstayed for an
aggregate of 60 days (whether or not consecutive); (iii) a Partner or its
Guarantor shall admit in writing its inability to pay its debts as they mature;
(iv) a Partner or its Guarantor shall give notice to any governmental body of
insolvency or pending insolvency, or suspension or pending suspension of
operations; or (v) a Partner or its Guarantor shall make an assignment for the
benefit of creditors or take any other similar action for the protection or
benefit of creditors.

                                 Appendix A-3
<PAGE>
 
     Book Value.  With respect to any asset of the Partnership, the asset's
adjusted basis as of the relevant date for federal income tax purposes, except
as follows:

(i)  The initial aggregate Book Value of all of the assets of the Partnership as
     of the Closing Date shall be equal to the sum of (A) the beginning
     aggregate Capital Accounts of the Partners immediately after the Closing
     Date, and (B) the aggregate amount of all liabilities of the Partnership
     for federal income tax purposes immediately after the Closing Date.

(ii) The initial Book Value of any asset contributed by a Partner to the
     Partnership after the Closing Date shall be the gross fair market value of
     such asset, which shall be equal to the amount credited to such Partner's
     Capital Account for such contribution (increased by the amount of any
     liabilities which the Partnership assumes or takes subject to).

(iii)     The Book Values of all Partnership assets (including intangible assets
such as goodwill) shall be adjusted (at the election of the Partnership
Governance Committee) to equal their respective gross fair market values upon
the occurrence of any of the events described in Regulation (S)1.704-
1(b)(2)(iv)(f)(5).

(iv) The Book Value of any asset distributed by the Partnership to a Partner
     shall be equal to the gross fair market value of such asset on the date of
     the distribution.

(v)  The Book Value of any Partnership asset with respect to which an adjustment
     to tax basis has occurred by reason of the application of Section 734(b) or
     754(b) of the Code shall be adjusted to the extent such adjustment to tax
     basis is taken into account pursuant to Regulation (S)1.704-1(b)(2)(iv)(m).

(vi) If the Book Value of an asset is not equal to its adjusted tax basis for
     federal income tax purposes, such Book Value shall be adjusted by the
     Depreciation taken into account with respect to such asset for purposes of
     computing Profits and Losses and other items allocated pursuant to Section
     4.1.

The foregoing definition of Book Value is intended to comply with the provisions
of Regulation (S)1.704-1(b)(2)(iv) and shall be interpreted and applied
consistently therewith.  Any determinations of "gross fair market value" in this
definition of Book Value shall be made by the Partnership Governance Committee.

     Business Day.  Any day other than a Saturday, Sunday or other day on which
banks are closed in New York City, New York.

     Business Opportunity.  See Section 9.3(c).

     Capital Account.  The separate capital account established and maintained
by the Partnership for each Partner, as contemplated by Section 2.


                                 Appendix A-4
<PAGE>
 
     Capital Expenditure Budget.  See Section 8.2(d).

     CEO.  See Section 7.1(b).

     Claim.  See Section 13.2(c).

     Closing Date.  The Closing Date under the Master Transaction Agreement.

     Code.  The Internal Revenue Code of 1986, as amended and in effect from
time to time and any successor thereto.

     Competing Opportunity.  See Section 9.3(c).

     Confidential Information.  All confidential documents and information
(including, without limitation, confidential commercial information and
information with respect to customers, trade secrets and proprietary
technologies or processes and the design and development of new products or
services) concerning the Partnership, the Partners or their Affiliates,
furnished to a Partner in connection with the transactions leading up to and
contemplated by this Agreement and the operation of the Partnership, except to
the extent that such information (i) is or becomes generally available to and
known by the public or the petrochemical industry (other than as a result of an
unpermitted disclosure directly or indirectly by the Partnership or a Partner),
(ii) is or becomes available to a Partner on a nonconfidential basis from a
source other than the Partnership or a Partner; provided, however, that such
source is not and was not bound by a confidentiality agreement with, or other
obligation of secrecy to, the Partnership or the other Partner, (iii) has
already been or is hereafter independently acquired or developed by a Partner
without violating any confidentiality agreement with or other obligation of
secrecy to the Partnership or another Partner or (iv) is otherwise generated by
the Partnership with the intention that it not be held as confidential.

     Conflict Circumstance.  Any transaction or dealing between the Partnership
(or any Wholly Owned Subsidiary) and a General Partner (the "Conflicted General
Partner") or any of its Affiliates pursuant to any agreement (including this
Agreement or any other Related Agreements) or otherwise, including action to be
taken by the Partnership pursuant to Section 9.3(c) or (d); provided, however,
that a Conflict Circumstance shall cease to exist if and when the third party
with which the transaction or dealing exists shall cease to be an Affiliate of a
General Partner.

     Conflicted General Partner.          As defined in the definition of
"Conflict Circumstance."

     Contributed Business.  As defined in the Asset Contribution Agreement.

     Damages.  With respect to a Person in connection with a Default, any and
all obligations (including all obligations to take an affirmative or curative
act), liabilities, damages (including damages arising out of any breach of any
representation or warranty, damages related to investigations, proceedings,
audits, the interruption of the Partnership's business, restrictions upon the
use of, or adverse impact on, the Assets or the Partnership's business, or the
interruption, breach or termination of any Related Agreements or other
agreements, including any lost profits attributable 


                                 Appendix A-5
<PAGE>
 
thereto), fines, penalties, deficiencies, losses, judgments, settlements, costs
and expenses (including costs and expenses incurred in connection with
performing obligations, bonding and appellate costs and attorneys',
accountants', engineers', health, safety, environmental and other consultants'
and investigators' fees and disbursements, liquidating, selling or offering for
sale the Partnership's business and assets or winding up the Partnership's
business, or other payments in respect of such payments) suffered or incurred by
such Person that arise out of or relate to such Default, regardless of whether
any of the foregoing are foreseeable, unforeseeable, matured or unmatured,
existing or contingent as of the date of such Default. "Damages" also shall
include, if and to the extent interest is not already included therein under
applicable law or other provisions hereof and subject to Section 13.20, interest
on amounts actually due until payment thereof is made at a rate per annum equal
to the rate set forth in Section 13.19(b). "Damages" shall not include any
punitive, exemplary, special or other similar damages.

     Deadlock Notice.  See Section 8.5.

     Default.  See Section 11.1.

     Default Date.  See Section 11.1.

     Defaulting Partners.  Lyondell GP and Lyondell LP, in the case of a Default
by Lyondell GP, Lyondell LP or their Guarantor; and Millennium GP and Millennium
LP, in the case of a Default by Millennium GP, Millennium LP or their Guarantor.

     Depreciation.  For each fiscal year or part thereof, an amount equal to the
depreciation, amortization, or other cost recovery deduction allowable for
federal income tax purposes with respect to an asset for such year or other
period, except that if the Book Value of an asset differs from its adjusted
basis for federal income tax purposes at the beginning of such year,
Depreciation shall be (i) an amount which bears the same ratio to such Book
Value as the federal income tax depreciation, amortization or other cost
recovery deduction for such year bears to such adjusted tax basis, or, (ii) if
the federal income tax depreciation, amortization or other cost recovery
deduction for such year is equal to zero, an amount determined with reference to
such Book Value using a reasonable method selected by the Tax Matters Partner.

     Executive Officers.  See Section 7.1(b).

     Expense.  See Section 13.3(a).

     Fair Market Value.  "Fair Market Value" with respect to the Partnership
shall mean the Asset Fair Market Value of all of the Partnership's assets
decreased by the fair value of all its liabilities, as of the most recently
ended fiscal quarter.  "Fair Market Value" with respect to a Related Business
shall mean the Asset Fair Market Value of all the assets of such Related
Business decreased by the fair value of all its liabilities, as of the most
recently ended fiscal quarter.  In either case, the following shall apply to the
determination of Fair Market Value:


                                 Appendix A-6
<PAGE>
 
(i)  The General Partners shall first attempt to agree on such value, which if
     agreed to shall be the Fair Market Value.

(ii) If the General Partners are unable to agree within 20 days of the first
     written notice from one General Partner to the other proposing an amount to
     be the Fair Market Value (the "Notice"), then if requested by either
     General Partner, each General Partner shall (at its own cost) cause an
     independent, qualified appraiser to deliver a written appraisal of its
     determination of the Fair Market Value within 50 days of the Notice.  If
     the lower appraised value is greater than or equal to 90% of the higher
     appraised value, then the average of the two appraised values shall be the
     Fair Market Value.

(iii)     If the lower appraised value is less than 90% of the higher appraised
value, then the General Partners shall jointly appoint a Neutral within 20 days
of the delivery of both such appraisals.  If the General Partners have been
unable to agree upon such appointment within such 20 days, then such Neutral
shall upon the application of either General Partner be appointed within 10 days
of the filing of such application by the Center for Public Resources, or if such
appointment is not so made promptly then promptly thereafter by the American
Arbitration Association in Philadelphia, Pennsylvania, or if such appointment is
not so made promptly then promptly thereafter by the senior United States
District Court judge sitting in Wilmington, Delaware.  The fees and expenses of
the Neutral shall be paid equally by the Partners.

(iv) The Neutral shall, within 30 days of the appointment of the Neutral,
     determine which of the two appraised values (without in any way modifying
     or compromising between the two appraised values) is closest to the fair
     market value of the enterprise's assets as determined by the Neutral, and
     that appraised value shall be the Fair Market Value.

     Fault.    Any act or omission of a Partner, its Affiliates or any of their
respective officers, directors or employees (acting in their capacities as such)
that constitutes or results from intentional misconduct, criminal intent or
gross negligence.

     Finally Determined.  Determined by any final, nonappealable judicial order
or pursuant to a binding alternative dispute resolution procedure.

     Funding Notice.  See Section 2.4.

     GAAP.  United States generally accepted accounting principles, as in effect
from time to time.

     General Partners.  Each Person who executes this Agreement and who is
hereby admitted to the Partnership as a general partner of the Partnership,
unless such General Partner ceases to be a General Partner hereunder or sells,
transfers, forfeits or otherwise disposes of its Units and is replaced by a
Substitute General Partner in accordance with this Agreement and the Act, and
each Person that becomes a Substitute General Partner, if any, of the
Partnership as provided herein, in such Person's capacity as a general partner
of the Partnership.

                                 Appendix A-7
<PAGE>
 
     Guarantor.  Lyondell Petrochemical Company, with respect to Lyondell GP and
Lyondell LP; and Millennium Chemicals Inc., with respect to Millennium GP and
Millennium LP; and any successor or additional guarantor party to an agreement
substantially in the form of the Parent Agreement and entered into in accordance
with Section 10.

     Highest Lawful Rate.  The maximum rate of interest, if any, that may be
charged to any person under all Applicable Usury Laws on any principal balance
from time to time outstanding pursuant to this Agreement.

     HSE Law. "HSE Law," as defined in Section 1 of the Asset Contribution
Agreement.

     Indemnified Party.  See Section 13.2(c).

     Indemnifying Party.  See Section 13.2(c).

     Initial Assets.  "Assets," as defined in Section 1 of the Asset
Contribution Agreements.

     Initial Notice.  See Section 10.2(a).

     IRS.  Internal Revenue Service.

     Liability.  Any loss, claim, damages, fine, penalty, assessment by public
agencies, settlement, cost or expense (including costs of investigation, defense
and attorneys' fees) or other liability.

     Limited Partner.  Each Person who executes this Agreement and who is hereby
admitted to the Partnership as a limited partner of the Partnership, unless such
Limited Partner ceases to be a Limited Partner hereunder or sells, transfers,
forfeits or otherwise disposes of its Units and is replaced by a Substitute
Limited Partner in accordance with this Agreement and the Act, and each Person
that becomes a Substitute Limited Partner, if any, of the Partnership as
provided herein, in such Person's capacity as a limited partner of the
Partnership.

     Limited Partners Pro Rata.  From or to the Limited Partners in the ratio of
the Units owned by each.

     Liquidation.  See Section 11.4.

     Losses.  See definition of "Profits and Losses."

     Lyondell.  Lyondell Petrochemical Company, a Delaware corporation.

     Lyondell Assumed Debt.  Debt issued by Lyondell having an aggregate
principal amount of $745 million, as specified in the Asset Contribution
Agreement with respect to Lyondell.

     Lyondell GP.  Lyondell Petrochemical G.P. Inc., a Delaware corporation, the
General Partner that is an Affiliate of Lyondell.

                                 Appendix A-8
<PAGE>
 
     Lyondell LP.  Lyondell Petrochemical L.P. Inc., a Delaware corporation, the
Limited Partner that is an Affiliate of Lyondell.

     Lyondell Note.  That certain promissory note to be dated as of the Closing
Date in the amount of $345 million payable by Lyondell LP to the Partnership, as
contemplated by the Master Transaction Agreement.

     Master Transaction Agreement.  That certain agreement between Lyondell
Petrochemical Company and Millennium Chemicals Inc. dated July 25, 1997, as
amended, providing for the execution of various agreements concerning the
Partnership and the Initial Assets.

     Maximum Amount.  The maximum nonusurious amount of interest that may be
lawfully contracted for, charged or received by any person in connection with
any indebtedness arising under this Agreement under all Applicable Usury Laws.

     Millennium.  Millennium Chemicals Inc., a Delaware corporation.

     Millennium America.  Millennium America Inc., a Delaware corporation.

     Millennium America Guarantee.  See Section 8.6(c).

     Millennium America Guaranteed Debt.  The portion, if any, of the debt
outstanding under the Bank Credit Agreement and the portion, if any, of any debt
that refinances the debt outstanding under the Bank Credit Agreement or any
subsequent refinancing thereof (in any case, not to exceed a guarantee of $750
million principal amount), in each case to the extent such debt is guaranteed by
Millennium America, or an Affiliate thereof,  as contemplated by Section 8.6(c).

     Millennium Debt.  That certain indebtedness of Millennium or an Affiliate
thereof in the amount of $750 million to be assumed by the Partnership pursuant
to the Millennium Asset Contribution Agreement.

     Millennium GP.  Millennium Petrochemicals GP LLC, a Delaware limited
liability company, the General Partner that is an Affiliate of Millennium.

     Millennium LP.  Millennium Petrochemicals LP LLC, a Delaware limited
liability company, the Limited Partner that is an Affiliate of Millennium.

     Neutral.  A neutral Person acceptable to all of the appointing Partners and
not affiliated with any of the Partners.

     Nonconflicted General Partner.  With respect to any Conflict Circumstance,
the General Partner that is not the Conflicted Partner with respect thereto.

     Non-Defaulting Partners.  The two Partners other than the two Defaulting
Partners.

                                 Appendix A-9
<PAGE>
 
     Offeree Partners.  See Section 10.2(a).

     Operating Budget.  See Section 8.2(c).

     Parent Agreement.  Parent Agreement to be entered into among Millennium,
Lyondell and the Partnership providing, among other things, for a guarantee from
each Guarantor to the Partnership, executed in connection with this Agreement,
as amended from time to time, the form of which is referenced in the Master
Transaction Agreement.

     Partners.  The General Partners and the Limited Partners on the date of
this Agreement until such Person ceases to be a partner of the Partnership.

     Partners Pro Rata.   From or to all Partners in the ratio of the Units
owned by each.

     Partnership.  Equistar Chemicals, LP,  a Delaware limited partnership, the
limited partnership formed and continued under the Act and this Agreement.

     Partnership Governance Committee.  See Section 6.1.

     Partnership Governance Committee Action.  See Section 6.1.

     Profits and Losses.  For each applicable period, the Partnership's taxable
income or loss for such period determined in accordance with Section 703(a) of
the Code (for this purpose, all items of income, gain, loss or deduction
required to be stated separately pursuant to Section 703(a)(1) of the Code shall
be included in taxable income or loss) with the following adjustments:

          (i) Any income of the Partnership that is exempt from federal income
     tax and not otherwise taken in account in computing Profits or Losses
     pursuant to this definition shall be added to such taxable income or loss.

          (ii) Any expenditures of the Partnership described in Section
     705(a)(2)(B) of the Code or treated as such pursuant to Regulation
     (S)1.704-1(b)(2)(iv)(i) and not otherwise taken in account in computing
     Profits or Losses pursuant to this definition shall be subtracted from such
     taxable income or loss.

          (iii)  Depreciation for such period shall be taken into account in
     lieu of the depreciation, amortization and other cost recovery deductions
     taken into account in computing such taxable income or loss.

          (iv) Gain or loss resulting from any disposition of Partnership
     property with respect to which gain or loss is recognized for federal
     income tax purposes shall be computed with reference to the Book Value of
     the property disposed of, rather than the adjusted tax basis of such
     property.

                                 Appendix A-10
<PAGE>
 
          (v) If any property is distributed in kind to any Partner, the
     difference between its fair market value and its Book Value at the time of
     distribution shall be treated as Profit or Loss, as the case may be,
     recognized by the Partnership.

          (vi) The amount of any adjustment to the Book Value of any Partnership
     asset pursuant to clause (iii) of the definition of Book Value herein shall
     be taken into account as Profit or Loss from the disposition of such asset.

     Percentage Interest.  The percentage determined by dividing the number of
Units owned by a Partner by the total number of outstanding Units.

     Person.  Any natural person or any corporation, limited liability company,
partnership, joint venture, association, trust or other entity.

     Pledge.  To mortgage, pledge, encumber or create or suffer to exist any
pledge, lien or encumbrance upon or security interest in.  Such defined term is
used in this Agreement as both a noun and a verb.

     Pro Rata.  In the ratio of the Units owned by a Partner to the total number
of Units.

     Proposing Partner.  See Section 9.3(c).

     Regulations.  The income tax regulations promulgated by Department of the
Treasury and in effect from time to time.

     Related Agreements.  The agreements (other than the Partnership Agreement)
defined as "Related Agreements" in the Master Transaction Agreement, as such
agreements may be amended from time to time after the Closing Date.

     Related Business.  See Section 9.3(c).

     Related Persons.  See Section 13.1.

     Representative.  See Section 6.4(a).

     SEC.  Securities and Exchange Commission.

     Selling Partners.  See Section 10.2(a).

     Specified Petrochemicals Businesses.  The businesses of:

     (i) Olefins and olefins coproducts consisting of:  ethylene, propylene,
butadiene, and mixed butylenes; aromatics and gasoline blending components
(benzene, toluene, MTBE, alkylate, pyrolysis gasolines); mixed C5 hydrocarbons;
resin formers (dicyclopentadiene, isoprene, piperylenes, resin oil); pyrolysis
liquid fuel products (pyrolysis gas oil, pyrolysis fuel oil);

                                 Appendix A-11
<PAGE>
 
     (ii) Polyolefins consisting of:  low-density, linear low-density, and high-
density polyethylene; polypropylene; ethylene/propylene copolymers; rotomolding
and polymeric powders; wire and cable resins; adhesive tie layers; hot melt
adhesive resins; colors  and concentrates; fuel additives; and

     (iii)  Ethyl alcohol and ethyl ether.

     Strategic Plan.  See Section 8.1.

     Substitute General Partner.  A Person who is admitted as a General Partner
to the Partnership in place of and with all the rights of a General Partner.

     Substitute Limited Partner.  A Person who is admitted as a Limited Partner
to the Partnership in place of and with all the rights of a Limited Partner.

     Taxes.  All taxes, charges, fees, levies or other assessments imposed by
any taxing authority, including, but not limited to, income, gross receipts,
excise, property, sales, use, transfer, payroll, license, ad valorem, value
added, withholding, social security, national insurance (or other similar
contributions or payments), franchise, severance and stamp taxes (including any
interest, fines, penalties or additions attributable to, or imposed on or with
respect to, any such taxes, charges, fees, levies or other assessments) and "Tax
Return" means any return, report, information return or other document
(including any related or supporting information) with respect to Taxes.

     Tax Matters Partner.  Lyondell GP shall serve as the tax matters partner.

     Third Party Claim.  Any allegation, claim, civil, criminal or other action,
proceeding, charge or prosecution brought by any Person other than the
Partnership, any Partner or any Affiliate of a Partner.

     Transfer.  To sell, assign or otherwise in any manner dispose of, whether
by act, deed, merger, consolidation, conversion or otherwise.  Such defined term
is used in this Agreement as both a noun and a verb.

     Unit.  A unit representing a partnership interest in the Partnership.

     Wholly Owned Affiliate.  As to any Person, an Affiliate of such Person all
of the equity interests of which are owned, directly or indirectly, by a
Partner, by another Wholly Owned Affiliate of such Person or by the ultimate
parent entity thereof.

     Wholly Owned Subsidiary.   As to any Person, a subsidiary of such Person
all of the equity interests of which are owned, directly or indirectly, by such
Person.

                                 Appendix A-12
<PAGE>
 
                                  APPENDIX B
                       TO LIMITED PARTNERSHIP AGREEMENT

                 PARTNERSHIP FINANCIAL STATEMENTS AND REPORTS
<TABLE>
<CAPTION>
 
 
Item & Frequency                                       Due Dates
<S>                                       <C>
Monthly:
   Income Statement - current period      10th work day following month-end
    and year-to-date
   Balance Sheet - current period         10th work day following month-end
   Cash Flow Statement - current period   10th work day following month-end
    and year-to-date
   Schedule of Income Allocation -        5th work day following month-end
    preliminary
   Schedule of Income Allocation - final  10th work day following month-end
   Calculation of Distribution of
    Available Net Operating               15th work day following month-end
      Cash - final
   Results of Operations Analysis         10th work day following month-end
Quarterly:
   Analysis for Investor Relations and
    Form 10-Q disclosures:                15th work day following quarter-end
      -  Results of Operations            15th work day following quarter-end
      -  Cash Flow                        15th work day following quarter-end
      -  Sales Variances                  15th work day following quarter-end
      -  Capital Expenditures             15th work day following quarter-end
      -  Intercompany Transactions        15th work day following quarter-end
      -  Volumes                          15th work day following quarter-end
      -  Prices                           15th work day following quarter-end
      -  Unusual Items               
Income Statement - current quarter and    10th work day following quarter-end
 year-to-date
Balance Sheet - current period            10th work day following quarter-end
Cash Flow Statement - current quarter     10th work day following quarter-end
 and year-to-date
Annual:
   Analysis for Investor Relations and
    Form 10-K disclosures
      -  Same as quarterly requirements   15th work day following year-end
      -  Plant Capacities                 
         Audited Financial Statements     60 days following year-end
</TABLE>

                                 Appendix B-1
<PAGE>
 
                                   APPENDIX C
                           INITIAL EXECUTIVE OFFICERS


Dan F. Smith             Chief Executive Officer
Eugene R. Allspach       President and Chief Operating Officer
Joseph M. Putz           Senior Vice President, Finance and Administration
Debra L. Starnes         Senior Vice President, Polymers       
John R. Beard            Vice President, Manufacturing         
J. R. Fontenot           Vice President, Engineering           
Alan Houlton             Vice President, Customer Supply Chain 
Gerald A. O'Brien        Vice President and Secretary          
Myra J. Perkinson        Vice President, Human Resources        
W. Norman Phillips, Jr.  Vice President, Petrochemicals
Kerry F. Williams        Vice President, Research and Development
Jeffrey L. Hemmer        Director, Business Process Improvement

                                 Appendix C-1
<PAGE>
 
                                   APPENDIX D

                         DISPUTE RESOLUTION PROCEDURES


     (1) Binding and Exclusive Means.  Except as otherwise provided in the
Partnership Agreement, the dispute resolution provisions set forth in this
Appendix shall be the binding and exclusive means to resolve all disputes
arising under the Agreement (each a "Dispute").

     (2) Standards and Criteria.  In resolving any Dispute, the standards and
criteria for resolving such Dispute shall, unless the Partners in their
discretion jointly stipulate otherwise, be as set forth in Appendix 1 to this
Appendix.

     (3) ADR and Binding Arbitration Procedures.  If a Dispute arises, the
following procedures shall be implemented:

     (a) Each Partner may at any time invoke the dispute resolution procedures
set forth in this Appendix as to any Dispute by providing written notice of such
action to the Secretary of the Partnership, who within five Business Days after
such notice shall schedule a meeting to be held in Houston, Texas between the
Partners.  The Partners' meeting shall occur within 10 Business Days after
notice of the meeting is delivered to the Partners.  The meeting shall be
attended by representatives of each Partner having decision-making authority
regarding the Dispute as well as the dispute resolution process and who shall
attempt in a commercially reasonable manner to negotiate a resolution of the
Dispute.

     (b) The representatives of the Partners shall cooperate in a commercially
reasonable manner and shall explore whether techniques such as mediation,
minitrials, mock trials or other techniques of alternative dispute resolution
might be useful.  In the event that a technique of alternative dispute
resolution is so agreed upon, a specific timetable and completion date for its
implementation shall also be agreed upon.  The representatives will continue to
meet and discuss settlement until the date (the "Interim Decision Date") that is
the earliest to occur of the following events:  (i) an agreement shall be
reached by the Partners resolving the Dispute; (ii) one of the Partners shall
determine and notify the other Partners in writing that no agreement resolving
the Dispute is likely to be reached; (iii) if a technique of alternative dispute
resolution is agreed upon, the completion date therefor shall occur without the
Partners having resolved the Dispute; or (iv) if another technique of
alternative dispute resolution is not agreed upon, two full meeting days (or
such other time period as may be agreed upon) shall expire without the Partners
having resolved the Dispute.

     (c) If, as of the Interim Decision Date, the Partners have not succeeded in
negotiating a resolution of the Dispute pursuant to subsection (b), the Partners
shall proceed under subsection (d).

     (d) The Partners shall jointly appoint a Neutral.  If the Partners have
been unable to agree upon such appointment within 30 days from the Interim
Decision Date, then such Neutral upon the application of any Partner shall be
appointed within 10 days of the filing of such application by the 
 
                                 Appendix D-1
<PAGE>
 
Center for Public Resources, or if such appointment is not so made promptly then
promptly thereafter by the American Arbitration Association in Philadelphia,
Pennsylvania, or if such appointment is not so made promptly then promptly
thereafter by the senior United States District Court judge sitting in
Wilmington, Delaware. The fees of the Neutral shall be paid equally by the
Partners except that the Neutral shall have discretion to award fees.

     (e) In consultation with the Neutral, the Partners shall agree upon a
binding schedule and procedure (which procedure may have been previously
discussed under subsection (b)) to be used as a means to resolve or to attempt
to resolve the Dispute, with the Neutral making the decision as to the schedule
and/or procedure if the Partners have been unable to agree on any of such
matters within 20 days after the initial selection of the Neutral.  The Partners
agree to participate in a commercially reasonable manner in the procedure to its
conclusion as determined by the Neutral.  If the Partners are not successful in
resolving the dispute through the procedure described above, then the Partners
agree that (i) the Neutral shall act as the arbitrator in a binding arbitration
in accordance with American Arbitration Association rules and shall render a
decision and (ii) judgment upon the decision rendered by the Neutral may be
entered in any court having jurisdiction.

     (4) Continuation of Business.  Notwithstanding the existence of any Dispute
or the pendency of any procedures pursuant to this Appendix, the Partners agree
and undertake that all payments not in dispute shall continue to be made and all
obligations not in dispute shall continue to be performed.
 
                                 Appendix D-2
<PAGE>
 
                            APPENDIX 1 TO APPENDIX D

     (a) First priority shall be given to maximizing the consistency of the
resolution of the Dispute with the satisfaction of all express obligations of
the Partners and their Affiliates as set forth in the Partnership Agreement.

     (b) Second priority shall be given to resolution of the Dispute in a manner
which best achieves the objectives of the business activities and arrangements
under the Partnership Agreement and the Related Agreements and permits the
Partners to realize the benefits intended to be afforded thereby.

     (c) Third priority shall be given to such other matters, if any, as the
Partners or the Neutral shall determine to be appropriate under the
circumstances.
 
                                 Appendix D-3
<PAGE>
 
                                   APPENDIX E

                        DIVISION OF PARTNERSHIP BUSINESS


     If the Partnership is dissolved and Section 12.2(e) applies to the winding
up of the affairs of the Partnership, the Partnership properties shall, to the
extent legally and contractually feasible and, after satisfaction of the
liabilities of the Partnership (whether by payment or reasonable provision for
payment), be distributed in kind to the Partners in accordance with a division
(the "Division") of the properties.  The Division shall be implemented by
dividing the properties, to the extent feasible, in accordance with the
following priorities and principles:

A.   First priority shall be given to maximizing the consistency of the Division
     with a division of the Partnership properties that allocates to each
     Partner (subject to such Partner's Percentage Interest of the Partnership's
     liabilities) Partnership properties in proportion to the value of such
     Partner's Percentage Interest in the Partnership's business taking into
     account the aggregate Asset Fair Market Value of the Partnership's
     properties and the value and benefits afforded to such Partner under the
     Partnership Agreement and the other Related Agreements.

B.   Second priority shall be given to the allocation of the Partnership's
     various assets and business units between the Partners so as to maximize
     the aggregate going concern value of the respective assets and business
     units allocated to each Partner, taking into account, without limitation,
     the potential synergies and efficiencies that are reasonably achievable in
     connection with the operation of such allocated assets and business units
     as an independent business entity.

C.   Third priority shall be given to maximizing the consistency of the Division
     with the nature and quality of the Assets and Contributed Business
     originally transferred to the Partnership by the respective Partners or
     their Affiliates.

     Absent an agreement by the Partners or direction by the Neutral as to both
(i) how the Partners should allocate Partnership debt and (ii) the process for
relieving each Partner of liability for that portion of Partnership debt
allocated to the other Partner, the Partners (A) shall be jointly and severally
liable to the holders of all Partnership debt and (B) as between the Partners,
each Partner shall be obligated to pay to holders of the debt its Percentage
Interest of all payments of principal and interest on Partnership Debt.
Notwithstanding the foregoing, the Neutral shall be entitled to direct, and any
Partner may propose, an alternative allocation of Partnership debt in any
circumstance where such alternative allocation is reasonably likely to result in
a Division that is more consistent with the priorities outlined above.

     For purposes of this Appendix E, Lyondell GP and Lyondell LP shall be
treated as if they were a single Partner and Millennium GP and Millennium LP
shall be treated as if they were a single Partner.
 
                                 Appendix E-1
<PAGE>
 
     The Partners shall attempt to agree on a plan for a mutually acceptable
Division.  If they are unable to so agree after 60 days following the occurrence
of the dissolution, a Neutral shall be appointed in accordance with Appendix D
and each Partner shall submit to the Neutral a written proposal for a Division.
The Neutral shall decide which of the two proposals (without in any way
modifying or compromising between the two proposals) more closely follows the
priorities and principles set forth above, and the proposal so chosen shall
thereupon be binding upon all Partners and shall be promptly implemented under
the direction of the Neutral. The Neutral shall be entitled to employ (at the
expense of the Partnership) such financial and accounting advisors and legal
counsel as he or she shall select, provided that no such advisor or counsel
shall have any affiliation with any Partner.

 
                                 Appendix E-2
<PAGE>
 
                                  SCHEDULE 2.3

      CREDITS TO LIMITED PARTNER CAPITAL ACCOUNTS PURSUANT TO SECTION 2.3


               Lyondell LP:              $1.975 billion

               Millennium LP:            $1.750 billion