EXHIBIT 4.4(a)

                        LYONDELL PETROCHEMICAL COMPANY


                                      AND


                   TEXAS COMMERCE BANK NATIONAL ASSOCIATION,

                                    Trustee

                         FIRST SUPPLEMENTAL INDENTURE


                           Dated as of May 31, 1989


                                    to the


                                   INDENTURE


                           Dated as of May 31, 1989


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


                             9.95% Notes Due 1996

                             10.00% Notes Due 1999

 
                               TABLE OF CONTENTS


                                                                     Page
                                                                     ----
                                                                
                 Recitals of the Company.............................  1

Section 1.       Terms Defined in the Indenture......................  1

Section 2.       Certain Defined Terms...............................  1

Section 3.       Designation.........................................  5

Section 4.       Dating of the Notes.................................  5

Section 5.       Maximum Aggregate Outstanding Amount................  5

Section 6.       Stated Maturity.....................................  6

Section 7.       Denomination of Notes...............................  6

Section 8.       Payments of Principal and Interest, Record Dates....  6

Section 9.       Place of Payment....................................  7

Section 10.      Form of Notes.......................................  7

Section 11.      Ranking.............................................  7

Section 12.      Defeasance..........................................  7

Section 13.      Limitation on Liens.................................  8

Section 14.      Put Right of Note Holders...........................  8

Section 15.      Definition of Restricted Property and Subsidiary;
                 Limitation on Olefins Subsidiary....................  9

Section 16.      Concerning the Trustee.............................. 10

Section 17.      Events of Default................................... 11

Section 18.      Governing Law....................................... 11

Section 19.      Counterparts........................................ 11

Section 20.      Miscellaneous....................................... 11


 
     FIRST SUPPLEMENTAL INDENTURE, dated as of May 31, 1989 (the "Supplement"),
between LYONDELL PETROCHEMICAL COMPANY, a Delaware corporation (the "Company"),
and Texas Commerce Bank National Association, a national banking association
(the "Trustee"), as Trustee under an Indenture, dated as of May 31, 1989 (the
"Indenture").

                            RECITALS OF THE COMPANY

     The Company has previously executed and delivered to the Trustee the
Indenture. Section 2.01 and 11.01 of the Indenture provide, among other things,
that the Company, when authorized by its Board of Directors, and the Trustee may
at any time and from time to time enter into an indenture supplemental to the
Indenture for the purpose of authorizing a series of Securities and specifying
the terms and form of each series of Securities. The Board of Directors of
the Company has duly authorized the creation, issuance, execution and delivery
of two series of notes consisting of the 9.95% Notes Due 1996 (the "1996 Notes")
and the 10.00% Notes Due 1999 (the "1999 Notes") in the maximum aggregate
principal amount of $300,000,000. The Company and the Trustee are executing and
delivering this Supplement in order to provide for the 1996 Notes and the 1999
Notes (collectively the "Notes").

     All things necessary to make this Supplement a valid and legally binding
agreement of the Company have been done.

     SECTION 1. Terms Defined in the Indenture.

     All capitalized terms used in this Supplement that are defined in the
Indenture have the meanings assigned to them in the Indenture, except to the
extent that such terms are otherwise defined in this Supplement.

     SECTION 2. Certain Defined Terms.

     (A) Definitions.

     "Applicable Percentage" means (1) in the case of each distribution referred
to in clause (5) of the definition of Designated Event, the percentage
determined, as of the Calculation Date corresponding with each such
distribution, by dividing the aggregate fair market value of such distribution
(as determined in good faith by the Board of Directors, whose determination
shall be conclusive), by the fair market value (based on the Current Market
Price) of all shares of all classes of the Company's capital stock outstanding
on the day immediately prior to each such Calculation Date, and (2) in the case
of each purchase or acquisition referred to in clause (5) of the definition of
Designated Event, the percentage determined, as of the Calculation Date
corresponding with each purchase or acquisition, by dividing all amounts
expended by the Company and its Subsidiaries or majority owned affiliates (the
amount expended, if other than cash, shall be determined in good faith by the

                                       1

 
Board of Directors, whose determination shall be conclusive) in connection with
the purchase or acquisition of any shares of any class of Voting Stock of the
Company, by the fair market value (based on the Current Market Price) of all
shares of all classes of the Company's capital stock outstanding on the day
immediately prior to each such Calculation Date.

     "Capital Expenditures" shall mean all expenditures for the maintenance,
repair or upgrade of the Restricted Properties existing as of the date of this
Supplement which expenditures are capitalized under generally accepted
accounting principles.

     "Current Market Price" means the closing price (or, if none, the average of
the last daily bid and asked prices) of the applicable class of capital stock as
quoted by the primary securities exchange on which the stock is traded, or, if
none, the primary inter-dealer quotation system, which reports quotations for
the class of capital stock, for the last trading day immediately prior to the
Calculation Date.

     "Designated Event" means any one or more of the following events which
occurs subsequent to the date of issuance of the Notes:

     (1) a "person" or "group" (within the meaning of Sections 13(d) and
14(d)(2) of the Securities Exchange Act of 1934, as amended (the "Exchange
Act")) (with the exception of the Company, Atlantic Richfield Company, or any of
their respective majority owned subsidiaries or affiliates) becomes the
"beneficial owner" (as defined in Rule 13d-3 of the Exchange Act) of more than
20% of the then outstanding Voting Stock of the Company; provided that such 20%
shall be 30% with respect to any "employee benefit plan" (as defined in Section
3(3) of the Employee Retirement Income Security Act of 1974, as amended)
maintained by the Company or any Subsidiary, or any trust or funding vehicle
maintained thereunder;

     (2) during any period of two consecutive years, individuals who at the
beginning of such period constitute the Company's Board of Directors (together
with any new Director whose election by the Company's Board of Directors or
whose nomination for election by the Company's stockholders was approved by a
vote of at least two-thirds of the Directors then still in office who either
were Directors at the beginning of such period or whose election or nomination
for election was previously so approved) cease for any reason to constitute a
majority of the Directors then in office;

     (3) (i) the Company shall consolidate with or merge into any other
corporation or convey, transfer or lease all or substantially all of its assets
to any person or (ii) any corporation shall consolidate with or merge into the
Company, in either event pursuant to a transaction in which any shares of Voting
Stock of the Company outstanding immediately prior to the effectiveness thereof
are changed into or exchanged for cash, securities or other property; provided
that any merger,

                                       2

 
consolidation, conveyance, transfer or lease between the Company and its
Subsidiaries or between Subsidiaries shall be excluded from the operation of
this clause (3);

     (4) the Company or any Subsidiary or majority owned affiliate shall
purchase or otherwise acquire, directly or indirectly, beneficial ownership of
Voting Stock of the Company if, after giving effect to such purchase or
acquisition, the Company (together with all Subsidiaries or majority owned
affiliates) shall have acquired, during any period of 12 consecutive months,
beneficial ownership of an aggregate of 30% or more of the Voting Stock of the
Company outstanding on the date immediately prior to the first such purchase or
acquisition during such period;

     (5) on any date (a "Calculation Date") (i) the Company shall make any
distribution or distributions of cash, securities or other properties (other
than (a) regular cash dividends, or (b) capital stock or rights to acquire
capital stock substantially equivalent to capital stock of the Company) to
holders of Voting Stock, whether by means of dividend, reclassification,
recapitalization or otherwise, or (ii) the Company or any Subsidiary shall
purchase or otherwise acquire, directly or indirectly, beneficial ownership of
Voting Stock of the Company, and the sum of the Applicable Percentages
corresponding with all such distributions, purchases and acquisitions covered by
this clause (5), which are being made currently or have occurred during the 12
consecutive months immediately preceding the Calculation Date shall be at least
30%. The $500 million special distribution paid on January 17, 1989 to the
Company's sole stockholder at that time, Atlantic Richfield Company, shall not
be deemed to be a distribution subject to this clause (5); or

     (6) during any fiscal year (i) the Company or any Subsidiary shall make any
distribution or distributions of cash, securities or other properties (other
than (a) regular cash dividends, and (b) capital stock or rights to acquire
capital stock substantially equivalent to capital stock of the Company) to
holders of Voting Stock, whether by means of dividend, reclassification,
recapitalization or otherwise, or (ii) the Company or any Subsidiary shall
purchase or otherwise acquire, directly or indirectly, beneficial ownership of
Voting Stock of the Company (other than Voting Stock purchased or acquired in
connection with employee benefit plans or in connection with other employee
compensation programs, having an aggregate purchase price or acquisition cost
not greater than $25 million), and the sum of the fair market value (as
determined in good faith by the Board of Directors, whose determination shall be
conclusive) of all such distributions, acquisitions or purchases during such
fiscal year shall exceed an amount equal to the Company's Net Cash Flow for the
prior fiscal year less the aggregate amount of regular quarterly dividends paid
during the same prior fiscal year. The $500 million special distribution paid on
January 17, 1989 to the Company's sole stockholder at that time, Atlantic
Richfield Company, shall not be deemed to be a distribution subject to this
clause (6).

                                       3

 
For purposes of clauses (5) and (6), regular dividends shall be deemed to be
those quarterly cash dividends, including increases in such dividends, paid from
time to time by the Company; provided, however, that, in the good faith judgment
of the Company's Board of Directors, whose determination shall be conclusive,
(i) the amount of the dividends is appropriate in light of the Company's results
of operations, and (ii) the Company is capable of sustaining the rate at which
the dividends are being paid.

     "Full Rating Category" means (1) with respect to S&P, any of the following
categories in descending order: AAA, AA, A, BBB, BB, B, CCC, CC and C, (2) with
respect to Moody's, any of the following categories in descending order: Aaa,
Aa, A, Baa, Ba, B, Caa, Ca and C and (3) with respect to any other rating
agency, the equivalent of any category of S&P or Moody's used by the other
rating agency. In determining whether the rating of the Notes has decreased by
the equivalent of one Full Rating Category, gradation within Full Rating
Categories (+ and - for S&P; 1, 2, and 3 for Moody's; or the equivalent
gradation for another rating agency) shall be taken into account (e.g., with
respect to S&P, a decline in rating from BB- to B- will constitute a decrease of
one Full Rating Category, and a decline in rating from BB- to B will constitute
a decrease of less than one Full Rating Category).

     "Investment Grade" means a rating of not less than Baa3, in the case of a
rating by Moody's, or a rating of not less than BBB-, in the case of a rating by
S&P, or the equivalent of such ratings by S&P or Moody's or by any other rating
agency.

     "Net Cash Flow" shall mean net income plus the following: (1) depreciation;
(2) amortization of goodwill and other intangible assets; (3) the deferred
portion of the Company's income tax provision; (4) the proceeds from the sale of
capital stock; and (5) the net change in accounts receivable, inventories,
accounts payable and other working capital accounts as shown on the Company's
Consolidated Statement of Cash Flows; reduced by the following: (1) the amount
of any after-tax gains on asset sales included in net income; (2) principal
repayments of Debt and payments of the principal portion of capital leases (to
the extent such repayments and payments have not been refinanced through the
issuance of new Debt or capital leases at any time after the beginning of the
fiscal year for which the calculation is made and ending on the date of any
distribution, acquisition or purchase referred to in clause (6) of the
definition of Designated Event); and (3) Capital Expenditures.

     "Public Notice" shall, without limitation, include any filing or report
made in accordance with the requirements of the Securities and Exchange
Commission or any press release or public announcement made by the Company.

     "Rating Agency" shall mean Standard & Poor's Corporation and its successors
("S&P"), and Moody's Investors Service, Inc. and its successors ("Moody's"), or,
if S&P or Moody's or both shall not make a rating on the Notes publicly
available, a nationally recognized securities rating agency or agencies, as the
case may be, selected by the

                                       4

 
Company which shall be substituted for S&P or Moody's or both, as the case may
be.

     "Rating Date" shall mean the date that is 121 days prior to Public Notice
of the occurrence of a Designated Event.

     "Rating Decline" shall be deemed to occur if on any date within the 90-day
period following Public Notice of the occurrence of a Designated Event (which
period shall be extended so long as the rating of the Notes is under publicly
announced consideration for possible downgrade by a Rating Agency) (1) in the
event the Notes are rated by one or both Rating Agencies on the Rating Date as
Investment Grade, the rating on the Notes by both Rating Agencies shall be below
Investment Grade, or (2) in the event the Notes are rated by both Rating
Agencies on the Rating Date below Investment Grade, the rating on the Notes by
each Rating Agency shall be at least one Full Rating Category below the rating
of the Notes by such Rating Agency on the Rating Date.

     "Voting Stock" means the capital stock of the Company normally entitled to
vote in the election of directors.

     (B) Other Definitions.

                                              Defined in
               Term                            Section
               ----                            -------

          Indenture                     Recital of the Company
          Moody's                       Definition of Full Rating Category
          1996 Notes                    Preliminary Statement
          1999 Notes                    Preliminary Statement
          S&P                           Definition of Full Rating Category
          Record Date                   8
          Repurchase Date               14

     SECTION 3. Designation.

     The Notes are hereby created and shall be issuable in two series, the 1996
Notes shall be designated as the "9.95% Notes Due 1996" and the 1999 Notes shall
be designated as the "10.00% Notes Due 1999."

     SECTION 4. Dating of the Notes.

     All Notes shall be dated the date of authentication.

     SECTION 5. Maximum Aggregate Outstanding Amount.

     The maximum aggregate principal amount of the 1996 Notes and 1999 Notes
that may be authenticated and delivered under this Supplement is limited to
$150,000,000 and

                                       5

 
$150,000,000, respectively, except for Notes authenticated and delivered upon
transfer of, or in exchange for, or in lieu of, other Notes pursuant to Sections
2.05, 2.06, 2.07, 3.03 or 11.04 of the Indenture.

     SECTION 6. Stated Maturity.

     The principal amount of the 1996 Notes shall be due and payable on June 1,
1996. The principal amount of the 1999 Notes shall be due and payable on June 1,
1999.

     SECTION 7. Denomination of Notes.

     The Notes shall be issued only in fully registered certificated form,
without coupon, in minimum denominations of $1,000 and any amount in excess
thereof that is an integral multiple of S1,000.

     SECTION 8. Payments of Principal and Interest, Record Dates.

     Each Note shall bear interest on its outstanding principal balance from
June 1, 1989 at the following interest rates, until payment of the principal
thereof has been made or duly provided for: the 1996 Notes, 9.95%; and the 1999
Notes, 10.00%. Interest on the Notes shall be paid semi-annually on June 1 and
December 1, commencing on December 1, 1989. Interest on the Notes of each series
shall be computed on the basis of a 360-day year of twelve 30-day months, from
the later of: (1) June 1, 1989, or (2) the most recent Interest Payment Date to
which interest has been paid or duly provided for. Interest on the Notes shall
be payable in lawful money of the United States of America.

     The principal of each Note shall be payable on the date due upon delivery
and surrender of such Note to the Trustee at the Place of Payment in lawful
money of the United States of America in next-day funds by check as provided in
Section 5.02 of the Indenture.

     The record date ("Record Date") for each Interest Payment Date shall be the
close of business on the May 15 and November 15 next preceding each Interest
Payment Date, whether or not such date shall be a Business Day.

     Any interest not paid on the Interest Payment Date therefor ("Defaulted
Interest") may be paid to the person in whose name this Note is registered at
the close of business on a special record date for the payment of such Defaulted
Interest, notice of which shall be given by the Company to Holders of Notes not
less than fifteen days prior to such special record date, or may be paid in any
other lawful manner.

     Payment of interest on each Note shall be made on each Interest Payment
Date to the Holder of each Note at the close of business on the Record Date for
each Interest Payment Date by check mailed to the Holder at its address as it
appears on the registration

                                       6

 
books maintained by the Company pursuant to Section 2.05 of the Indenture or at
any other address that is furnished to the Trustee in writing by the Holder at
least 15 Business Days prior to the Interest Payment Date.

     Any payment of principal or interest required to be made on an Interest
Payment Date or at Maturity of a Note that is not a Business Day need not be
made on that day, but may be made on the next succeeding Business Day with the
same force and effect as if made on the Interest Payment Date or at Maturity, as
the case may be, and no additional interest shall accrue as a result of such
delayed payment. The Company shall pay any administrative costs imposed by banks
in connection with making payments by wire transfer in accordance with the
requirements of this Section 8, but any tax, assessment or governmental charge
imposed upon or required to be withheld from payments shall be borne by the
Holders of the Notes in respect to which payments are made.

     SECTION 9. Place of Payment.

     The Place of Payment of the Notes shall be at the offices or agencies of
the Trustee in Houston, Texas, or, at the option of the Holder, in the Borough
of Manhattan, the City of New York, New York, which shall be maintained for such
purpose in accordance with Section 5.02 of the Indenture.

     SECTION 10. Form of Notes.

     The front of the 1996 Notes, the front of the 1999 Notes, and the back of
the Notes are attached hereto as Exhibits A-I, A-II and A-III, respectively.
Each of the 1996 Notes shall be numbered consecutively from A-1000 upward. Each
of the 1999 Notes shall be numbered consecutively from B-1000 upward. The Notes
shall bear CUSIP numbers, but any failure to indicate or any error in such CUSIP
numbers shall not in any way affect the validity of the Notes.

     SECTION 11. Ranking.

     The Notes shall constitute unsecured and unsubordinated indebtedness of the
Company and shall rank pari passu with any other unsecured and unsubordinated
indebtedness of the Company.

     SECTION 12. Defeasance.

     The Notes shall be subject to defeasance as provided in Article Fourteen of
the Indenture. Upon any defeasance of the 1996 Notes or 1999 Notes, the Company
shall cease to be under any obligation to comply with any term, provision or
condition of Sections 13, 14, 15, 16 and 17 of this Supplement.

                                       7

 
     SECTION 13. Limitation on Liens.

     Clause (h) of Section 5.03 of the Indenture shall be amended to provide
that the Company may not extend, renew or replace any Restricted Subsidiary's
obligations under the two 20-year capital leases existing on the date hereof on
the Company's two Channelview olefins plants (the "Olefins Plants"), which
leases were entered into in 1976 and 1977, by issuing Debt after the date hereof
that is secured by a Mortgage on the Olefins Plants which matures after the
stated maturity of the existing capital lease obligations. Except for the
limitation set forth in the preceding sentence, Section 5.03 shall remain
unchanged. This amendment shall not affect any Security of any series created
after the date of this Supplement.

     SECTION 14. Put Right of Note Holders.

     (A) In the event that there shall occur both (1) a Designated Event and (2)
a Rating Decline, each registered Holder of Notes shall have the right, at the
Holder's option, to require the Company to purchase, and upon the exercise of
such right the Company shall purchase, all or any part of the Holder's Notes on
the date (the "Repurchase Date") that is 100 days after the last to occur of (1)
Public Notice of the Designated Event and (2) the Rating Decline, at a purchase
price of 100% of the principal amount thereof, plus accrued interest to the
Repurchase Date.

     (B) On or before the 28th day following the last to occur of (1) Public
Notice of such Designated Event and (2) the Rating Decline, the Company shall
notify the Trustee in writing of the Designated Event and Rating Decline and of
the repurchase right set forth herein arising as a result thereof.  Promptly
following notification of the Trustee, the Company (or, at the request of the
Company, the Trustee) shall give notice by registered or certified mail, to each
Holder of Notes at the Holder's address appearing in the Note register. The
Company shall also cause a copy of the notice of a repurchase right to be
published in an Authorized Newspaper. The Company will not be obligated to
purchase the Notes or to give notice to Holders of Notes with respect to more
than one Designated Event and Rating Decline.

     Each notice of a repurchase right shall include the following:

     (1) the Repurchase Date;
     (2) the date by which the repurchase right must be exercised;
     (3) the price at which the repurchase is to be made, if the repurchase
         right is exercised;
     (4) a description of the procedure which a Holder of Notes must follow to
         exercise a repurchase right; and
     (5) a statement that the Company will not be obligated to purchase the
         Notes or to give notice to any Holder of any subsequent Designated
         Event and Rating Decline.

                                       8

 
     No failure of the Company to give the forgoing notice shall limit any
Holder's right to exercise a repurchase right.

     (C) To exercise a repurchase right, a Holder of Notes shall deliver to the
Company (or an agent designated by the Company for such purchase in the notice
referred to in (B) above) at least ten days prior to the Repurchase Date (1)
written notice of the Holder's exercise of such right, which notice shall set
forth the name of the Holder, the principal amount of the Note or Notes (or
portion thereof) to be repurchased, and a statement that the option to exercise
the repurchase right is being made thereby and (2) the Note with respect to
which the repurchase right is being exercised, duly endorsed for transfer to the
Company. Such written notice shall be irrevocable and interest on the Note or
Notes (or portion thereof) presented and surrendered for purchase shall cease to
accrue from and after the Repurchase Date. The right of the Holder to sell any
Notes (or portion of a Note) to the Company will terminate as of the close of
business on the 10th day preceding the Repurchase Date, and the Company will not
be obligated to purchase any Note presented or surrendered from and after such
termination date.

     (D) In the event a repurchase right shall be exercised in accordance with
the terms of this Section 14, on the Repurchase Date the Company shall pay or
cause to be paid the price payable with respect to the Note or Notes (or portion
thereof), as to which the repurchase right has been exercised, in cash or
immediately available funds to the Holder of such Note or Notes. In the event
that a repurchase right is exercised with respect to less than the entire
principal amount of a surrendered Note, the Company shall execute and deliver to
the Trustee, and the Trustee shall authenticate for issuance in the name of the
Holder, a new Note or Notes in the aggregate principal amount of that portion of
such surrendered Note not repurchased.

     SECTION 15. Definition of Restricted Property and Subsidiary; Limitation on
                 Olefins Subsidiary Debt.

     The definition of Restricted Property in the Indenture shall be amended to
include any plant for the refining of petroleum or the production of
petrochemicals that as of the date hereof is leased by the Company or its
Subsidiary. The definition of Restricted Subsidiary in the Indenture shall be
amended to include any Subsidiary that as of the date hereof leases Restricted
Property. Except for the inclusion of such leased property, the definitions
shall remain unchanged.

     During any period that title to the Olefins Plants is owned by one or more
Subsidiaries (for purposes of this Section 15 hereinafter referred to
collectively as the "Olefins Subsidiary"), the Company shall not permit any
Olefins Subsidiary to issue, guarantee, assume, incur or have outstanding
directly or indirectly, any Debt (as defined in Section 5.03 of the Indenture),
except that this limitation shall not apply to Debt secured by Mortgages
permissible under clauses (a) through (h) of Section 5.03 of the Indenture.
Notwithstanding the foregoing, the Olefins Subsidiary may issue, assume,
guarantee or

                                       9

 
have outstanding Debt which would otherwise be subject to the foregoing
restriction in an aggregate principal amount which, together with the
outstanding principal amount of (A) any Debt permitted under the last paragraph
of Section 5.03 of the Indenture and (B) all other Debt of the Olefins
Subsidiary subject to the foregoing restriction, does not at any one time exceed
the greater of $50 million or 10% of the Consolidated Net Tangible Assets of the
Company and its consolidated Subsidiaries.

     This provision shall not affect any Security of any series created after
the date of this Supplement.

     SECTION 16. Concerning the Trustee.

     (A) Section 8.02 of the Indenture shall be amended to add the following
clause as Clause (i):

     "(i) the Trustee shall not be required to take notice of or be deemed to
     have notice of any Event of Default under the Indenture, except for Events
     of Default specified in Subsection (a), (b) or (c) of Section 7.01 of the
     Indenture, unless the Trustee shall be specifically notified in writing of
     such Event of Default by the Company or any Holder of the Notes, and all
     notices in order to be effective must be delivered to the Principal Office
     of the Trustee, and in the absence of such notice so delivered, the Trustee
     may conclusively assume there is no Event of Default except as
     aforementioned."

     (B) Section 9.04 of the Indenture shall be amended to add at the end of
Section 9.04 the following paragraph:

     "Upon request of the Trustee, the Company shall furnish the Trustee
     promptly an Officer's Certificate listing and identifying all Notes if any,
     known by the Company to be owned or held by or for the account of any of
     the above described persons; and subject to Sec. 8.01, the Trustee shall be
     authorized to accept such Officer's Certificate as conclusive evidence of
     the facts therein set forth and the fact that all Notes not listed therein
     are outstanding for the purpose of any such determination."

     (C) Except as amended above, Sections 8.02 and 9.04 shall remain unchanged.
These amendments shall not affect any Security of any series created after the
date of this Supplement.

                                      10

 
     SECTION 17. Events of Default.

     In addition to the Events of Default specified in Section 7.01 of the
Indenture, an Event of Default with respect to the Notes shall include the
following:

     (a) the failure on the part of the Company to observe or perform any
covenant or agreement under Sections 13 and 15 hereof and the continuance of
such default or breach for a period of 90 days after the date on which written
notice specifying such default or breach and requiring it to be remedied and
stating that such a notice is a "Notice of Default" shall have been given to the
Company by the Trustee, or to the Company by the Holders of at least 25% in
aggregate principal amount of the Notes at the time outstanding; or

     (b) default by the Company in the payment of the principal amount due for
repurchase of the Notes pursuant to Section 14 hereof.

     SECTION 18. GOVERNING LAW.

     THIS SUPPLEMENT AND EACH NOTE ISSUED HEREUNDER SHALL BE CONSTRUED IN
ACCORDANCE WITH AND GOVERNED BY THE LAWS OF THE STATE OF NEW YORK APPLICABLE TO
AGREEMENTS MADE AND TO BE PERFORMED THEREIN.

     SECTION 19. Counterparts.

     This Supplement may be executed in any number of counterparts, each of
which so executed shall be deemed to be an original, but both of which shall
together constitute but one and the same instrument.

     SECTION 20. Miscellaneous.

     (a) Except as expressly amended and supplemented by this Supplement, the
Indenture shall remain in full force and effect.

     (b) This Supplement shall be construed as supplemental to the Indenture and
shall form a part thereof.

                                      11

 
        IN WITNESS, WHEREOF, the Company and the Trustee have caused this
Supplement to be duly executed by their respective officers thereunto duly
authorized as of the day and year first above written.



                                LYONDELL PETROCHEMICAL 
                                  COMPANY

                                By: /s/ Russell S. Young
                                   --------------------------------------
                                Name:   Russell S. Young
                                Title:  Vice President and Treasurer



                                TEXAS COMMERCE BANK NATIONAL
                                  ASSOCIATION


                                By: /s/ Roy H. Trice, Jr.
                                   ---------------------------------------
                                Name:   Roy H. Trice, Jr.
                                Title:  Vice President and Trust Officer




                                      12

 
                                  EXHIBIT A-1

No. A-                                                             $


                        LYONDELL PETROCHEMICAL COMPANY

                              9.95% NOTE DUE 1996


     LYONDELL PETROCHEMICAL COMPANY, a corporation duty organized and existing
under the laws of the State of Delaware (herein called the "Company), for value
received, hereby promises to pay to ____________________ or registered assigns,
the principal sum of __________________ Dollars on June 1, 1996, and to pay
interest thereon from June 1, 1989 or from the most recent June 1 or December 1
to which interest has been paid or duly provided for, semiannually on June 1 and
December 1 in each year (each an "Interest Payment Date"), commencing
December 1, 1989, at the rate per annum specified in the title hereof, until the
principal hereof is paid or duly provided for. The interest so payable on any
Interest Payment Date will be paid, except as provided in the Indenture, to the
person in whose name this Note is registered at the close of business on the
Record Date for such interest, which shall be the May 15 or November 15 (whether
or not a Business Day), as the case may be, next preceding such Interest Payment
Date. Any interest not paid on the Interest Payment Date therefor ("Defaulted
Interest") may be paid to the person in whose name this Note is registered at
the close of business on a special record date for the payment of such Defaulted
Interest, notice of which shall be given by the Company to Holders of Notes not
less than fifteen days prior to such special record date, or may be paid in any
other lawful manner. For purposes of this Note, "Business Day" means any day,
other than a Saturday or Sunday, that is not a day on which banking institutions
are authorized or required by law or regulation to be closed in The City of New
York or The City of Houston.

     Payment of the principal and interest on this Note will be payable (in such
coin or currency of the United States of America as at the time of payment is
legal tender for payment of public and private debts) at the office or agency of
the Trustee maintained for that purpose in the City of Houston, Texas, or, at
the option of the Holder, in the Borough of Manhattan, The City of New York, New
York; provided, however, that at the option of the Company payment of interest
may be made by check mailed to the address of the person entitled thereto as
such address shall appear in the register for the Notes.

     Interest will be computed on the basis of a 360-day year of twelve 30-day
months.

                                       1

 
     Reference is made to the further provisions of this Note set forth on the
reverse hereof. Such further provisions shall for all purposes have the same
effect as though fully set forth at this place.

     This Note shall not be valid or become obligatory for any purpose until the
certificate of authentication hereon shall have been signed by the Trustee under
the Indenture referred to on the reverse hereof.

     IN WITNESS WHEREOF, LYONDELL PETROCHEMICAL COMPANY has caused this
instrument to be signed, manually or by facsimile, by its duly authorized
officers and its corporate seal to be printed, engraved or otherwise reproduced
hereon, by facsimile or otherwise.



                         LYONDELL PETROCHEMICAL COMPANY

By                                      By


    ----------------------------           -------------------------------------
    Vice President and Treasurer           President and Chief Executive Officer





Dated:

                TRUSTEE'S CERTIFICATE OF AUTHENTICATION

    THIS IS ONE OF THE SECURITIES ISSUED UNDER THE WITHIN-MENTIONED INDENTURE.


        Texas Commerce Bank National Association, as Trustee


        By.................................
               Authorized Officer


                                       2

 
                                 EXHIBIT A-II


No. B-                                                 $

                        LYONDELL PETROCHEMICAL COMPANY

                             10.00% NOTE DUE 1999


     LYONDELL PETROCHEMICAL COMPANY, a corporation duly organized and existing
under the laws of the State of Delaware (herein called the "Company"), for value
received, hereby promises to pay to _______________________ or registered
assigns, the principal sum of ___________________ Dollars on June 1, 1999, and
to pay interest thereon from June 1, 1989 or from the most recent June 1 or
December 1 to which interest has been paid or duly provided for, semiannually on
June 1 and December 1 in each year (each an "Interest Payment Date"), commencing
December 1, 1989, at the rate per annum specified in the title hereof, until the
principal hereof is paid or duly provided for. The interest so payable on any
Interest Payment Date will be paid, except as provided in the Indenture, to the
person in whose name this Note is registered at the close of business on the
Record Date for such interest, which shall be the May 15 or November 15 (whether
or not a Business Day), as the case may be, next preceding such Interest Payment
Date. Any interest not paid on the Interest Payment Date therefor ("Defaulted
Interest") may be paid to the person in whose name this Note is registered at
the close of business on a special record date for the payment of such Defaulted
Interest, notice of which shall be given by the Company to Holders of Notes not
less than fifteen days prior to such special record date, or may be paid in any
other lawful manner. For purposes of this Note, "Business Day" means any day,
other than a Saturday or Sunday, that is not a day on which banking institutions
are authorized or required by law or regulation to be closed in The City of New
York or The City of Houston.

     Payment of the principal and interest on this Note will be payable (in such
coin or currency of the United States of America as at the time of payment is
legal tender for payment of public and private debts) at the office or agency of
the Trustee maintained for that purpose in the City of Houston, Texas, or, at
the option of the Holder, in the Borough of Manhattan, The City of New York, New
York; provided, however, that at the option of the Company payment of interest
may be made by check mailed to the address of the person entitled thereto as
such address shall appear in the register for the Notes.

     Interest will be computed on the basis of a 360-day year of twelve 30-day
months.

                                       1

 
     Reference is made to the further provisions of this Note set forth on the
reverse hereof. Such further provisions shall for all purposes have the same
effect as though fully set forth at this place.

     This Note shall not be valid or become obligatory for any purpose until the
certificate of authentication hereon shall have been signed by the Trustee under
the Indenture referred to on the reverse hereof.

     IN WITNESS WHEREOF, LYONDELL PETROCHEMICAL COMPANY has caused this
instrument to be signed, manually or by facsimile, by its duly authorized
officers, and its corporate seal to be printed, engraved or otherwise reproduced
hereon, by facsimile or otherwise.

                         LYONDELL PETROCHEMICAL COMPANY

By                                      By


     --------------------------------      -------------------------------------
     Vice President and Treasurer          President and Chief Executive Officer




Dated:


            TRUSTEE'S CERTIFICATE OF AUTHENTICATION


     THIS IS ONE OF THE SECURITIES ISSUED UNDER THE WITHIN-MENTION INDENTURE.



            Texas Commerce Bank National Association, as Trustee


            By............................
                 Authorized Officer

                                       2

 
                                 EXHIBIT A-III


                        LYONDELL PETROCHEMICAL COMPANY


                          ___% NOTE DUE [1996] [1999]

     This Note is one of a duly authorized issue of debentures, notes or other
evidences of indebtedness of the Company (herein called the "Securities"), of
the series hereinafter specified, all issued or to be issued under and pursuant
to an Indenture dated as of May 31, 1989 (herein called the "Indenture"), duly
executed and delivered by the Company to Texas Commerce Bank National
Association, Trustee (hereinafter called the "Trustee"), to which Indenture, and
all indentures supplemental thereto, if any, reference is hereby made for a
description of the rights, limitation of rights, obligations, duties and
immunities thereunder of the Trustee, the Company and the Holders of the
Securities. In the event of any inconsistency between the provisions of this
Note and the provisions of the Indenture, and any indentures supplemental
thereto, the terms of the Indenture and any indentures supplemental thereto
shall control.

     This Note is one of a series of Securities of the Company issued pursuant
to the First Supplemental Indenture dated as of May 31, 1989 (herein called
the "Supplement"), and the Indenture (as used herein the "Indenture" refers to
the Indenture as supplemented by the Supplement) designated as the ___% Notes
Due [1996][1999] (herein called the "Notes") limited in aggregate principal
amount to $________________.

     In the event that there occurs (a) a Designated Event (as defined in the
Supplement) with respect to the Company and (b) a Rating Decline (as defined in
the Supplement), Holders of the Notes shall have the right, at the Holders'
option, to require the Company to purchase all or any part of such Holders'
Notes at 100% of the principal amount thereof, plus interest accrued through the
Repurchase Date (as defined in the Supplement). The Company is obligated to
provide notice to each Holder that a Designated Event and a Rating Decline has
occurred and of the Repurchase Date. The Company is not obligated to provide
notice or repurchase the Notes with respect to more than one Designated Event
and Rating Decline.

     In case an Event of Default shall occur and be continuing, the principal
hereof may be declared, and upon such declaration shall become, due and payable,
in the manner, with the effect and subject to the conditions provided in the
Indenture.

     The Indenture contains provisions permitting the Company and the Trustee,
with the consent of the Holders of not less than 50% in aggregate principal
amount at Stated Maturity of the Securities at the time outstanding of each
series affected by such

                                       1

 
supplemental indenture or indentures, evidenced as provided in the Indenture, to
execute supplemental indentures adding any provisions to or changing in any
manner or eliminating any of the provisions of the Indenture, or of any
supplemental indenture or indentures, as such provisions apply to such
Securities, or modifying in any manner the rights of the Holders of the
Securities; provided, however, that no such supplemental indenture shall (i)
extend the fixed maturity of any Security or reduce the rate, or extend the time
of payment of interest thereon or reduce the principal thereof or the time
during which interest is payable thereon or change the method of computing the
amount of principal thereof or make the principal thereof or interest thereon
payable in any coin or currency other than that provided in the Securities
without the consent of the Holder thereof, or (ii) reduce the percentage in
principal amount at Stated Maturity of the outstanding Securities, the consent
of whose Holders is required for any such supplemental indenture, or the consent
of whose Holders is required for any waiver of compliance with certain
provisions of the Indenture or of certain defaults under, and their consequences
provided for in, the Indenture, without the consent of the Holders of each
Security of such series so affected. Any such consent or waiver by the Holder
of this Note (unless revoked as provided in the Indenture) shall be conclusive
and binding upon such Holder and upon all future Holders and owners of this Note
and any Notes which may be issued in exchange or substitution herefor,
irrespective of whether any notation thereof is made upon this Note or such
other Notes.

     No reference herein to the Indenture and no provision of this Note or of
the Indenture shall alter or impair the obligation of the Company, which is
absolute and unconditional, to pay the principal of and interest on this Note
at the place, at the respective times, at the rate, and in the coin or currency
herein prescribed.

     The Notes are issuable in registered form without coupons in denominations
of $1,000 and whole multiples of $1,000 in excess of that amount. Notes may be
exchanged for a like aggregate principal amount of Notes of other authorized
denominations, without charge except for any tax or other governmental charge
imposed in relation thereto, at the office or agency of the Trustee, and in the
manner and subject to the limitations provided in the Indenture.

     The Notes are unsecured obligations of the Company ranking pari passu
without any preference among themselves and equally with all other unsecured
indebtedness (other than subordinated indebtedness) of the Company from time to
time outstanding.

     Upon due presentment for registration of transfer of this Note at the
office or agency of the Trustee, a new Note or Notes of authorized denominations
for an equal aggregate principal amount at Stated Maturity will be issued to the
transferee in exchange therefor, in the manner and subject to the limitations
provided in the Indenture, without charge except for any tax or other
governmental charge imposed in relation thereto.

     Prior to due presentment for registration of transfer of this Note, the
Company, the Trustee, any paying agent and any registrar for the Notes may deem
and treat the

                                       2

 
registered Holder hereof as the absolute owner of this Note (whether or not this
Note shall be overdue and notwithstanding any notation of ownership or other
writing hereon by anyone other than the Company, any registrar for the Notes or
the Trustee), for the purpose of receiving payment hereof or on account hereof,
and for all other purposes (subject to the provisions appearing on the face
hereof), and neither the Company nor the Trustee nor any paying agent nor any
registrar for the Notes shall be affected by any notice to the contrary.

     No recourse for the payment of principal or interest on this Note, or for
any claim based hereon or otherwise in respect hereof, and no recourse under or
upon any obligation, covenant or agreement of the Company in the Indenture, or
any indenture supplemental thereto, or in any Note, or because of the creation
of any indebtedness represented thereby, shall be had against any incorporator,
stockholder, officer or director, as such, past, present or future, of the
Company or of any successor corporation, either directly or through the Company
or any successor corporation, whether by virtue of any constitution, statute or
rule of law or by the enforcement of any assessment or penalty or otherwise, all
such liability being, by the acceptance hereof and as a condition of and as part
of the consideration for the issue hereof, expressly waived and released.

     Terms used herein which are defined in the Supplement or Indenture shall
have the meanings assigned to them in the Supplement or Indenture.

     THIS NOTE SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAW OF
THE STATE OF NEW YORK.

                                       3