<PAGE>
 
                                AMENDMENT NO. 2
                                      TO
                             ARCO CHEMICAL COMPANY
                      DEFERRAL PLAN FOR OUTSIDE DIRECTORS
                          --------------------------

     Pursuant to resolutions adopted by the Board of Directors on October 17,
1996, the following amendment is hereby made to the ARCO Chemical Deferral Plan
for Outside Directors (the "Plan") effective as of January 1, 1997.

1.   Article I, Section 3.1 of the Plan is amended to read as follows:

     "3.1 Account means a separate bookkeeping account maintained by the
     Company for each Director and which measures and determines the amounts to
     be paid to the Director under the Plan for each component of Deferred
     Compensation. Separate subaccounts will be established for separate
     components of Deferred Compensation, as applicable, deferred by a
     Director."

2.   Article I, Section 3.9 of the Plan is amended to read as follows:

     "3.9 Deferral Commitment means a promise made by a Director to defer
     compensation pursuant to Article III for which a Participation Agreement
     has been submitted by the Director to the Company."

3.   Article I, Section 3.11 of the Plan is deleted and Sections 3.12 through 
     3.29 are redesignated as Sections 3.11 through 3.28.

4.   Article II, Section 2 of the Plan is amended to read as follows:

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                                 EXHIBIT 10.2
<PAGE>
 
      "Section 2. Basic Forms of Deferral

      2.1 A Participant may elect to defer the following forms of compensation
      in a Participation Agreement:


         (a) Board Retainer and Meeting Fees. Commencing with Board Retainer and
      Meeting Fees earned on and after October 1, 1990, a Participant may elect
      to defer such amounts earned during a Deferral Period, subject to any
      limitations, conditions or restrictions, such as minimum or maximum
      amounts that may be deferred, as are prescribed by the Administrative
      Committee in advance of the Deferral Period.

          (b) Committee Chairmanship and Meeting Fees. "Commencing with
      Committee Chairmanship and Meeting Fees earned on and after October 1,
      1990, a Participant may elect to defer such amounts earned during a
      Deferral Period, subject to any limitations, conditions or restrictions,
      such as minimum or maximum amounts that may be deferred, as are prescribed
      by the Administrative Committee in advance of the Deferral Period."

5.    Article II, Section 4 of the Plan is amended to read as follows:

      "Section 4. Limitation on Deferral 

      4.1 Deferral Commitments shall be subject to any limitations, including
      minimum amounts that may be deferred for the Deferral Period relating to a
      Deferral Commitment, as are established by the Administrative Committee in
      advance of the Deferral Period. Any minimum amounts shall be allocable
      among the forms of Deferred Compensation described in Article II, Section
      2.1(a) and (b)."

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<PAGE>
 
6.    Article III, Section 1 of the Plan is amended to read as follows:

      "Section 1. Accounts

      1.1      For record-keeping purposes only, an Account shall be maintained
      for each Participant. Separate subaccounts shall be maintained for each
      form of Deferred Compensation of a Participant."

7.    Article III, Section 3 of the Plan is amended to read as follows:

      "Section 3. Interest Rate

      3.1      A Participant's Account shall be credited as of each Valuation
      Date during each Plan Year at the interest rate previously announced by
      the Company to be applicable for the Plan Year, compounded annually.
      Interest shall be credited as of each Valuation Date from the dates when
      deferred amounts are credited to Accounts based on the balance of each
      Account."

8.    Article IV, Section 1 of the Plan is amended to read as follows:

      "Section 1.  Plan Benefit

      1.1      If a Participant has a Termination of Service for any reason the
      Company shall pay a Plan benefit equal to the Participant's Account
      balance, as determined below:

           (a) A Participant's Account shall be credited with the rate of
      interest previously determined under Article III, Section 3.1, and
      communicated in advance of each Deferral Period, to be applicable for each
      Plan Year that the Account has been maintained.

           (b) The Interest Rates provided under Section 1.1(a) of this Article,
      shall be payable until the Participant's Account is distributed in full."




          
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9.   Article IV, Section 2, Paragraph 2.1 of the Plan is amended to read as 
     follows:

     "2.1      Retirement Distributions shall be paid at the time and in the 
     form of benefit elected by the Participant for the total Deferred
     Compensation, at the time of the Deferral Commitment establishing such
     deferral, on the Participation Agreement. A Participant's election shall be
     irrevocable, except as follows:

           (a) Once each Plan Year prior to a Plan Year previously designated by
     the Administrative Committee and communicated to Participants, at a time
     and on a form prescribed by the Administrative Committee, each Participant
     may change the time and/or form of the Retirement Distribution of the Total
     Deferred Compensation in the Participant's Account. Effective as of the
     Plan Year previously designated by the Administrative Committee under the
     preceding sentence, the election by the Participant on file on such date
     shall govern the time and form of the Retirement Distribution for all
     amounts in the Participant's Account, whether attributable to deferrals
     before or after such date.

           (b) A Participant may request, by application to the Administrative 
     Committee, approval of a change of the prior election at any time prior to
     retirement or commencement of benefits, or in the case of installment
     payments, following commencement of payments, (i) without any reduction in,
     or imposition of any penalty on, the Participant's Account, provided that
     the Administrative Committee determines, upon application of the
     Participant, that the Participant has experienced a Financial Hardship
     justifying the request for a change of election; or (ii) the Administrative
     Committee, in its sole discretion, determines that it is appropriate to
     grant the Participant's request. Absent an election by the Participant of
     the form and/or commencement date of the Retirement Distribution, payment
     will be made in a lump sum immediately following the Participant's date of
     retirement."

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<PAGE>
 
10.   Article IV, Section 4 of the Plan is amended to read as follows:

      "Section 4. Survivor Benefits

      4.1 (a)  Death Prior to Termination of Service. If the Participant dies
               --------------------------------------
      prior to Termination of Service, the Survivor Benefit shall be paid to the
      Participant's Beneficiaries in a lump sum or in monthly installments, as
      elected by the Participant, and shall be the sum of the Participant's
      Account Balance plus one hundred percent (100%) of the Participant's
      unfulfilled Deferral Commitment, if any.

          (b) Death After Termination of Service. If the Participant dies after
              -----------------------------------
      Termination of Service, the Participant's Account balance, if any, shall
      be paid to the Participant's Beneficiary by continuation of the form of
      benefit which was payable to the Participant for the remaining payments
      which would have been made to the Participant if the Participant had
      lived, increased by the applicable Interest Rate credited on unpaid
      Account balances of deceased Participants during each year of the payment
      period to the Beneficiary."

11.   Article IV, Section 5 of the Plan is amended to read as follows:

      "Section 5.  In-Service Distributions

      5.1       A Participant may elect to receive an In-Service Distribution 
      from the Participant's Account subject to the following restrictions:

           (a)  Timing of Election.  The election to take an In-Service 
      Distribution from an Account must be made at the same time the Participant
      makes the annual Deferral Commitment.

           (b)  Amount of Withdrawal.  The amount which a Participant can elect 
      to receive as an In-Service Distribution with respect to an Account shall
      be such

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<PAGE>
 
      portions of the Participant's Account balance, as prescribed by the
      Administrative Committee in advance of the Deferral Period. If a
      previously elected amount exceeds the Account balance when an In-Service
      Distribution is to be made, only the Account balance will be paid.

           (c)   Timing and Form of In-Service Distribution. The In-Service
      Distribution shall commence at the time and in the form elected by the
      Participant on the Participation Agreement at the time of the Deferral
      Commitment; provided, however, that if the Participant terminates service,
      the In-Service Distribution election will be canceled and distribution
      will be made pursuant to Section 3 of this Article, and provided, further,
      that if the Participant commences retirement, the In-Service Distribution
      election will be canceled and distribution will be made pursuant to
      Section 2 of this Article."

12.   Sections 7 and 8 of Article IV of the Plan are amended to read as follows:

      "Section 7. Valuation and Settlement

             7.1   The date on which a lump sum is paid or the date on which
      installment payments commence shall be the "Settlement Date." The
      Settlement Date shall be no more than thirty (30) days after the last day
      of the month in which the Participant or his Beneficiary becomes entitled
      to payments on account of retirement, other Termination of Service or
      death, unless the Participant elects to defer commencement of payments
      following retirement to a later date in the Participation Agreement. The
      Settlement Date for an In-Service Distribution or delayed payments
      following retirement shall be the month which the Participant elects for
      commencement of such payments in the election form for designation of form
      of payment. The amount of a lump sum and the initial amount of installment
      payments shall be based on the value of the Participant's Account as of
      the Valuation Date at the end of the immediately preceding month



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<PAGE>
 
        before the Settlement Date. For example, the Valuation Date at the end
        of December shall be used to determine lump sum or the initial amount of
        installment payments which will be made in the following January.

        Section 8.  Small Benefit

        8.1     Notwithstanding any election made by the Participant, the
        Administrative Committee, in its sole discretion, may pay any benefit in
        the form of a lump sum payment to the Participant or any Beneficiary, if
        the lump sum amount of the Account balance which remains in the Account
        following a distribution for any reason, or which is payable to the
        Participant or Beneficiary when payments to such Participant or
        Beneficiary would otherwise commence is less than $2,000."

13.     Article V of the Plan is amendment to read as follows:

                                 "ARTICLE V
                        DESIGNATION OF BENEFICIARY      

        Section 1.      Designation of Beneficiary
        
        1.1             Each Participant shall have the right to designate a
        Beneficiary or Beneficiaries to receive Participant's interest in
        Participant's Account upon the Participant's death. Such designation
        shall be made on a form prescribed by and delivered to the
        Administrative Committee. The Participant shall have the right to change
        or revoke any such designation from time to time by filing a new
        designation or notice of revocation with the Company, and no notice to
        any Beneficiary nor consent by any Beneficiary shall be required to
        effect any such change or revocation.



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<PAGE>
 
     Section 2.  Failure to Designate Beneficiary

     2.1         If a Participant shall fail to designate a Beneficiary before 
     the Participant's death, or if no designated Beneficiary survives the
     Participant, the Administrative Committee shall direct the Company to pay
     the balance in Participant's Account in a lump sum to the executor or
     administrator for Participant's estate."

Executed This 22nd day of November, 1996.

ATTEST:                                ARCO CHEMICAL COMPANY


BY: /s/ John G. Chou                    BY: /s/ Frank W. Welsh
    ------------------------              ---------------------------
                                           FRANK W. WELSH
                                           Vice President
                                           Human Resources

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