UNOCAL CORP
11-K, 1998-06-29
CRUDE PETROLEUM & NATURAL GAS
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<PAGE>
 
                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                            Washington, D. C.  20549
                                        

                                   FORM 11-K
                                        

                 Annual Report Pursuant to Section 15(d) of the
                        SECURITIES EXCHANGE ACT OF 1934
                                        

                                        
(Mark One)

[X]   Annual report pursuant to Section 15(d) of the Securities Exchange Act of
      1934

      For the fiscal year ended  DECEMBER 31, 1997
                                 -----------------


                                       Or


[_]   Transition report pursuant to Section 15(d) of the Securities Exchange Act
      of 1934

      For the transition period from _______________ to ________________


                         Commission file number 1-8483
                                                ------
                                        

   A.  Full title of the plan and the address of the plan, if different from
that of the issuer named below:


                 MOLYCORP, INC. 401(k) RETIREMENT SAVINGS PLAN
                                        
   B.  Name of issuer of the securities held pursuant to the Plan and the
address of its principal executive office:

 Unocal Corporation, 2141 Rosecrans Avenue, Suite 4000, El Segundo, California
                                     90245
<PAGE>
 
                        INDEX TO FINANCIAL STATEMENTS OF
                 MOLYCORP, INC. 401(k) RETIREMENT SAVINGS PLAN


    The following financial statements reflect the status of the Molycorp, Inc.
401(k) Retirement Savings Plan as of December 31, 1997 and 1996, and the results
of its transactions for each of the years then ended.

<TABLE>
<CAPTION>
                                                                                                   Page Number
                                                                                                   -----------
<S>                                                                                                <C>
Statements included herein:

Report of Independent Accountants                                                                      2           
                                                                                                                   
Statements of Net Assets Available for Benefits with Fund Information                                  3           
                                                                                                                   
Statements of Changes in Net Assets Available for Benefits with Fund Information                       4           
                                                                                                                   
Notes to Financial Statements                                                                        5-8           
                                                                                                                   
Item 27(a) - Schedule of Assets Held for Investment Purposes                                          10           
                                                                                                                   
Item 27(d) - Schedule of Reportable Transactions                                                      11           
                                                                                                                   
Exhibit Index                                                                                         12           
</TABLE>

    Schedules I, II and III are omitted because the subject matter did not exist
or the required information is given in the financial statements or notes to
financial statements.

                                       1
<PAGE>
 
                       REPORT OF INDEPENDENT ACCOUNTANTS




The Administrative Committee of the Molycorp, Inc. 401(k) Retirement Savings
Plan:


    We have audited the accompanying statements of net assets available for
benefits of the Molycorp, Inc. 401(k) Retirement Savings Plan (the "Plan") as of
December 31, 1997 and 1996, and the related statements of changes in net assets
available for benefits for the years then ended.  These financial statements are
the responsibility of the Plan's management.  Our responsibility is to express
an opinion on these financial statements based on our audits.

    We conducted our audits in accordance with generally accepted auditing
standards.  Those standards require that we plan and perform the audit to obtain
reasonable assurance about whether the financial statements are free of material
misstatement.  An audit includes examining, on a test basis, evidence supporting
the amounts and disclosures in the financial statements.  An audit also includes
assessing the accounting principles used and significant estimates made by
management, as well as evaluating the overall financial statement presentation.
We believe that our audits provide a reasonable basis for our opinion.

    In our opinion, the financial statements referred to above present fairly,
in all material respects, the net assets available for benefits of the Plan as
of December 31, 1997 and 1996, and the changes in net assets available for
benefits for the years then ended, in conformity with generally accepted
accounting principles.

    Our audits were performed for the purpose of forming an opinion on the basic
financial statements taken as a whole.  The supplemental schedules of assets
held for investment purposes and reportable transactions are presented for the
purpose of additional analysis and are not a required part of the basic
financial statements but are supplementary information required by the
Department of Labor's Rules and Regulations for Reporting and Disclosure under
the Employee Retirement Income Security Act of 1974.  These supplemental
schedules are the responsibility of the Plan's management.  The fund information
in the statement of net assets available for benefits and the statements of
changes in net assets available for benefits is presented for purposes of
additional analysis rather than to present the net assets available for plan
benefits and changes in net assets available for plan benefits of each fund.
The supplemental schedules and fund information have been subjected to the
auditing procedures applied in the audits of the basic financial statements and,
in our opinion, are fairly stated in all material respects in relation to the
basic financial statements taken as a whole.



COOPERS & LYBRAND L. L. P.
June 26, 1998
Los Angeles, California

                                       2
<PAGE>
 

                 MOLYCORP, INC. 401(k) RETIREMENT SAVINGS PLAN
      STATEMENT OF NET ASSETS AVAILABLE FOR BENEFITS WITH FUND INFORMATION
                          DECEMBER 31, 1997 AND 1996

<TABLE>
<CAPTION>





                                                                             PARTICIPANT DIRECTED
                                                              -----------------------------------------------
                                                                                        1997
                                                              ---------------------------------------------------------
                                                                                    UNOCAL
                                                                 FIDELITY           COMMON          GIC
                                                                   FUND             STOCK           FUND        TOTAL
                                                              -------------      ------------    ---------    ---------
ASSETS
<S>                                                           <C>                 <C>             <C>          <C> 
  Investments at fair value (Note 2)
    Shares of registered investment companies
      Fidelity Puritan Mutual Fund                              $   3,362         $       --    $      --    $    3,362
    Unocal Common Stock                                                --             47,003           --        47,003
                                                                ---------         ----------    ---------    ----------
                                                                    3,362             47,003           --        50,365

 Investments at contract value (Note 3)
   Union Bank of California Employee Benefit
    Investment Contract Fund                                           --                 --        6,622         6,622
                                                                ---------         ----------    ---------    ----------
      Total Investments                                             3,362             47,003        6,622        56,987

Cash                                                                   --                  1            1             2
                                                                ---------         ----------    ---------    ----------
NET ASSETS AVAILABLE FOR BENEFITS                               $   3,362         $   47,004    $   6,623    $   56,989
                                                                =========         ==========    =========    ==========


                                                                             PARTICIPANT DIRECTED
                                                              -----------------------------------------------
                                                                                        1996
                                                              ---------------------------------------------------------
                                                                                    UNOCAL
                                                                 FIDELITY           COMMON          GIC
                                                                   FUND             STOCK           FUND        TOTAL
                                                              -------------      ------------    ---------    ---------
ASSETS
  Investments at fair value (Note 2)
    Shares of registered investment companies
      Fidelity Puritan Mutual Fund                              $  20,829         $       --    $      --    $   20,829
    Unocal Common Stock                                                --             43,195           --        43,195
                                                                ---------         ----------    ---------    ----------
                                                                   20,829             43,195           --        64,024
  Investments at contract value (Note 3)
    Union Bank of California Employee Benefit
      Investment Contract Fund                                         --                 --        1,336         1,336
                                                                ---------         ----------    ---------    ----------
       Total Investments                                           20,829             43,195        1,336        65,360

Cash                                                                6,587                463            2         7,052
                                                                ---------         ----------    ---------    ----------
NET ASSETS AVAILABLE FOR BENEFITS                               $  27,416         $   43,658    $   1,338    $   72,412
                                                                =========         ==========    =========    ==========
</TABLE>


   The accompanying notes are an integral part of these financial statements


                                       3

<PAGE>
 

                 MOLYCORP, INC. 401(k) RETIREMENT SAVINGS PLAN
STATEMENT OF CHANGES IN NET ASSETS AVAILABLE FOR BENEFITS WITH FUND INFORMATION
                  FOR YEARS ENDED DECEMBER 31, 1997 AND 1996

<TABLE> 
<CAPTION> 
                                                                  Participant Directed
                                                          -----------------------------------------------
                                                                                     1997
                                                          ----------------------------------------------------------------   
                                                                               Unocal
                                                           Fidelity            Common           GIC
                                                             Fund               Stock           Fund               Total
                                                          ----------         -----------      --------          ----------   
<S>                                                       <C>                <C>              <C>               <C> 
ADDITIONS TO NET ASSETS ATTRIBUTED TO:
 Investment income
  Net appreciation/(depreciation) in fair value
   of investments                                         $   1,114          $  (2,341)       $      -          $  (1,227) 
  Interest                                                      359                 17             201                577  
  Dividends                                                       -                870               -                870   
                                                          ---------          ---------        --------          --------- 
   Total investment income                                    1,473             (1,454)            201                220

 Participant contributions                                        -              6,538           5,084             11,622
                                                          ---------          ---------        --------          ---------   
                                                              1,473              5,084           5,285             11,842       
   TOTAL ADDITIONS

DEDUCTIONS FROM NET ASSETS ATTRIBUTED TO:
 Participants withdrawals and distributions                  25,527              1,738               -             27,265
                                                          ---------          ---------        --------          ---------   

   NET (DECREASE) INCREASE                                  (24,054)             3,346           5,285            (15,423)  

NET ASSETS AVAILABLE FOR BENEFITS:
 BEGINNING OF YEAR                                           27,416             43,658           1,338             72,412 
                                                          =========          =========        ========          =========   
 END OF YEAR                                              $   3,362          $  47,004        $  6,623          $  56,989  
                                                          =========          =========        ========          =========   
</TABLE> 

<TABLE> 
<CAPTION> 

                                                                  Participant Directed
                                                          -----------------------------------------------
                                                                                     1996
                                                          ----------------------------------------------------------------   
                                                                               Unocal
                                                           Fidelity            Common           GIC
                                                             Fund               Stock           Fund               Total
                                                          ----------         -----------      --------          ----------   
<S>                                                       <C>                <C>              <C>               <C> 
ADDITIONS TO NET ASSETS ATTRIBUTED TO:
 Investment income
  Net appreciation in fair value
   of investments                                         $  13,326          $  80,131        $       -         $  93,457
  Interest                                                      623                471                4             1,098
  Dividends                                                  32,870              5,528            3,204            41,602 
                                                          ---------          ---------        ---------         ---------   
   Total investment income                                   46,819             86,130            3,208           136,157  

Participant contributions                                    45,091             30,761           12,597            88,449
                                                          ---------          ---------        ---------         ---------   
 
   TOTAL ADDITIONS                                           91,910            116,891           15,805           224,606
 
DEDUCTIONS FROM NET ASSETS ATTRIBUTED TO:
 Participants withdrawals and distributions                 315,947            252,915           62,924           631,786  
                                                          ---------          ---------        ---------         ---------   
 
NET DECREASE PRIOR TO INTERFUND TRANSFERS                  (224,037)          (136,024)         (47,119)         (407,180)

INTERFUND TRANSFERS                                          10,310             (9,568)            (742)                0
                                                          ---------          ---------        ---------         ---------   

   NET DECREASE                                            (213,727)          (145,592)         (47,861)         (407,180) 

NET ASSETS AVAILABLE FOR BENEFITS:
 BEGINNING OF YEAR                                         (241,143)           189,250           49,199           479,592
                                                          ---------          ---------        ---------         ---------   
 END OF YEAR                                              $  27,416          $  43,658        $   1,338         $  72,412  
                                                          =========          =========        =========         =========    
</TABLE> 

  The accompanying notes are an integral part of these financial statements


                                      4  

<PAGE>
 
                 MOLYCORP, INC. 401(k) RETIREMENT SAVINGS PLAN
                         NOTES TO FINANCIAL STATEMENTS

                                        
NOTE 1 - DESCRIPTION OF THE PLAN

General
- -------

    The Molycorp, Inc. 401(k) Retirement Savings Plan (the "Plan") is sponsored
by Molycorp, Inc. (the "company"), an indirect wholly owned subsidiary of Unocal
Corporation.  The Plan provides for voluntary contributions by participants.
Each individual participant is allowed to choose how their funds are invested
from among three investment options.  All funds remain with Union Bank of
California (the "Trustee") for the exclusive benefit of Plan participants until
distributed after termination of employment.  The Plan is subject to certain
provisions of the Employee Retirement Income Security Act of 1974 ("ERISA") as a
defined contribution plan.

    The Molycorp 401(k) Retirement Savings Plan booklet dated December 1, 1996
replaces the April 1, 1991 booklet and constitutes part of a prospectus covering
securities that have been registered under the Securities Act of 1933.  The
December 1, 1996 booklet can be referenced for other information about the Plan.

CONTRIBUTIONS
- -------------

    Voluntary participant contributions to the Plan are made on a pre-tax basis
and cannot exceed 15 percent of a participant's base pay.  The pre-tax
contributions are also known as 401(k) contributions.  Contributions cannot
exceed the amount prescribed by law and cannot be calculated on a base pay in
excess of the amount allowed by law.

PARTICIPATION
- -------------

    Collective bargaining unit employees at the Questa or York facilities are
eligible to participate in the Plan as of January 1, 1991 if at least six months
of service was completed prior to January 1, 1991.  Otherwise, participants are
eligible to participate in the Plan beginning the first of the calendar quarter
that next follows the date the participant completed six months of service.

    As a result of labor contract negotiations, employees at the Mountain Pass
facility were no longer eligible to commence participation in the Plan or make
contributions to the Plan after June 30, 1996.  In October 1996, employees at
Mountain Pass were extended a special election period to rollover account
balances existing prior to June 30, 1996 into the Unocal Savings Plan.  Account
balances totaling $614,739 were transferred in December 1996 to the Unocal
Savings Plan and are included in participants withdrawals and distributions in
the statement of changes in net assets available for benefits for the year ended
December 31, 1996.

PARTICIPANT ACCOUNTS
- --------------------

    Each participant's account is credited with the participant's contributions
and the respective investment earnings of the individual funds as governed by
the participant's investment selection.

VESTING
- -------

    Participants are always 100 percent vested in participant contributions and
the investment earnings on those contributions.

PAYMENT OF BENEFITS
- -------------------

    On termination of employment or at such time that participants become
eligible to receive benefits, participants may elect to receive their account
balance or defer their distribution until a later date, but no later than 60
days after the end of the plan year in which the latest of the following occurs:
the participant attains age 65, or two years after the participant's employment
terminates.  If a participant continues to

                                       5
<PAGE>
 
                 MOLYCORP, INC. 401(k) RETIREMENT SAVINGS PLAN
                   NOTES TO FINANCIAL STATEMENTS (continued)
                                        
work after age 70-1/2, distribution of a portion of the participant's account
balance is required by April 1 of the calendar year following the calendar year
in which the participant attains age 70-1/2.

INVESTMENT PROGRAM
- ------------------

    All contributions are held in trust and invested by the Trustee in
accordance with the option or options elected by the participant.  A
participant's account may be invested in one or any combination of the following
funds administered by the Trustee:

 .   Fidelity Puritan Mutual Fund - Funds are invested in shares of a mutual fund
    maintained by a registered investment company that invests in common and
    preferred stocks, as well as bonds, of various U.S. corporations.

 .   Unocal Corporation Common Stock Fund ("Unocal Common Stock") - Funds are
    invested in common stock of Unocal Corporation, the company's ultimate
    parent.

 .   Employee Benefit Guaranteed Investment Contract Fund ("GIC") - Funds are
    invested in a bank commingled trust fund which holds fixed-rate investment
    contracts with various insurance companies.

Federal Income Tax Status
- -------------------------

    The company obtained a ruling dated December 26, 1996, from the Los Angeles
District Director of the Internal Revenue Service that the Plan meets the
requirements of Section 401(a) of the Internal Revenue Code of 1986, as amended,
and that the Trustee established thereunder is entitled to exemption under the
provisions of such Code; therefore, the Plan is not required to pay any federal
income taxes.  Earnings on Plan accounts will not be taxable to participants
prior to withdrawal from the Plan.

Withdrawals from the Plan are generally subject to federal income tax.  Also,
in-service withdrawals and withdrawals following termination of employment prior
to retirement may be subject to a 10 percent federal income tax penalty.

Plan Termination
- ----------------

    The company expects to continue the Plan indefinitely, but, as future
conditions cannot be foreseen, the company may at any time or from time to time
amend or terminate the Plan in whole or in part, subject to the requirements of
ERISA and other applicable laws.  An amendment may affect present, as well as
future participants, but may not diminish the account of any participant
existing on the effective date of such amendment.  The company has no present
intent to terminate the Plan.

NOTE 2 - SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

Basis of Accounting
- -------------------

    The accompanying financial statements are prepared on the accrual basis of
accounting in conformity with generally accepted accounting principles.  In
addition, the following accounting policies are applied:

   a. Purchases and sales of securities are recorded on a trade-date basis.

   b. Dividends are recorded on an ex-dividend basis.

   c. Interest income is recorded on the accrual basis.

   d.  Benefits are recorded when paid.

                                       6
<PAGE>
 
                 MOLYCORP, INC. 401(k) RETIREMENT SAVINGS PLAN
                   NOTES TO FINANCIAL STATEMENTS (continued)
                                        
    The Plan presents in the statement of changes in net assets available for
benefits with fund information the net appreciation (depreciation) in the fair
value of its investments which consists of the realized gains or losses and the
unrealized appreciation (depreciation) on those investments.

    Substantially all of the administrative and other costs of the Plan are paid
by the company.

VALUATION OF INVESTMENTS
- ------------------------

   The Plan's investments are stated at fair value except for its investment
contract fund which is valued at contract value (Note 3).  Shares of registered
investment companies are valued at quoted market prices from national exchanges
which represent the net asset value of shares held by the Plan at year-end.  The
Unocal common stock is valued at the closing price as reported for the New York
Stock Exchange Composite Transactions at December 31, 1997 and 1996.

Use of Estimates in Preparation of the Financial Statements
- -----------------------------------------------------------

    The preparation of financial statements in conformity with generally
accepted accounting principles requires the Plan's management to make estimates
and assumptions that affect the reported amounts of assets and liabilities and
disclosure of contingent assets and liabilities at the dates of the financial
statements and the reported amounts of additions to and deductions from net
assets during the reporting periods.  Actual results could differ from those
estimates.

NOTE 3 - INVESTMENTS AT CONTRACT VALUE

    Funds invested in the GIC fund, which holds fixed-rate investment contracts
with various insurance companies, are valued at contract value.  The Plan's
ownership interest in this bank commingled trust fund is based upon units of
equal value referred to as units of participation.  Each unit of participation
represents a proportionate undivided beneficial interest in the total value of
all investment contracts which are held by the bank commingled trust fund.  The
number of units of participation allocated to the Plan are determined by the
Trustee on a monthly basis.  The crediting interest rate for all outstanding
fixed-rate investment contracts was .4881 percent and .5100 percent as of
December 31, 1997 and 1996, respectively, and the average yield rate for such
contracts was 6.08 percent and 6.49 percent for the years then ended,
respectively.

NOTE 4 - CONCENTRATION OF CREDIT RISK

   The GIC fund consists of a series of fixed-rate investment contracts with
various insurance companies.  Although this fund contains a diversified
portfolio of investment contracts, the ultimate performance of the contract is
dependent upon the ability of the underlying companies to honor them.

NOTE 5 - PARTIES-IN-INTEREST

  The Plan's investment in the Employee Benefit Investment Contracts Fund is
managed by Union Bank of California.  Union Bank of California is the Trustee as
defined by the Plan and, therefore, these transactions qualify for an exemption
from the party-in-interest rules.

                                       7
<PAGE>
 
                 MOLYCORP, INC. 401(k) RETIREMENT SAVINGS PLAN
                   NOTES TO FINANCIAL STATEMENTS (continued)

NOTE 6 -RECONCILIATION OF FINANCIAL STATEMENTS TO THE FORM 5500

   The following is a reconciliation of net assets available for benefits per
the financial statements to the Form 5500:

<TABLE>
<CAPTION>
                                                                                  December 31, 1997
                                                                            ---------------------------
<S>                                                                         <C>
Net assets available for benefits per the financial statements                                  $56,989
Participant contributions receivable                                                              1,220
                                                                            ---------------------------
Net assets available for benefits per the Form 5500                                              58,209
</TABLE>

   The following is a reconciliation of participant contributions per the
financial statements to the Form 5500:

<TABLE>
<CAPTION>
                                                                                  For the Year Ended
                                                                                  December 31, 1997
                                                                            ---------------------------
<S>                                                                         <C>
Participant contributions per the financial statements                                          $11,622
Participant contributions receivable                                                              1,220
                                                                            ---------------------------
Participant contributions per the Form 5500                                                     $12,842
</TABLE>

                                       8
<PAGE>
 
                                   SIGNATURE


Pursuant to the requirements of the Securities Exchange Act of 1934, the
Committee appointed by the Board of Directors of the company to administer the
Plan has duly caused this annual report to be signed on its behalf by the
undersigned hereunto duly authorized.


                     MOLYCORP, INC. 401(k) RETIREMENT SAVINGS PLAN
                     ---------------------------------------------
                                     (Name of Plan)



 
Date:  June 26, 1998
                                    By: /s/ JOE D. CECIL
                                       -----------------
                                      Joe D. Cecil
                                      Vice President and Comptroller

                                       9
<PAGE>


                 MOLYCORP, INC. 401(k) RETIREMENT SAVINGS PLAN
         ITEM 27(a) - SCHEDULE OF ASSETS HELD FOR INVESTMENT PURPOSES
                               DECEMBER 31, 1997

<TABLE> 
<CAPTION> 

(a)       (b)                               (c)                                                         (d)            (e)
          Identity of Issue, Borrower,      Description of Investment Including Maturity Date,                         Current
          Lessor or Similar Party           Rate of Interest, Collateral, Par or Maturity Value         Cost           Value
- ----------------------------------------------------------------------------------------------------------------------------------
<S>       <C>                               <C>                                                         <C>            <C> 
          Fidelity Investments              Fidelity Puritan Mutual Fund                                 $ 2,910        $ 3,362
                                            (173.449 shares)

          Unocal Corporation                Unocal Corporation Common Stock                               36,569         47,003
                                            (1,211.000 shares)

    *     Union Bank of California          Short-Term Money Market Fund                                       2              2

    *     Union Bank of California          Employee Benefit Investment Contract Fund                      6,623          6,622
                                            (6622.66 shares)
                                                                                                         -------        -------
                                                                                                         $46,104        $56,989
                                                                                                         =======        =======
</TABLE> 

*  Trustee for the Plan and, therefore, a party-in-interest for which an
   statutory exemption exists

                                      10
<PAGE>
 

                 Molycorp, Inc. 401(k) Retirement Savings Plan
             Item 27(d) - Schedule of Reportable Transactions (1)
                       For Year Ended December 31, 1997

<TABLE> 
<CAPTION> 
(a)                               (b)                                          (c)            (d)       (e)       (f)
                                  Description of Assets                                                           Expense
                                  (including Interest Rate And Maturity        Purchase       Selling   Lease     Incurred With
Identity of Party Involved        in case of loan)                             Price          Price     Rental    Transaction
- ------------------------------------------------------------------------------------------------------------------------------------
<S>                               <C>                                          <C>            <C>       <C>       <C> 
Union Bank of California          Employee Benefit Investment Contract Fund    (2) 
                                    Purchased 5,279 shares (21 transactions)      $ 5,280
                                                                              
Fidelity Investments              Puritan Fund                                
                                    Sold 1,059,220 shares (2 transactions)                     18,884
                                                                              
Unocal Corporation                Unocal Corporation Common Stock             
                                    Purchased 202 shares (11 transactions)          8,210
                                                                              
Union Bank of California          Employee Benefit Investment Contract Fund    (2)
                                    Purchased 29,831 shares (32 transactions)      29,831
                                    Sold 36,882 shares (21 transactions)                       36,882

<CAPTION> 
(a)                               (b)                                          (g)            (h)                 (i)
                                  Description of Assets                                       Current Value
                                  (Including Interest Rate And Maturity                       of Asset on         Net Gain
Identity of Party Involved        in case of loan)                             Cost of Asset  Transaction Date    or (Loss)
- ---------------------------------------------------------------------------------------------------------------------------
<S>                               <C>                                          <C>            <C>                 <C> 
Union Bank of California          Employee Benefit Investment Contract Fund     
                                    Purchased 5,279 shares (21 transactions)    $ 5,280        $ 5,280
                                                                             
Fidelity Investments              Puritan Fund                               
                                    Sold 1,059,220 shares (2 transactions)       17,530         18,884             1,354
                                                                             
Unocal Corporation                Unocal Corporation Common Stock            
                                    Purchased 202 shares (11 transactions)        8,210          8,210
                                                                             
Union Bank of California          Employee Benefit Investment Contract Fund    
                                    Purchased 29,831 shares (32 transactions)    29,831         29,831
                                    Sold 36,882 shares (21 transactions)         36,882         36,882
</TABLE> 

(1)  Under ERISA, a reportable transaction is a transaction or series of
     transactions during the Plan year that involves more than 5 percent of the
     fair value of the Plan assets at the beginning of the plan year.

(2)  Trustee for the Plan and, therefore, a party-in-interest for which an
     statutory exemption exists.

                                      11
<PAGE>
 
                              UNOCAL CORPORATION


                                 EXHIBIT INDEX
                                        

                                        
<TABLE>
<CAPTION>

      Exhibit                                 Description
- --------------------------------------------------------------------------------
<S>                                <C>
        23                         Consent of Coopers & Lybrand L.L.P.
</TABLE>

                                       12

<PAGE>
 
                                                                      EXHIBIT 23


                       CONSENT OF INDEPENDENT ACCOUNTANTS

We consent to the incorporation by reference in the Registration Statement of
Unocal Corporation on Form S-8 (No. 33-43232) of our report, dated June 26,
1998, on our audits of the financial statements and supplemental schedules of
the Molycorp, Inc. 401(k) Retirement Savings Plan as of December 31, 1997 and
1996 and for the years then ended which report appears in this annual report on
Form 11-K.







COOPERS & LYBRAND L. L. P.
Los Angeles, California
June 26, 1998
 


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