UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D. C. 20549


                                    FORM 10-Q

        (Mark One)

 [X]  QUARTERLY  REPORT  PURSUANT  TO SECTION 13 OR 15(D) OF THE  SECURITIES
      EXCHANGE ACT OF 1934 For the quarterly  period ended March 31, 1998

                                       OR

 [ ]  TRANSITION  REPORT  PURSUANT TO SECTION 13 OR 15(D) OF THE  SECURITIES
      EXCHANGE ACT OF 1934


       For the transition period from               to
                                      --------------  -------------------


                          Commission file number 1-8483

                               UNOCAL CORPORATION
             (Exact name of registrant as specified in its charter)




                 DELAWARE                             95-3825062
         (State or other jurisdiction of           (I.R.S. Employer
          incorporation or organization)            Identification No.)


         2141 ROSECRANS AVENUE, SUITE 4000, EL SEGUNDO, CALIFORNIA 90245        
                    (Address of principal executive offices)
                                   (Zip Code)

                                 (310) 726-7600                                 
              (Registrant's Telephone Number, Including Area Code)


     Indicate by check mark  whether the  registrant:  (1) has filed all reports
required to be filed by Section 13 or 15(d) of the  Securities  Exchange  Act of
1934  during  the  preceding  12 months  (or for such  shorter  period  that the
registrant was required to file such reports),  and (2) has been subject to such
filing requirements for the past 90 days. Yes X No

Number of shares of Common  Stock, $1 par value,  outstanding  as of October 31,
1997: 241,369,372




                         PART I - FINANCIAL INFORMATION
  
ITEM 1.  FINANCIAL STATEMENTS                                UNOCAL CORPORATION
CONSOLIDATED EARNINGS
(Unaudited)
                                                           For the Three Months
                                                              Ended March 31
                                                         ----------------------
Millions of dollars except per share amounts                   1998       1997
- --------------------------------------------------------------------------------
  Revenues
  Sales and operating revenues ................               $ 1,171   $ 1,408
  Gain on sales of assets and other revenues ..                    36        48
- --------------------------------------------------------------------------------
        Total revenues ........................                 1,207     1,456
  Costs and Other Deductions
  Crude oil and product purchases .............                   416       459
  Operating expense ...........................                   331       288
  Selling, administrative and general expense .                    20        28
  Depreciation, depletion and amortization ....                   181       211
  Dry hole costs ..............................                    50        16
  Exploration expense .........................                    47        28
  Interest expense ............................                    41        61
  Property and other operating taxes ..........                    16        20
  Distributions on convertible preferred
     securities of subsidiary trust ...........                     8         8
- --------------------------------------------------------------------------------
        Total costs and other deductions ......                 1,110     1,119
- --------------------------------------------------------------------------------
  Earnings from continuing operations
     before income taxes ......................                    97       337
  Income taxes ................................                    79       149
- --------------------------------------------------------------------------------
 Earnings from continuing operations
    before discontinued operations ...........               $    18      $ 188
 Loss from discontinued operations ..........                     --        (44)
- --------------------------------------------------------------------------------
       Net earnings applicable to common stock                $    18     $ 144
- --------------------------------------------------------------------------------
Basic earnings per share of common stock (a)
   Continuing operations ..........................           $   0.07    $0.75
   Net earnings ...................................           $   0.07    $0.57
Diluted earnings per share of common stock (b)  (c)
   Continuing operations ..........................           $   0.07    $0.73
   Net earnings ...................................           $   0.07    $0.56
Cash dividends declared per share of common stock .           $   0.20    $0.20
- --------------------------------------------------------------------------------
(a)  Basic weighted average shares outstanding 
      (in thousands)                                           241,430   250,510
(b)  Diluted weighted average shares outstanding 
      (in thousands)                                           242,861  264,773
(c)  Distributions on preferred securities (net of tax)
       excluded in numerator.  In 1998,                       $      -    $   6
       the effect of assumed conversion of preferred 
       securities on earnings per share is antidilutive.

               See notes to the consolidated financial statements.




                                       1




CONSOLIDATED BALANCE SHEET                                 UNOCAL CORPORATION

                                                          March 31  December  31
                                                          ----------------------
Millions of dollars                                       1998 (a)         1997
- --------------------------------------------------------------------------------
Assets
Current assets
   Cash and cash equivalents .............................   $   275    $   338
   Accounts and notes receivable .........................       848        897
   Inventories ...........................................       165        172
   Deferred income taxes .................................        54         71
   Other current assets ..................................        31         23
- --------------------------------------------------------------------------------
      Total current assets ...............................     1,373      1,501
Investments and long-term receivables ....................     1,128      1,113
Properties (b) ...........................................     4,882      4,816
Deferred income taxes ....................................        14          7
Other assets .............................................       181         93
- --------------------------------------------------------------------------------
      Total assets .......................................   $ 7,578    $ 7,530
- --------------------------------------------------------------------------------
Liabilities and Stockholders' Equity
Current liabilities
   Accounts payable ......................................   $   655    $   785
   Taxes payable .........................................       112        126
   Interest payable ......................................        34         54
   Current portion of environmental liabilities ..........        99        100
   Other current liabilities .............................        82         95
 -------------------------------------------------------------------------------
      Total current liabilities ..........................       982      1,160
Long-term debt ...........................................     2,427      2,169
Deferred income taxes ....................................       132        137
Accrued abandonment, restoration
    and environmental liabilities ........................       640        627
Other deferred credits and liabilities ...................       629        601
Company-obligated mandatorily redeemable convertible
   preferred securities of a subsidiary
   trust holding solely 6-1/4%
   convertible junior subordinated debentures of Unocal ..       522        522
Common stock ($1 par value) ..............................       252        252
Capital in excess of par value ...........................       460        452
Foreign currency translation adjustment ..................       (17)       (18)
Unearned portion of restricted stock issued ..............       (31)       (31)
Retained earnings ........................................     1,992      2,021
Treasury stock - at cost  (c) ............................      (410)      (362)
- --------------------------------------------------------------------------------
      Total stockholders' equity .........................     2,246      2,314
 -------------------------------------------------------------------------------
         Total liabilities and stockholders' equity ......   $ 7,578    $ 7,530
- --------------------------------------------------------------------------------
(a)  Unaudited
(b)  Net of accumulated depreciation:                        $ 10,040  $  9,896
(c)  Number of shares (in thousands):                          10,595     9,262

               See notes to the consolidated financial statements.

                                       2




CONSOLIDATED CASH FLOWS                                     UNOCAL CORPORATION
(Unaudited)

                                                           For the Three Months
                                                             Ended March 31
                                                           ---------------------
Millions of dollars                                         1998           1997
- --------------------------------------------------------------------------------

Cash Flows from Operating Activities
Net earnings .............................................   $    18    $   144
Adjustments to reconcile net earnings to
   net cash provided by operating activities
      Loss on disposal of discontinued
        operations (before-tax) ..........................        --         71
      Depreciation, depletion and amortization ...........       181        211
      Dry hole costs .....................................        50         16
      Deferred income taxes ..............................        13         10
      Gain on sales of assets (before-tax) ...............        --        (10)
      Other ..............................................        20        (27)
      Working capital and other changes
        related to operations
         Accounts and notes receivable ...................        69        (87)
         Inventories .....................................         7        (33)
         Accounts payable ................................      (131)       105
         Taxes payable ...................................       (14)        48
         Other ...........................................      (119)      (114)
- --------------------------------------------------------------------------------
            Net cash provided by operating activities ....        94        334

Cash Flows from Investing Activities
   Capital expenditures
     (includes dry hole costs) ...........................      (326)      (286)
   Proceeds from sale of
     discontinued operations .............................        --      1,390
   Proceeds from sales of assets .........................         4         16
- --------------------------------------------------------------------------------
            Net cash provided by (used in)
               investing activities ......................      (322)     1,120

Cash Flows from Financing Activities
   Long-term borrowings ..................................       395        341
   Reduction of long-term debt ...........................      (133)      (166)
   Dividends paid on common stock ........................       (48)       (50)
   Repurchases of common stock ...........................       (48)       (46)
   Other .................................................        (1)        (1)
- --------------------------------------------------------------------------------
         Net cash provided by financing activities .......       165         78

Increase (decrease) in cash and cash equivalents .........       (63)     1,532
Cash and cash equivalents at beginning of year ...........       338        217
- --------------------------------------------------------------------------------
Cash and cash equivalents at end of period ...............   $   275    $ 1,749
- --------------------------------------------------------------------------------

Supplemental  disclosure of cash flow  information: 
 Cash paid during the period for:
      Interest (net of amount capitalized)                   $    60    $    86
      Income taxes (net of refunds)                          $    92    $    62


               See notes to the consolidated financial statements.


                                       3



NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
(Unaudited)

(1)  The consolidated financial statements included herein are unaudited and, in
     the opinion of  management,  include all  adjustments  necessary for a fair
     presentation  of  financial   position  and  results  of  operations.   All
     adjustments are of a normal recurring nature. Such financial statements are
     presented in  accordance  with the  Securities  and  Exchange  Commission's
     (Commission) disclosure requirements for Form 10-Q.

     These  interim   consolidated   financial  statements  should  be  read  in
     conjunction  with  the  Consolidated  financial  statements  and the  Notes
     thereto  filed with the  Commission  in Unocal  Corporation's  1997  Annual
     Report on Form 10-K.

     Results for the three  months  ended March 31,  1998,  are not  necessarily
     indicative of future financial results.

     Certain items in the prior year financial statements have been reclassified
     to conform to the 1998 presentation.

(2)  For the  purpose  of  this  report,  Unocal  Corporation  (Unocal)  and its
     consolidated subsidiaries,  Union Oil Company of California (Union Oil) and
     its consolidated subsidiaries and Unocal Capital Trust, will be referred to
     as the company.

(3)  Other Financial Information

     Sales  and  operating  revenues  are  derived  from the sale of crude  oil,
     natural gas, natural gas liquids, geothermal steam, electricity,  specialty
     minerals and nitrogen-based  agricultural products produced by the company.
     During the first quarters of 1998 and 1997, approximately 31 percent and 32
     percent,   respectively,   of  total  sales  and  operating  revenues  were
     attributed  to the resale of purchased  crude oil,  natural gas and natural
     gas liquids  produced by others,  that the company  purchased in connection
     with its trading  and  marketing  activities.  Related  purchase  costs are
     classified  as expense in the crude oil and product  purchases  category of
     the consolidated earnings statement.

     Capitalized  interest  totaled  $8  million  and $5  million  for the first
     quarters of 1998 and 1997, respectively.

     During the first quarter of 1998, the company  recorded  after-tax  foreign
     exchange losses of  approximately  $6 million.  These losses were primarily
     due to foreign  currency  forward  contracts  which  locked in U.S.  dollar
     exchange rates for the Thai baht.

(4)  Income Taxes

     Taxes on earnings from continuing  operations for the first quarter of 1998
     were $79 million  compared with $149 million for the first quarter of 1997.
     The  effective  tax rates for the first  quarters  of 1998 and 1997 were 81
     percent and 44 percent,  respectively.  The increase in the  effective  tax
     rate for 1998 was  primarily  due to  adjustments  totaling $21 million for
     deferred taxes and $11 million for current taxes related to appreciation of
     the baht in Thailand.

(5)  Comprehensive Income

     Effective March 31, 1998, the company adopted Financial Accounting Standard
     No. 130, "Reporting  Comprehensive Income", which establishes standards for
     reporting and displaying  comprehensive income and its components in a full
     set of financial statements.  The company's  comprehensive earnings were as
     follows:

                                                          For the Three Months
                                                            Ended March 31
                                                      --------------------------
Millions of dollars                                     1998              1997
- ------------------------------------------------------------------------------
Net earnings .................................        $        18 $         144
Change in equity due to foreign
currency translation adjustments .............                  1            (1)
- --------------------------------------------------------------------------------
      Comprehensive earnings .................        $        19 $         143
- --------------------------------------------------------------------------------

                                       4



NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
(Unaudited)

(6)  Earnings Per Share

     The following are reconciliations of the numerators and denominators of the
     basic and diluted  earnings per share (EPS)  computations for earnings from
     continuing operations for the first quarters ended March 31, 1998 and 1997:

                                


                                                                                   Earnings             Shares             Per Share
Millions except per share amounts                                                 (Numerator)       (Denominator)            Amount
- ------------------------------------------------------------------------------------------------------------------------------------
Three Months ended March 31, 1998
                                                                                                          
      Earnings from continuing operations .........................................            $ 18             241
            Basic EPS .............................................................                                         $   0.07
                                                                                                                               =====
      Effect of Dilutive Securities
         Options ..................................................................             --                1
                                                                                               -------------------------------------
         Diluted EPS ..............................................................            $ 18            $242             0.07
                                                                                                                               =====
         Distributions on preferred securities (after-tax) ........................               6              12
                                                                                               -------------------------------------
         Antidilutive .............................................................            $ 24            $254             0.09
                                                                                                                               =====
Three Months ended March 31, 1997
      Earnings from continuing operations .........................................            $188             251
            Basic EPS .............................................................                                         $   0.75
                                                                                                                               =====
      Effect of Dilutive Securities
         Options ..................................................................             --                1
                                                                                               -------------------------------------
                                                                                                188            $252             0.75
                                                                                                                               =====
         Distributions on preferred securities (after-tax) ........................               6              12
                                                                                               -------------------------------------
            Diluted EPS ...........................................................            $194            $264             0.73
                                                                                               -------------------------------------


     Not included in the computation of diluted EPS were options  outstanding at
     March 31,  1998 to purchase  approximately  827  thousand  shares of common
     stock. These options were not included in the computation,  as the exercise
     prices were greater than the average market price of the common shares. The
     exercise prices of these options range from $38.81 to $44.75 per share. The
     options will expire in 2007.

     At March 31, 1997,  the basic and diluted  loss per share for  discontinued
     operations were $.18 and $.17, respectively.

(7)  Long Term Debt and Credit Agreements

     Financing  activities during the first quarter of 1998 primarily  consisted
     of increased  borrowings through the issuance of $395 million in commercial
     paper,  bringing the outstanding balance to $495 million. In addition,  the
     company  retired $25 million in  medium-term  notes and $108 million of the
     $250 million  Thailand  revolving credit  facility.  The balance  remaining
     outstanding under the Thailand  revolving credit facility at March 31, 1998
     was $52 million.  Commercial  paper was used to refinance  the  medium-term
     notes and the retired portion of the credit facility.

(8)  Financial Instruments

     The fair values of the company's  financial  instruments  at March 31, 1998
     are described below:


                                       5


NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
(Unaudited)

     The Deutsche  Mark currency  swap  agreement  had a notional  value of $110
     million and an increased value of approximately $25 million based on dealer
     quotes.

     The company had four foreign currency  forward  contracts to purchase 1,505
     million  baht for $35  million  to hedge a series  of known  United  States
     dollar  requirements.   Based  upon  quoted  market  prices  of  comparable
     instruments,  at March 31, 1998,  the net fair value of the contracts  were
     approximately $32 million.

     The company had  outstanding  commodity  futures  contracts  covering 2,360
     thousand  barrels of crude oil with a notional  amount of $39 million and 4
     billion  cubic feet of natural gas with a notional  amount of $10  million.
     The company  also had  outstanding  contracts  for the purchase and sale of
     18,900  thousand  gallons of heating  oil and  10,500  thousand  gallons of
     unleaded  gasoline  with  notional  amounts of $9 million  and $6  million,
     respectively,  at March 31, 1998.  Fair values of the  outstanding  futures
     contracts approximated their carrying values at March 31, 1998.

     The  estimated  fair  value of the  company's  long-term  debt  was  $2,550
     million. The estimated fair value of the mandatorily redeemable convertible
     preferred securities of the company's subsidiary trust was $581 million.

(9)  Accrued Abandonment, Restoration and Environmental Liabilities

     At March 31, 1998,  the company had accrued $453 million for the  estimated
     future costs to abandon and remove  wells and  production  facilities.  The
     total  costs  for   abandonments  are   predominately   accrued  for  on  a
     units-of-production  basis  and  are  estimated  to be  approximately  $629
     million.  This  estimate  was derived in large part from  abandonment  cost
     studies  performed  by an  independent  firm and is used to  calculate  the
     amount to be amortized. The company's reserve for environmental remediation
     obligations  at March 31, 1998 totaled $286  million,  of which $99 million
     was included in current liabilities.

(10) Contingent Liabilities

     The company has certain  contingent  liabilities  with  respect to material
     existing or potential  claims,  lawsuits and other  proceedings,  including
     those involving environmental,  tax and other matters, certain of which are
     discussed more specifically  below. The company accrues liabilities when it
     is  probable  that  future  costs  will be  incurred  and such costs can be
     reasonably estimated.  Such accruals are based on developments to date, the
     company's  estimates of the outcomes of these matters and its experience in
     contesting,  litigating  and settling  other  matters.  As the scope of the
     liabilities becomes better defined,  there will be changes in the estimates
     of future costs, which could have a material effect on the company's future
     results of operations and financial condition or liquidity.

     Environmental  matters  - The  company  is  subject  to loss  contingencies
     pursuant to federal,  state and local  environmental  laws and regulations.
     These include  existing and possible future  obligations to investigate the
     effects of the  release or  disposal  of certain  petroleum,  chemical  and
     mineral  substances at various sites;  to remediate or restore these sites;
     to  compensate  others for damage to property  and natural  resources;  for
     remediation and  restoration  costs and for personal  injuries;  and to pay
     civil  penalties  and,  in some  cases,  criminal  penalties  and  punitive
     damages.  These obligations  relate to sites owned by the company or others
     and are associated  with past and present  operations,  including  sites at
     which the company has been  identified as a potentially  responsible  party
     (PRP)  under  the  federal   Superfund  laws  and  comparable  state  laws.
     Liabilities  are  accrued  when it is probable  that  future  costs will be
     incurred  and such  costs can be  reasonably  estimated.  However,  in many
     cases,  investigations  are not yet at a stage where the company is able to
     determine  whether it is liable or, if liability  is probable,  to quantify
     the liability or estimate a range of possible exposure.  In such cases, the
     amounts  of  the  company's   liabilities  are  indeterminate  due  to  the
     potentially  large number of claimants for any given site or exposure,  the
     unknown magnitude of possible contamination,  the imprecise and conflicting
     engineering evaluations and estimates of proper clean-up methods and costs,
     the  unknown  timing  and  extent  of the  corrective  actions  that may be
     required,  the  uncertainty  attendant  to the  possible  award of punitive
     damages,  the recent  judicial  recognition  of new  causes of action,  the
     present  state of the law,  which  often  imposes  joint  and  several  and
     retroactive  liabilities  on PRPs, and the fact that the company is usually
     just one of a number of companies identified as a PRP.

     As  disclosed  in note 9, at March 31,  1998,  the company had accrued $286
     million for estimated future environmental assessment and remediation costs
     at various sites where  liabilities  for such costs are probable.  At those
     sites where


                                       6


NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
(Unaudited)

     investigations  or  feasibility  studies  have  advanced  to the  stage  of
     analyzing feasible alternative remedies and/or ranges of costs, the company
     estimates  that it could incur  additional  remediation  costs  aggregating
     approximately $240 million.

     Tax matters - In December 1994,  the company  received a Notice of Proposed
     Deficiency  (Notice) from the Internal Revenue Service (IRS) related to the
     years 1985 through 1987. In February  1995,  the company filed a protest of
     the  proposed  tax  deficiency   with  the  Appeals  section  of  the  IRS.
     Discussions  with the  Appeals  Officer  are  nearly  complete,  and it now
     appears  unlikely  that any  issues  raised in the Notice  will  proceed to
     either litigation or mediation, and it is expected that all matters will be
     settled.  The settlement  will require  approval by the Joint  Committee on
     Taxation of the U.S. Congress and such approval should be granted.

     The total amount of tax and interest  that the company would be required to
     pay if the IRS were ultimately to prevail on the material issues  described
     in the Notice,  after  application of foreign tax credits and  overpayments
     related to other issues,  and assuming a full disallowance of the claim for
     refund discussed below, is estimated at $508 million as of March 31, 1998.

     During the first quarter of 1997,  the IRS  examination  team completed its
     review of a claim for refund filed by the company  relating to its 1985 tax
     liability. The IRS has not formally allowed the claim, however, as a result
     of the expected  settlement  described  above,  the company believes that a
     portion of the claim will be allowed and that such allowance should entitle
     it to a small  refund  for  overpayment  of tax or  interest  for all  open
     taxable years preceding 1988.

     The company  believes it has adequately  provided in its accounts for items
     and issues not yet resolved.

     Other  matters - In  February  1996,  Bridas  Corporation  filed a petition
     against the company and others in the  District  Court of Fort Bend County,
     Texas,  alleging  that  the  defendants  conspired  to and  did  tortiously
     interfere  with Bridas'  rights under  agreements  with the  government  of
     Turkmenistan  to develop the Yashlar  Field and to transport  gas from that
     field to Pakistan. The petition also alleges that the defendants interfered
     with Bridas'  exclusive right to lay a gas pipeline in Afghanistan.  Bridas
     seeks actual damages as well as punitive  damages,  plus interest.  Bridas'
     expert  witnesses  have stated in pre-trial  discovery  that Bridas'  total
     actual damages for loss of future profits are  approximately  $1.7 billion.
     In the  alternative,  Bridas is expected to seek an award of  approximately
     $430 million with respect to its total  expenditures in  Turkmenistan.  The
     company  believes the  assertions  made by Bridas are without  merit and is
     vigorously defending the lawsuit.

     The company also has certain other  contingent  liabilities with respect to
     litigation,  claims and  contractual  agreements  arising  in the  ordinary
     course of business.  Although these  contingencies could result in expenses
     or judgments that could be material to the company's  results of operations
     for a given reporting  period, on the basis of management's best assessment
     of the  ultimate  amount  and  timing of these  events,  such  expenses  or
     judgments  are  not  expected  to have a  material  adverse  effect  on the
     company's consolidated financial condition or liquidity.


                                       7


NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (CONTINUED)
(Unaudited)

(11) Unocal guarantees  certain  indebtedness of Union Oil.  Summarized below is
     financial information for Union Oil and its consolidated subsidiaries:
                                
                                                         For the Three Months
                                                             Ended March 31
                                                      --------------------------
Millions of dollars                                           1998        1997
- --------------------------------------------------------------------------------
Total revenues ............................                 $ 1,207     $ 1,455
Total costs and other deductions
   (including income taxes) ...............                   1,184       1,262
- --------------------------------------------------------------------------------
Earnings from continuing operations .......                      23         193
Discontinued operations
   Loss on disposal (a) ...................                      --         (44)
- --------------------------------------------------------------------------------
Net earnings ..............................                 $    23     $   149
- --------------------------------------------------------------------------------
(a)  Net of tax benefit of:                                 $     -     $   (27)


                                                                     At December
                                                     At March 31        31 (b)
                                                      --------------------------
Millions of dollars                                       1998             1997
- --------------------------------------------------------------------------------
Current assets ...............................           $1,373           $1,576
Noncurrent assets ............................            6,231            6,053
Current liabilities ..........................              983            1,124
Noncurrent liabilities .......................            3,828            3,534
Shareholder's equity .........................            2,793            2,971
- --------------------------------------------------------------------------------
(b)  Audited


(12) Subsequent Event

     On May 6, 1998,  Union Oil issued $100  million of 6-1/2%  notes due May 1,
     2008 and $200  million  of 7%  debentures  due May 1,  2028,  in each  case
     guaranteed  by Unocal.  The proceeds  from the sale were used to retire the
     maturing  $110  million  Deutsche  Mark  bonds  and to  reduce  outstanding
     commercial paper borrowings.



                                       8



OPERATING HIGHLIGHTS                                       UNOCAL CORPORATION
(Unaudited)


                                                           For the Three Months
                                                              Ended March 31
                                                           ---------------------
                                                               1998        1997
- --------------------------------------------------------------------------------
NET DAILY PRODUCTION
   Crude oil and condensate (thousand barrels daily)
      United States
         Spirit Energy 76 ..............................          44          48
         Alaska ........................................          30          34
- --------------------------------------------------------------------------------
           Total United States .........................          74          82
      International
         Far East (a) ..................................          89          93
         Other .........................................          31          27
- --------------------------------------------------------------------------------
           Total International .........................         120         120
      Worldwide ........................................         194         202
- --------------------------------------------------------------------------------

   Natural gas (million cubic feet daily)
      United States
         Spirit Energy 76 ..............................         788         910
         Alaska ........................................         138         156
- --------------------------------------------------------------------------------
           Total United States .........................         926       1,066
      International
         Far East (a) ..................................         826         805
         Other .........................................          52          67
- --------------------------------------------------------------------------------
           Total International .........................         878         872
      Worldwide ........................................       1,804       1,938
- --------------------------------------------------------------------------------

   Natural gas liquids (thousand barrels daily) ........          18          20
   Geothermal (million kilowatt-hours daily) ...........          21          16

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

(a) Includes host country share in Indonesia of:
      Crude oil and condensate                                    18         30
      Natural gas                                                 33         33
                          



                                       9

 
OPERATING HIGHLIGHTS (continued)                             UNOCAL CORPORATION
(Unaudited)


                                                           For the Three Months
                                                              Ended March 31
                                                          ----------------------
                                                                1998      1997
- --------------------------------------------------------------------------------
AVERAGE SALES PRICES (a)
   Crude oil and condensate (per barrel)
      United States
         Spirit Energy 76 ..............................     $13.94      $20.79
         Alaska ........................................      10.84       18.51
           Total United States .........................      12.66       19.85
      International
         Far East ......................................     $13.97      $21.03
         Other .........................................      12.30       20.07
           Total International .........................      13.50       20.75
      Worldwide ........................................     $13.15      $20.32
- --------------------------------------------------------------------------------
   Natural gas (per thousand cubic feet)
      United States
         Spirit Energy 76 ..............................     $ 2.14      $ 2.78
         Alaska ........................................       1.47        1.35
           Total United States .........................       2.03        2.57
      International
         Far East ......................................     $ 2.03      $ 2.40
         Other .........................................       2.09        2.22
           Total International .........................       2.04        2.38
      Worldwide ........................................     $ 2.04      $ 2.49
- --------------------------------------------------------------------------------
AGRICULTURAL PRODUCTS PRODUCTION VOLUMES
(thousand tons)
   Ammonia .............................................        374         391
   Urea ................................................        260         275
   Other products ......................................        175         207

AGRICULTURAL PRODUCTS SALES VOLUMES (thousand tons)
   Ammonia .............................................        220         156
   Urea ................................................        325         210
   Other products ......................................        174         252
(a)  Excludes Global Trade margins

                                       10
        

ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
OF OPERATIONS

The following  discussion and analysis of the financial condition and results of
operations  of  Unocal  should  be  read  in  conjunction   with  the  company's
Management,  Discussion and Analysis in Item 7 of the 1997 Annual Report on Form
10-K.  Unless  otherwise  specified,  the following  discussion  pertains to the
company's continuing operations.

CONSOLIDATED RESULTS

                                                           For the Three Months
                                                              Ended March 31
                                                        ------------------------
Millions of dollars                                              1998      1997
- ------------------------------------------------------------------------------
After-tax earnings from continuing operations ................   $  18    $ 188
Special items (net of tax):
    Environmental and litigation provisions ..................     (33)      (9)
    Asset sales ..............................................      --        7
    Deferred tax adjustment ..................................     (21)      --
- --------------------------------------------------------------------------------
   Total special items .......................................     (54)      (2)
 -------------------------------------------------------------------------------
   Adjusted after-tax earnings from continuing operations ....      72      190
Net loss on disposal of discontinued operations ..............      --      (44)
Special item:  discontinued operations .......................      --      (44)
- --------------------------------------------------------------------------------
   Adjusted after-tax loss from discontinued operations ......      --       --
- --------------------------------------------------------------------------------
      Adjusted after-tax earnings ............................   $  72    $ 190
- --------------------------------------------------------------------------------

The company's first quarter 1998 adjusted  earnings from  continuing  operations
decreased 62 percent over the same period last year.  The lower  earnings  level
was primarily due to  significantly  lower  average  worldwide  sales prices for
crude oil and natural  gas,  lower U.S.  natural  gas and crude oil  production,
higher  U.S.  dry hole  costs and  higher  international  exploration  expenses.
Partially  offsetting  these negative factors were increased power generation at
Salak in  Indonesia,  higher  agricultural  products  sales  volumes  and  lower
interest expense.

EXPLORATION AND PRODUCTION

Exploration and Production involves the exploration for, and production of crude
oil and natural gas.

UNITED STATES - Included in the United  States  category is Spirit Energy 76 and
Alaska oil and gas  operations.  Spirit Energy 76 is responsible for oil and gas
operations  in the Lower 48  United  States  with  emphasis  on the Gulf  Coast,
deepwater  areas in the Gulf of Mexico and the Permian  Basis in West  Texas.  A
substantial  portion of crude oil and natural gas produced  domestically is sold
interdivision  to the company's  Global Trade group. The remainder is contracted
to third parties, sold in the spot market or used in the company's  agricultural
products operations.

                                                            For the Three Months
                                                                Ended March 31
                                                          ----------------------
Millions of dollars                                            1998        1997
- --------------------------------------------------------------------------------
After-tax earnings:
   Spirit Energy 76 ..................................         $ 10         $ 95
   Alaska ............................................           12           21
- --------------------------------------------------------------------------------
      Total after-tax earnings .......................           22          116
Special items:
     Asset sales .....................................           --            2
- --------------------------------------------------------------------------------
            Adjusted after-tax earnings ..............         $ 22         $114
- --------------------------------------------------------------------------------

During the first three months of 1998,  adjusted after-tax earnings decreased 81
percent compared with the same period a year ago. The decrease was primarily due
to  substantially  lower  average  sales  prices for crude oil and natural  gas,
decreased crude oil and natural gas production and higher dry hole costs.

                                       11


ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
OF OPERATIONS (CONTINUED)

Compared with the first quarter of 1997,  average sales prices for United States
crude oil decreased by $7.19 per barrel, or 36 percent, and average sales prices
for United States  natural gas decreased by $.54 per thousand cubic feet (mcf) ,
or 21 percent.

The company's United States crude oil and natural gas production decreased by 10
percent  and 13  percent,  respectively,  over the same  period a year ago.  The
decreased  production  volumes  were  primarily  due  to two  separate  pipeline
curtailments and mechanical-related shut-ins.

Dry hole expense  increased by $20 million  (after-tax)  compared with the first
quarter of 1997 due to increased  exploratory drilling activities in the Gulf of
Mexico.

INTERNATIONAL  - The  company's  international  operations  pursue  oil  and gas
exploration and exploitation opportunities outside the United States.

                                                           For the Three Months
                                                              Ended March 31
                                                          ----------------------
Millions of dollars                                         1998           1997
- --------------------------------------------------------------------------------
After-tax earnings                                            13             102
Special items:
     Deferred tax adjustment ....................            (21)              1
- --------------------------------------------------------------------------------
Adjusted after-tax earnings .....................           $ 34            $101
- --------------------------------------------------------------------------------

During the first  quarter of 1998,  international  adjusted  after-tax  earnings
decreased  compared  with 1997  results  primarily  due to  substantially  lower
average  sales  prices  for crude oil and  natural  gas,  increased  exploration
expenses and higher current income taxes in Thailand.

Compared  with the first  quarter  of 1997,  total  international  crude oil and
condensate  average  sales prices  decreased 35 percent to $13.50 per barrel and
natural gas average sales prices decreased by 14 percent to $2.04 per mcf.

During the first quarter of 1998, crude oil and condensate  production  remained
at the 1997 level of 120  thousand  barrels per day and  natural  gas  increased
slightly  from the 1997 level of 872  million  cubic feet  (mmcf) per day to 878
mmcf per day.

During the first quarter of 1998,  exploration  expense was higher by $7 million
(after-tax), primarily due to increased exploration activities in Indonesia.

GLOBAL TRADE

The Global Trade group handles the company's worldwide crude oil, condensate and
natural gas marketing and trading activities.  Global Trade also purchases crude
oil,  condensate  and natural gas from the  company's  joint  venture  partners,
royalty owners and other unaffiliated oil and gas producers for resale.

During the first  quarters of 1998 and 1997 Global  Trade's  after-tax  earnings
were $6 million.

GEOTHERMAL AND POWER OPERATIONS

The Geothermal and Power  Operations  segment  explores for,  produces and sells
geothermal  resources,  and  constructs and operates  electric power  generation
plants and sells the related electricity.

First quarter 1998 and 1997 adjusted  after-tax earnings were $14 million and $6
million, respectively.  Improved 1998 earnings were primarily the result of a 31
percent   increase  in  power   generation  and  related  sale  of  electricity,
principally  from the  Indonesian  Salak  field Units 3 through 6, which came on
line during the fourth quarter of 1997.
Partially offsetting these positive factors were higher dry hole provisions.

                                       12


ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
OF OPERATIONS (CONTINUED)

DIVERSIFIED BUSINESS GROUP

                                                           For the Three Months
                                                             Ended March 31
                                                        -----------------------
Millions of dollars                                           1998         1997
- -------------------------------------------------------------------------------
After-tax earnings
   Agricultural Products ............................         $  9          $ 20
   Carbon and Minerals ..............................           15            10
   Pipelines ........................................           15            14
   Other ............................................          --              1
- --------------------------------------------------------------------------------
   Total ............................................           39            45
Special items:
   Carbon and Minerals (Litigation) .................           (1)          --
- -------------------------------------------------------------------------------
Adjusted after-tax earnings .........................         $ 40          $ 45
- --------------------------------------------------------------------------------

The Diversified Business group's lower adjusted after-tax earnings for the first
quarter  of  1998  were  primarily  due to  lower  margins  on the  Agricultural
Products' export sales activity.  The lower export sales activity was the result
of lower sales prices and production  volumes at the Kenai,  Alaska plant.  This
negative impact to earnings was partially offset by higher Agricultural Products
export sales volumes and sales margins associated with its West Coast operation.
The  higher  adjusted  net  earnings  for the  Carbon  and  Minerals  group were
primarily due to increased earnings from its Brazilian affiliate.

CORPORATE AND UNALLOCATED

Corporate and Unallocated  expense  includes  general  corporate  overhead,  the
non-exploration  and production related activities of the New Ventures group and
other unallocated costs. Net interest expense represents  interest expense,  net
of interest income and capitalized interest.

                                                           For the Three Months
                                                                Ended March 31
                                                           ---------------------
Millions of dollars                                                1998    1997
- --------------------------------------------------------------------------------
After-tax earnings effect
   Administrative and general expense ..........................   $(11)   $(13)
   Net interest expense ........................................    (26)    (42)
   Environmental and litigation expense ........................    (33)    (11)
   New Ventures ................................................     (7)     (7)
   Other .......................................................      1     (14)
- --------------------------------------------------------------------------------
   Total .......................................................    (76)    (87)
Special items:
     Environmental and litigation provisions ...................    (32)     (9)
     Asset sales (Other) .......................................    --        4
- --------------------------------------------------------------------------------
   Total special items .........................................    (32)     (5)
- --------------------------------------------------------------------------------
Adjusted after-tax earnings effect from continuing operations ..   $(44)   $(82)
- --------------------------------------------------------------------------------

Net interest  expense  decreased 38 percent from the first  quarter of 1997 as a
result of a decreased debt level and increased capitalized  interest.  The Other
category  decreased  $15 million  primarily  due to  dividends  from a petroleum
industry mutual insurance company.  Asset sales for 1997 primarily  consisted of
the sale of a company airplane.

FINANCIAL CONDITION AND CAPITAL EXPENDITURES

For the first  three  months  of 1998,  cash  flow  from  operating  activities,
including working capital changes,  was $94 million,  compared with $334 million
in 1997. This decrease was principally due to lower commodity prices, payment to
Thailand
                                      13


ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
OF OPERATIONS (CONTINUED)

for 1997 income  taxes and  extension of payment  terms for certain  foreign and
domestic fertilizer sales.

Proceeds from asset sales were $4 million for the first three months of 1998 and
primarily consisted of miscellaneous real estate properties.

Consolidated  working capital at March 31, 1998 was $391 million, an increase of
$50 million from the year-end 1997 level of $341 million.

Capital expenditures for the first three months of 1998 totaled $326 million, an
increase of $40 million from the 1997 level of $286  million,  primarily  due to
increased drilling activities in the U.S. Gulf Coast.

The company's  total debt  including  capital leases was $2,428 million at March
31, 1998,  an increase of $258  million  from the year-end  1997 level of $2,170
million. The debt-to-total  capitalization ratio increased to 47 percent from 43
percent at year-end 1997.

During the first quarter of 1998,  the company  repurchased  approximately  1.33
million shares of common stock for a total cost of approximately $48 million.

ENVIRONMENTAL MATTERS

At  March  31,  1998,  the  company's  reserves  for  environmental  remediation
obligations  totaled $286 million,  of which $99 million was included in current
liabilities. During the first quarter, cash payments of $14 million were applied
against the reserve and an additional $32 million in  liabilities  were recorded
to the  reserve  account.  The  company  also  estimates  that  it  could  incur
additional remediation costs aggregating approximately $240 million as discussed
in  note  10 to the  consolidated  financial  statements.  The  company's  total
environmental reserve amount is grouped into the following five categories:

                                                                        March 31
Millions of dollars                                                        1998
- --------------------------------------------------------------------------------
   Superfund and similar sites ....................................         $ 21
   Former company-operated sites ..................................           26
   Company facilities sold with retained liabilities ..............           68
   Inactive or closed company facilities ..........................          140
   Active company facilities ......................................           31
- --------------------------------------------------------------------------------
      Total reserves ..............................................         $286
- --------------------------------------------------------------------------------

The additional $32 million in reserves were for estimated cleanup and associated
costs primarily for various company  facilities  where the company's  operations
have been closed or shut down, including the Avila Beach and Guadalupe sites. On
April 3, 1998, the California Central Coast Regional Water Quality Control Board
issued  Cleanup and Abatement  Orders for both sites.  The order for Avila Beach
requires  excavation  of the  affected  sections  of the  beach  and  town.  The
Guadalupe order requires  excavation of 18 locations and bioremediation at other
locations  of the site in addition to the  recovery  of  contaminants  utilizing
shallow wells.  Estimates for possible  additional  remediation costs related to
these  sites  are  included  in  the  $240  million  total  possible  additional
remediation costs disclosed in note 10 to the consolidated financial statements.
(See  notes  9 and 10 to  the  consolidated  financial  statements  for  related
information.)


                                       14


ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
OF OPERATIONS (CONTINUED)

OUTLOOK

Certain of the statements in this discussion,  as well as other  forward-looking
statements within this document, contain estimates and projections of amounts of
or increases in future revenues,  earnings,  cash flows,  capital  expenditures,
assets,  liabilities  and  other  financial  items  and of  future  levels of or
increases in reserves, production, sales including related costs and prices, and
other  statistical  items;  plans and  objectives  of  management  regarding the
company's  future  operations,  products and services;  and certain  assumptions
underlying  such  estimates,   projection  plans  and  objectives.  While  these
forward-looking  statements are made in good faith,  future  operating,  market,
competitive, legal, economic, political, environmental, and other conditions and
events  could  cause  actual  results  to differ  materially  from  those in the
forward-looking statements.

The current  economic  problems  continue to be  significant  in  Indonesia  and
Thailand.  The company remains optimistic about Asia's long-term economic growth
and is working  closely with host  governments and business  associates  through
this difficult period.

The  company  expects  energy  prices to remain  volatile in 1998 due to climate
conditions,  the  production  quotas  set by OPEC  and the ongoing  developments
between Iraq and the United Nations.

As a result of the  current  crude oil price  outlook,  the  company  expects to
reduce its capital  spending  below the original  1998 forecast of $1.5 billion.
Estimated expenditures for the full year 1998 are expected to total between $1.3
and $1.4 billion. The company is also reducing its expectations for 1998 oil and
gas  production  levels from the United States Lower 48 by about five percent to
178,000  barrels  of oil  equivalent  (boe)  per day  compared  with an  earlier
forecast  of 188,000  boe per day.  However,  long-term,  high-potential  growth
projects in Indonesia, Bangladesh, Argentina and the Caspian Sea, as well as the
exploration of high-potential prospects in shelf and deepwater areas of the Gulf
of Mexico, are expected to proceed as planned. The company is focused on reserve
replacement from  high-potential  prospects,  rather than short-term projects to
boost production.

ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK.

Market risk generally  represents the risk that losses may occur in the value of
financial  instruments  as a result of  movements  in  interest  rates,  foreign
currency  exchange  rates and  commodity  prices.  As part of its  overall  risk
management  strategies,  the company uses  derivative  financial  instruments to
manage and reduce risks associated with these factors.  The following discussion
and analysis focuses on significant  changes in the company's position regarding
these risk factors since year end 1997.

Interest  Rate Risk - The  company's  primary  market  exposure  for  changes in
interest rates relates to the company's long term debt  obligations.  During the
first  quarter  of 1998,  the  company  increased  its  outstanding  debt  level
(excluding  capital lease  obligations)  by $258 million or twelve  percent,  to
$2,426 million from its year end 1997 level of $2,168 million  primarily through
the additional issuance of commercial paper. The addition was principally due to
increased cash requirements for capital  expenditures and lower than anticipated
first quarter  commodity  prices.  The company expects to have cash available to
repay a portion of the commercial paper borrowings in 1998 through a combination
of cash  generated  by  operations,  sales of  assets,  new debt  offerings  and
decreases in planned  capital  spending.  However,  a continuation  of depressed
commodity  prices may lead to a further  increase in the company's debt level at
December 31, 1998. The following  table provides  principal  amounts and related
weighted average  interest rates for the company's  outstanding debt obligations
at March 31, 1998 by expected  maturity dates and constitutes a  forward-looking
statement.  Circumstances  could  arise which may cause the timing and amount of
actual cash flows to differ materially from the projections.

                                       15


ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK (CONTINUED)



Debt Obligation Principal Amounts by Expected Maturity Dates at March 31, 1998
(excludes capital leases)
                                                                                                                             Fair
Millions of U.S. dollars                                               1998-2002      There-after         Total              Value
- ------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                   
Fixed rate ...................................................           $ --           $1,744            $1,744            $1,868
  Average Interest Rates .....................................                            8.18%             8.18%
Fixed rate (DM denominated) (a) ..............................             --              135               135               135
  Average Interest Rates .....................................             --            6.125%            6.125%
Variable rate ................................................             --              547               547               547
  Average Interest Rates .....................................             --             5.94%             5.94%
- ------------------------------------------------------------------------------------------------------------------------------------
                                                                         $ --           $2,426            $2,426            $2,550
- ------------------------------------------------------------------------------------------------------------------------------------


(a)  The underlying  debt  obligation is a 6.125 percent  Deutsche Mark (DM) 250
     million bond which was hedged by a currency swap agreement. Under the terms
     of the  currency  swap  agreement,  the company was to pay $110 million and
     receive DM 250  million at  maturity.  On May 6, 1998,  the DM bond and the
     currency swap agreement  matured.  The company  retired the DM bond with DM
     250 million  received  from the currency swap  agreement.  The company used
     proceeds  received  from  two  new  debt  issues  to pay its  $110  million
     obligation  under the  currency  swap  agreement  and to retire  commercial
     paper. See note 12 to the consolidated financial statements for information
     regarding the new debt issues.

Foreign  exchange rate risk - Due to the recent  volatility in foreign  currency
exchange rates,  the company  entered into foreign  currency  forward  contracts
primarily to lock in exchange  rates for funds to be converted to U.S.  dollars.
At March 31, 1998, the company had four foreign currency forward contract hedges
outstanding related to its Thailand oil and gas operations with notional amounts
totaling $35 million.  Two of the outstanding  contracts call for the company to
pay  920,100,000  Thai baht in exchange  for $20  million  (U.S.) at maturity on
April  9,  1998.  The  remaining  two  contracts  call  for the  company  to pay
584,500,000  Thai baht in exchange for $15 million  (U.S.) at maturity on May 8,
1998. The contracts had a total value of approximately  $32 million (U.S.) based
upon the exchange  rates in effect on March 31, 1998.  The company will continue
to monitor  its  exposure to foreign  exchange  rate  volatility  as part of its
strategy to mitigate foreign currency risks.

Commodity price risk - The company  generally uses  hydrocarbon  commodity based
derivative  financial  instruments,  such as options or futures  contracts  with
maturities  of 18 months or less,  to mitigate its exposure to  fluctuations  in
petroleum commodity prices. The company also trades hydrocarbon-based derivative
financial  instruments on a limited basis. The company has controls in place and
monitors its trading activities to ensure compliance.

The  company  uses a value  at risk  model  to  assess  the  market  risk of its
commodity price  sensitive  derivative  financial  instruments for internal risk
management  purposes.  Value at risk represents the potential loss in fair value
the  company  would  experience  on its  commodity  price  sensitive  derivative
financial  instruments,  using calculated  volatilities and correlations  over a
specified time period with a given confidence  level. The company's  calculation
model is based on  historical  data and uses a one week time  interval  and a 95
percent  confidence  level. The total amount of commodity  derivative  financial
instruments  held for trading  purposes and purposes other than trading were not
material at March 31, 1998. Based upon the company's  calculations,  the risk of
loss  in  fair  value  associated  with  commodity  price  sensitive  derivative
financial instruments at March 31, 1998 was immaterial.

                           PART II - OTHER INFORMATION

ITEM 1.   LEGAL PROCEEDINGS

There is incorporated by reference the information with respect to certain legal
proceedings previously reported in Item 1 of Unocal's Annual Report on Form 10-K
for the year ended December 31, 1997 (1997 Form 10-K), the information regarding
environmental  remediation  reserves  in  note 9 to the  consolidated  financial
statements  in  Item  1  of  Part  I  hereof,  the  discussion  thereof  in  the
Environmental Matters section of Management's' Discussion and Analysis in Item 2
of Part I, and the  information  regarding  certain legal  proceedings and other
contingent liabilities in note 10 to the consolidated financial

                                       16


ITEM 1.   LEGAL PROCEEDINGS (CONTINUED)

         statements.

(1)      In Citizens  for a Better  Environment,  et al. v. Union Oil Company of
         California, described in Paragraph (3) of Item 3 of the 1997 Form 10-K,
         the  trial has been  postponed  to  September  1998  while the  parties
         continue with mediation in an attempt to settle the case.

(2)      With  reference  to the  matters  involving  the  Guadalupe  oil field,
         described in Paragraph (4) of Item 3 of the 1997 Form 10-K, a letter of
         intent (LOI) to settle the civil  proceeding  brought by the California
         Attorney  General was  executed by the parties in April 1998;  however,
         final documentation and court approval are still necessary.  The County
         of San Luis Obispo certified the  Environmental  Impact Report (EIR) in
         late March  1998,  and on April 3, 1998,  the  Regional  Water  Quality
         Control   Board   (RWQCB)   issued  a  Cleanup  and   Abatement   Order
         substantially reflecting the agreement reached in the LOI.

(3)      With  reference  to the  matters  involving  the town of  Avila  Beach,
         California, described in Paragraph (5) of Item 3 of the 1997 Form 10-K,
         on April 3, 1998, the RWQCB  certified the EIR and issued a Cleanup and
         Abatement Order.

(4)      With reference to the preliminary determinations of underpaid royalties
         described  in  Paragraph  (10) of Item 3 of the  1997  Form  10-K,  the
         company has now received notices from the U.S.  Department of Interior,
         Minerals  Management  Service,  alleging  underpaid  royalties totaling
         approximately  $48  million,  as  well  as  undetermined  late  payment
         charges.

(5)      With reference to the matters involving the Mountain Pass,  California,
         lanthanide  facility  of  the  company's  Molycorp,   Inc.  (Molycorp),
         subsidiary,  described  in  Paragraph  (14) of Item 3 of the 1997  Form
         10-K,  on March 5, 1998,  Molycorp was served by the Lahontan  Regional
         Water  Quality  Control  Board  (LRWQCB)  with  a  Notice  of  Proposed
         Administrative  Civil  Liability  which  seeks civil  penalties  in the
         amount  of  approximately  $550,000  for  alleged  failures  to  submit
         self-monitoring  reports  and  discharge  reports  in a timely  manner.
         Molycorp has the opportunity to contest the proposed civil penalties at
         a hearing scheduled in July 1998. In addition,  the LRWQCB issued three
         Cleanup and Abatement Orders on March 25, 1998, relating to the present
         wastewater   evaporation  pond,  a  former  and  now-closed  wastewater
         evaporation  pond,  and the mine  and mill  site,  all  located  at the
         Mountain  Pass  facility.   These  three  orders  do  not  carry  civil
         penalties,  but may require significant  expenditures for environmental
         investigation and remediation.

(6)      With reference to the matter involving the company's former refinery in
         Rodeo,  California,  described in Paragraph  (18) of Item 3 of the 1997
         Form 10-K, in April 1998 the company settled the claims of the Bay Area
         Air Quality  Management  District  for  aggregate  civil  penalties  of
         $285,000, which was paid in May.

ITEM 2.   CHANGES IN SECURITIES

During the first quarter of 1998,  the company  awarded 4,496  restricted  stock
units to nonemployee directors pursuant to the terms of the company's Directors'
Restricted Stock Plan. The units were not registered under the Securities Act of
1933 (the Act) in reliance upon the  exemption  contained in Section 4(2) of the
Act for transactions by an issuer not involving any public  offering.  The units
were  awarded  (1) in  consideration  of  the  prior  election  by  each  of the
nonemployee  directors to defer all or a portion of his or her cash fees and (2)
upon the credit of dividend  equivalents upon units previously issued. The units
are paid out in an equal number of shares of Unocal common stock at the end of a
restriction  period  elected  by  each  director,  or  upon  his or her  earlier
termination of service as a director.

During the first  quarter of 1998,  Unocal  issued 46 shares of its common stock
upon the conversion of 40 of the 6-1/4% trust convertible  preferred  securities
of Unocal Capital Trust.  The common shares were not registered under the Act in
reliance  upon  the  exemption  contained  in  Section  3(a)(9)  of the  Act for
securities   exchanged  by  the  issuer  with  its   existing   security-holders
exclusively where no commission or other  remuneration is paid or given directly
or indirectly for soliciting such exchange.

ITEM 6.   EXHIBITS AND REPORTS ON FORM 8-K

     (a)  Exhibits:  The  Exhibit  Index  on page 20 of this  report  lists  the
          exhibits that are filed as part of this report.

     (b)  Reports on Form 8-K:

                                       17


ITEM 6.   EXHIBITS AND REPORTS ON FORM 8-K (CONTINUED)

                 Filed during the first quarter of 1998:

                 1. Current Report on Form 8-K dated and filed January 28, 1998,
                    for the purpose of  reporting,  under Item 5, the  company's
                    fourth  quarter  and full year  1997  earnings  and  related
                    information.

                 2. Current Report on Form 8-K dated February 13, 1998 and filed
                    February 17, 1998, for the purpose of reporting,  under Item
                    5,  the  company's   Unocal  Canada   Limited   subsidiary's
                    agreement  to exchange  certain of its  Canadian oil and gas
                    properties  with  Tarragon  Oil and Gas Limited for Tarragon
                    common stock and debentures.

                 3. Current Report on Form 8-K dated February 25, 1998 and filed
                    March 3, 1998,  for the purpose of reporting,  under Item 5,
                    the company's crude oil and natural gas reserve data.

                 Filed during the second quarter of 1998 to the date hereof:

                 1. Current  Report on Form 8-K dated  April 15,  1998 and filed
                    April 21, 1998, for the purpose of reporting,  under Item 5,
                    the  completion  of  Unocal  Canada   Limited   subsidiary's
                    exchange of certain of its Canadian  oil and gas  properties
                    with  Tarragon  Oil and Gas for  Tarragon  common  stock and
                    debentures.

                 2. Current  Report on Form 8-K dated  April 28,  1998 and filed
                    April 29, 1998, for the purpose of reporting,  under Item 5,
                    Unocal's   first   quarter   1998   earnings   and   related
                    information.


                                       18



                                    SIGNATURE


Pursuant  to the  requirements  of the  Securities  Exchange  Act of  1934,  the
registrant  has duly  caused  this  report  to be  signed  on its  behalf by the
undersigned thereunto duly authorized.



                                      UNOCAL CORPORATION
                                         (Registrant)


Dated:  May 13, 1998                  By:   /s/ Joe D. Cecil
                                            ----------------
                                                Joe D. Cecil
                                                Vice President and Comptroller
                                                (Duly Authorized Officer and
                                                Principal Accounting Officer)



                                       19




                                  EXHIBIT INDEX


     3    Bylaws of Unocal, as amended to be effective June 1, 1998.

     10   Amendments to 1985 and 1991 Incentive Plan Awards.

     12.1 Statement regarding  computation of ratio of earnings to fixed charges
          of Unocal for three months ended March 31, 1998 and 1997.

     12.2 Statement regarding  computation of ratio of earnings to fixed charges
          of Union Oil Company of  California  for the three  months ended March
          31, 1998 and 1997.

     27   Financial  data schedule for the period ended March 31, 1998 (included
          only  in the  copy  of  this  report  filed  electronically  with  the
          Commission).

                                       20