SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549



                                    FORM 8-K



                             Current Report Pursuant
                          to Section 13 or 15(d) of the
                         Securities Exchange Act of 1934



    Date of report (Date of earliest event reported)        April 12, 1999
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                               UNOCAL CORPORATION
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             (Exact name of registrant as specified in its charter)



                                    Delaware
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                 (State or Other Jurisdiction of Incorporation)



    1-8483                                   95-3825062
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(Commission File Number)                (I.R.S. Employer Identification No.)



2141 Rosecrans Avenue, Suite 4000, El Segundo, California         90245
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(Address of Principal Executive Offices)                       (Zip Code)



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


Item 5.      Other Events




The company's  Spirit Energy 76 business unit has participated in an oil and gas
discovery on the Mad Dog prospect in the Gulf of Mexico  deepwater  Green Canyon
block 826. The well  encountered 300 net feet of  hydrocarbons,  primarily crude
oil.  Although  further  appraisal  drilling is required to  determine  the full
extent of the discovery, the company believes the find to be significant.

Spirit Energy 76 holds a 25-percent  interest in the  2-1/2-block  drilling unit
that encompasses most of the Mad Dog structure.  The drilling unit is located in
5,000 to 7,000 feet of water in Green Canyon blocks 825, 826 and 782,  about 150
miles southwest of Venice, La. The well spudded in May 1998 and was drilled to a
total depth of 22,410 feet. The pay zones were sampled, but not tested. BP Amoco
p.l.c. is the operator of the Mad Dog well.

Mad Dog is the second  deepwater  discovery  announced by Spirit  Energy 76 this
year.  In March,  Spirit  Energy  76 and  Vastar  Resources  Inc.,  announced  a
discovery on the Mirage prospect in Mississippi Canyon block 941.

The  company  has also  reached  an  agreement  with  Conoco  Inc.  to acquire a
50-percent working interest in the oil and gas lease covering Green Canyon Block
562 which encompasses the K2 prospect.  The K2 prospect is located just north of
Mad Dog on the same geologic trend.

Forward-looking   statements  regarding  exploration   activities  and  resource
potential  in  this  filing  are  based  on   assumptions   concerning   market,
competitive,  regulatory,  environmental,  operational and other considerations.
Actual  results  could  differ  materially  as a result of factors  discussed in
Unocal's  1998  Form  10-K  report  filed  with  the   Securities  and  Exchange
Commission.




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)





Date:  April 12, 1999                        By:   /s/ JOE D. CECIL             
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                                                  Joe D. Cecil
                                                  Vice President and Comptroller