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)        January 13, 2004
                                                        ------------------------



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



                                    Delaware
- --------------------------------------------------------------------------------
                 (State or Other Jurisdiction of Incorporation)



    1-8483                                   95-3825062
- --------------------------------------------------------------------------------
(Commission File Number)                (I.R.S. Employer 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)


Item 5.  Other Events.

Puma Discovery
- --------------
         Unocal Corporation (the "Company") announced that the exploratory well
in the Puma prospect, operated by BP PLC ("BP") in Green Canyon block 823, is a
significant discovery in a hydrocarbon-rich area near existing developments.

         Drilled to a depth of 19,034 feet, the Puma discovery well encountered
approximately 500 net feet of oil pay in Miocene-age reservoirs. Two subsequent
sidetrack bores encountered oil in reservoir intervals of a similar age. Initial
indications of reservoir productivity are encouraging, based on preliminary
analysis of sidewall cores and fluid samples taken from the well. The Puma
discovery's proximity to the Mad Dog field allows the option of either a
stand-alone development or a tie-back, depending on future appraisal results.
Puma is structurally complex and will require additional seismic data and
appraisal drilling to determine the size of the field. The BP-operated Puma well
lies immediately to the west of the Mad Dog development (Green Canyon 826),
where production startup is planned for early 2005.

         The Puma well was spud on August 14th and was drilled in 4,130 feet of
water. As operator, BP holds a 51.66 percent working interest in this prospect.
The Company holds 15 percent, and the remaining 33.34 percent is held by BHP
Billiton Ltd.

Drilling of Hawkes Prospect Well in Deepwater Gulf of Mexico
- ------------------------------------------------------------
         A second well at the Hawkes prospect in Mississippi Canyon block 508
encountered non-commercial quantities of hydrocarbons and has been plugged and
abandoned. The Company will take a pre-tax charge of approximately $8 million to
fourth quarter 2003 earnings for this well.


This filing contains certain forward-looking statements about Unocal's
assessment of the quality of the hydrocarbon formation. These statements are not
guarantees of future performance. The statements are based upon Unocal's current
expectations and beliefs and are subject to a number of known and unknown risks
and uncertainties that could cause actual results to differ materially from
those described in the forward looking statements. Actual results could differ
materially as a result of factors discussed in Unocal's 2002 Annual Report on
Form 10-K and subsequent reports 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:  January 14, 2004                          By:  /s/ JOE D. CECIL
      ------------------                         -------------------------------
                                                 Joe D. Cecil
                                                 Vice President and Comptroller