UNOCAL [LOGO]
THIS PROXY IS SOLICITED ON BEHALF OF THE BOARD OF          Please mark 
DIRECTORS FOR THE ANNUAL MEETING OF STOCKHOLDERS OF        your votes as [X]
UNOCAL CORPORATION                                         indicated in
							   this example

The Board of Directors recommends votes FOR Items 1 and 2

Item 1.  Election of the following    FOR ALL  [ ]    WITHHOLD AUTHORITY  [ ]
	 nominees as directors for    Nominees        to vote for ALL
	 three-year terms to expire                   nominees.
	 in 1999:

	 Malcolm R. Currie,
	 Neal E. Schmale,
	 Charles R. Weaver

Withhold authority to vote for the following nominee(s):

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

Item 2:  Ratification of appointment of Coopers &   FOR    AGAINST   ABSTAIN
	 Lybrand L.L.P. as independent accountants  [_]      [_]       [_]

The Board of Directors recommends votes AGAINST Items 3, 4, and 5

Item 3:  Stockholder proposal: Review and report    FOR    AGAINST   ABSTAIN
	 on Company's international code of conduct [_]      [_]       [_]

Item 4:  Stockholder proposal:  Report on a gas     FOR    AGAINST   ABSTAIN
	 plant in Northern Alberta, Canada          [_]      [_]       [_]

Item 5:  Stockholder proposal:  Review and report   FOR    AGAINST   ABSTAIN
	 annually on pollution prevention options   [_]      [_]       [_]

		    CHECK THIS BOX FOR OPEN BALLOT          [_]
		    (If you check this box, the
		    company will be given access
		    to your proxy)

Please mark, date and sign as your name appears to the left and return 
in the enclosed envelope.  If acting as executor, administrator, trustee 
or guardian, you should so indicate when signing.  If the signer is a 
corporation, please sign the full corporate name, by duly authorized officer.  
If shares are held jointly, each stockholder should sign.

Dated
     -------------------------------------
Signature(s)
	   -------------------------------

- ------------------------------------------
  see other side for important information

			 ^  FOLD AND DETACH HERE   ^


UNOCAL [Logo]

				       May 1996

Dear Stockholder:

According to our latest records, your proxy for the Annual Meeting of 
Stockholders to be held on June 3, 1996 has not yet been received.

It is important that your shares be represented and voted at the meeting.  
Please complete, sign and detach the proxy at the top of this letter and 
return it in the enclosed postage-paid envelope.

				    Sincerely,

				    /s/Dennis P.R. Codon
				    Vice President, Chief Legal Officer
				    and Corporate Secretary




				    UNOCAL CORPORATION
				    C/O CHEMICAL MELLON SHAREHOLDER SERVICES
				    P.O. Box 1474, Church Street Station
				    New York, NY 10277-1474

[LOGO OF UNOCAL]

				    Board of Directors Proxy
				    1996 ANNUAL MEETING OF STOCKHOLDERS


MacDonald G. Becket, Frank C. Herringer and Donald P. Jacobs, or any of 
them, with full power of substitution, are hereby appointed by the signatory 
of this Proxy to vote all shares of Common Stock held by the signatory on 
April 4, 1996, at the June 3, 1996 Annual Meeting of Stockholders of Unocal 
Corporation, and any adjournment thereof, on each of the items on the reverse 
side and in accordance with the directions given there and, in their 
discretion, on all other matters that may properly come before the Annual 
Meeting and any adjournment thereof.

THIS PROXY WILL BE VOTED IN THE MANNER DIRECTED ON THE REVERSE SIDE, OR IF NO 
DIRECTION IS GIVEN, WILL BE VOTED FOR ITEMS 1 AND 2 AND AGAINST ITEMS 3, 4 
AND 5.

	  (Continued, and to be dated and signed on reverse side)


		       ^  FOLD AND DETACH HERE   ^




		YOUR VOTE IS IMPORTANT TO THE COMPANY


		 PLEASE SIGN AND RETURN YOUR PROXY BY
	       TEARING OFF THE TOP PORTION OF THIS SHEET
	  AND RETURNING IT IN THE ENCLOSED POSTAGE-PAID ENVELOPE