UNOCAL [LOGO]
     2141 ROSECRANS AVE., SUITE 4000
          EL SEGUNDO, CA  90245

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      AMENDMENT TO PROXY STATEMENT
              MAY 4, 1998

A Proxy Statement dated April 20, 1998 
soliciting proxies by the Board of Directors 
of Unocal Corporation (the "Company" or 
"Unocal") to be voted at the Annual Meeting 
of Stockholders to be held at 10:00 A.M. on 
June 1, 1998, or any adjournments thereof, 
was mailed to Unocal's stockholders 
commencing April 20, 1998.  A proxy and a 
postage-paid, return envelope were provided 
with the Proxy Statement.

The first full paragraph on page 18 of the 
Proxy Statement, under the Background 
discussion of Item 3, Approval of 1998 
Management Incentive Program, incorrectly 
stated that the aggregate number of shares 
of the Company's Common Stock remaining 
available for future grants under the 
existing Management Incentive Program as of 
the  close of business on March 30, 1998 was 
2,587,101 shares.  The correct number as of 
March 30, 1998 was 1,037,749 shares, 
reflecting additional grants that were made 
on that date.  The same paragraph indicated 
that under the Long-Term Incentive Plan of 
1991 there were outstanding stock options on 
3,630,941 shares as of the close of business 
on March 30, 1998 and the target number of 
all outstanding performance shares was 
952,002 shares.  There were actually 
outstanding as of March 30, 1998 stock 
options on 5,110,233 shares and the target 
number of all outstanding performance shares 
was 953,721 shares, reflecting the 
additional grants that were made on that 
date. 

If you have not executed and returned your 
proxy, please do so.  Your vote is 
important.  A stockholder who has returned a 
proxy may revoke it at any time before it is 
voted at the meeting by executing a later-
dated proxy, by voting by ballot at the 
meeting, or by filing an instrument of 
revocation with the Inspector of Elections.  
Registered stockholders can obtain a 
duplicate proxy by contacting the Corporate 
Secretary at the above address, or by 
contacting the Company's Stockholder 
Services Department (phone: 800-252-2233, E-
mail: stockholder_services@unocal.com).  
Beneficial stockholders holding Unocal stock 
through a bank or broker must contact their 
broker or account representative for a 
duplicate proxy.