Unocal Corporation
				2141 Rosecrans Avenue
				Suite 4000
				El Segundo, California  90245
				Telephone (310) 726-7651
				Facsimile (310) 726-7815

                 Unocal [Logo]


Dennis P.R. Codon
Vice President, Chief Legal Officer
And General Counsel

                                April 21, 1998


[Name and Address Here]

	Re:	Unocal's Annual Meeting June 1, 1998

Dear [name here]:

	Since your organization is a substantial investor in the 
Common Stock of Unocal Corporation, I am enclosing with this 
letter a copy of the proxy statement and annual report for the 
upcoming Annual Meeting of Stockholders, to be held on Monday, 
June 1, 1998.  Knowing that your shares are held through a 
custodian and that the normal path of distribution of these items 
could result in some delay, I thought you would appreciate 
receiving your personal copy of the materials at the same time they 
are being sent to holders of record.

	We would welcome the opportunity to personally discuss 
the proxy statement items with you, and we will be contacting you 
shortly in this regard.  In particular, we would like to answer any 
questions you may have regarding the 1998 Management Incentive 
Program.  Unocal is in the forefront of innovative compensation in 
the petroleum industry with the use of performance  options for 
senior executives.  The performance options are high-risk and will 
be a significant part of senior management compensation. They 
will more closely align the interests of senior management with 
those of our stockholders as they offer rewards only if the 
Company achieves exceptional returns.

        The strike price for the initial grants of performance 
options will be the higher of $50 per share or 133-1/3 percent of 
the average Unocal Common Stock price for the period January 
26, 1998 to May 29, 1998.  The options are not exercisable until 
March 2001, the end of the performance period, and they become 
exercisable only if Unocal's stock price is at or above the strike 
price for 10 out of 20 consecutive trading days during the 
performance period, or the comparative return to stockholders 
places Unocal in the top quartile of its peer group companies for 
the performance period; otherwise, they are forfeited.



[name here]
April 21 1998
Page 2


	A total of 8.25 million shares are to be approved for the 
Program.  Of that total, performance options for 3 million shares 
have been granted to senior executives, subject to stockholder 
approval, and 500,000 shares will be available for future grants.  
Of the remaining 4.75 million shares, no more than 1.75 million 
shares will be granted for restricted stock or performance shares.  
Unocal currently has 241.3 million shares outstanding and 4.6 
million shares reserved for outstanding grants under the previous 
Management Incentive Program.  

	We look forward to talking with you soon.

						Regards,


						/s/ Dennis P.R. Codon