press release

Unocal makes deepwater discovery on Tobago prospect in Gulf of Mexico

Sugar Land, Texas, May 5, 2004 - Unocal Corporation (NYSE: UCL) today said its exploratory well on the Tobago prospect in Alaminos Canyon block 859 is a discovery.

Drilled to a total depth of 18,510 feet, the well found about 50 net feet of oil pay in high quality reservoir sandstones. The discovery was further delineated by a sidetrack that was drilled to 18,425 feet. Gross costs for the original well and the sidetrack totaled approximately $25 million.

The Tobago well was one of several that have been drilled in the Alaminos Canyon area to evaluate the development potential for the Perdido Foldbelt. The company said that the discovery confirms its previous expectations that Tobago could be part of any Alaminos Canyon area development that may be built in the future to produce a number of other existing discoveries, including Unocal's Trident field.

Unocal is the operator at Tobago and holds a 40.01-percent working interest. Unocal's co-venturers are Shell, 30 percent; ChevronTexaco, 16.66 percent, and Nexen, Inc., with 13.33 percent.

The Tobago well has been temporarily plugged and abandoned, and the Discoverer Spirit drillship has moved to Walker Ridge block 678 to conduct appraisal drilling on the St. Malo discovery.

About Unocal Corporation

Unocal is one of the world's leading independent natural gas and crude oil exploration and production companies. The company's principal oil and gas activities are in North America and Asia.

This news release contains certain forward-looking statements including, but not limited to, statements regarding any future drilling and development plans for the Alaminos Canyon area. These statements are not guarantees of future performance or outcomes. 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 a variety of factors, including changes in commodity prices; the extent of the company's operating cash flow and other capital resources available to fund its capital expenditures; regulatory, political, geological, operating and other conditions; performance by third parties of their contractual obligations; and other factors discussed in Unocal's 2003 Annual Report on Form 10-K, as amended, and subsequent reports filed with the Securities and Exchange Commission (SEC File No. 1-8483). Copies of the company's SEC filings are available from the company by calling 800-252-2233 or from the SEC by calling 800-SEC-0330. The reports are also available on the Unocal web site. Unocal undertakes no obligation to update the forward-looking statements in this news release to reflect future events or circumstances. All such statements are expressly qualified in their entirety by this cautionary statement.

Updated: May 2004