Exhibit 99.1

Mesa-Royalty-Trust

Mesa Royalty Trust Announces Trust Income for May 2005

MESA ROYALTY TRUST

JPMorgan Chase Bank, N.A., Trustee	NEWS
	RELEASE

FOR IMMEDIATE RELEASE

AUSTIN, TEXAS May 20, 2005 — Mesa Royalty Trust (NYSE symbol-MTR)

announced the Trust income distribution for the month of May 2005. Unitholders of record on May 31, 2005 will receive distributions amounting to $779,219 or  $0.418127983 per unit payable on July 29, 2005. Royalty income from the San Juan Basin Properties totaled $411,333. Royalty income from the Hugoton Properties totaled $374,260.

The extent of future distributions from the properties in which the Trust has an interest will continue to be dependent on normal factors associated with oil and gas operations such as oil and gas production levels, prices and associated cost, accruals for future abandonment costs, timing and extent of capital expenditures.

Contact:	Mesa Royalty Trust
	JPMorgan Chase Bank, N.A., as Trustee
	Mike Ulrich
	1(800) 852-1422
	(512) 479-2562

www.businesswire.com/cnn/mtr.htm

700 Lavaca          Austin, TX 78701