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                                                                  EXHIBIT 99.1


CAPSTAR RADIO BROADCASTING PARTNERS, INC. ANNOUNCES OFFER TO
PURCHASE OUTSTANDING NOTES AND SOLICITATION OF CONSENTS TO INDENTURE


         AUSTIN, TEXAS, MARCH 30, 1998 -- Capstar Radio Broadcasting Partners,
Inc. ("Capstar Radio"), a subsidiary of Capstar Broadcasting Partners, Inc.
("Capstar Partners"), announced today that it is commencing a tender offer to
purchase for cash all of its outstanding 13 1/4% Senior Subordinated Notes due
2003 (the "Notes"). Capstar Radio also announced today that it will solicit
consents to proposed amendments to eliminate certain restrictive covenants and
to amend certain other provisions of the indenture pursuant to which the Notes
were issued (the "Indenture"). As of the commencement date, there was
approximately $76.8 million principal amount of Notes outstanding. The principal
purposes of the offer and solicitation are to acquire all of the outstanding
Notes to reduce Capstar Radio's overall indebtedness and to amend the Indenture
to provide Capstar Radio with financial flexibility.

         The tender offer consideration to be paid for Notes purchased by
Capstar Radio and properly delivered consents in the tender and solicitation
will be an amount equal to the greater of (x) $1,131.42 per $1.00 principal
amount or (y) a price based upon a fixed spread of 75 basis points over the
yield to maturity on the 6.250% U.S. Treasury Note maturing May 31, 1999, as
calculated in accordance with standard market practice, together, in each case,
with accrued and unpaid interest up to but not including the date of payment.
Using the fixed spread formula, the purchase price for the 6.250% Notes will be
set at 2:00 p.m., New York City time, on Monday, April 13, 1998. Capstar Radio
intends to finance the purchase of the Notes out of available cash.

         Holders who tender their Notes in the tender offer are obligated to
consent to the proposed amendments to the Indenture and may not deliver consents
without tendering Notes. No separate payment will be made for the consents
delivered concurrently with tenders of Notes.

         The tender offer will expire at 5:00 p.m., New York City time, on
Monday, April 27, 1998, unless extended.

         BT Alex. Brown Incorporated will be acting as the Dealer Manager for
the tender offer and the consent solicitation. The tender offer and consent
solicitation will be made pursuant to an Offer to Purchase and Consent
Solicitation Statement and the related Consent and Letter of Transmittal, which
more fully set forth the terms of the tender offer and consent solicitation.
Requests for additional information concerning the terms of the tender offer and
consent solicitation, tendering Notes and the delivery of consents and
conditions to the tender offer and consent solicitation may be directed to BT
Alex. Brown Incorporated at (212) 250-9503. Copies of the Offer to Purchase and
Consent Solicitation Statement and related documents may be obtained from BT
Alex. Brown Incorporated at the same telephone number.

         Capstar Broadcasting Partners was formed in May 1996, by Chief
Executive Officer, R. Steven Hicks, and the Dallas private investment firm of
Hicks, Muse, Tate & Furst Incorporated. Capstar currently owns and operates or
has agreed to acquire over 300 radio stations in mid-sized markets across the
country, making it the largest owner of radio stations in the nation, based on
station count, and one of the largest owners and operators of radio stations in
terms of revenue and cash flow.

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For more information contact:


         Lisa Dollinger
         Capstar Radio Broadcasting Partners, Inc.
         600 Congress Avenue, Suite 1400
         Austin, Texas
         Telephone No. (512) 340-7800