Exhibit 99.1

                    Clear Channel Purchases Stock

    SAN ANTONIO--(BUSINESS WIRE)--May 6, 2005--On May 5, 2005 Clear
Channel Communications, Inc. (the "Company") (NYSE:CCU) agreed to
purchase 5,690,800 shares of the Company's common stock from
affiliates of Hicks, Muse, Tate & Furst, L.P. at $31.63 per share, the
closing price of our common stock on May 4, 2005. The transaction will
settle and close on May 9, 2005. The Company does not expect this
transaction to have any impact on its previously announced strategic
realignment transactions.

    About Clear Channel Communications, Inc.

    Clear Channel Communications, Inc. (NYSE:CCU), headquartered in
San Antonio, Texas, is a global leader in the out-of-home advertising
industry with radio and television stations, outdoor displays, and
entertainment venues in 63 countries around the world.

    Certain statements in this release constitute "forward-looking
statements" within the meaning of the Private Securities Litigation
Reform Act of 1995. Such forward-looking statements involve known and
unknown risks, uncertainties and other factors which may cause the
actual results, performance or achievements of the Company to be
materially different from any future results, performance or
achievements expressed or implied by such forward-looking statements.
Visit our Web site at www.clearchannel.com.

    CONTACT: Clear Channel Communications, San Antonio
             Investor Relations:
             Randy Palmer, 210-832-3315
             or
             Corporate Communications:
             Lisa Dollinger, 210-832-3474