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                                                                    EXHIBIT 23.4
 
                       CONSENT OF INDEPENDENT ACCOUNTANTS
 
We hereby consent to the incorporation by reference in the Prospectus
constituting part of this Registration Statement on Form S-4 (No. 333-      ) of
Evergreen Media Corporation of our report dated May 2, 1997, relating to the
financial statements of Century Chicago Broadcasting, L.P., which appears in the
Current Report on Form 8-K of Evergreen Media Corporation dated May 30, 1997 and
filed June 4, 1997. We also consent to the reference to us under the heading
"Experts" in such Prospectus.
 
PRICE WATERHOUSE LLP
 
Chicago, Illinois
July 31, 1997
