
<PAGE>
 
                                                                    Exhibit 23.4


                      CONSENT OF INDEPENDENT ACCOUNTANTS

We consent to the incorporation by reference in this Registration Statement of 
Evergreen Media Corporation on Form S-3 filed pursuant to Rule 462(b) and 
relating to the Registration Statement of Evergreen Media Corporation on Form
S-3 (File No. 333-12453) of our report dated February 24, 1995, on our audits of
the consolidated financial statements of Broadcasting Partners, Inc. and 
Subsidiaries as of June 30, 1993 and December 31, 1993 and 1994, and the related
consolidated statements of operations, changes in stockholders' equity (deficit)
and cash flows for each of the two years in the period ended June 30, 1993 and 
the six month period from July 1, 1993 to December 31, 1993 and the year ended 
December 31, 1994 which report is included in Form 8-K/A of Evergreen Media 
Corporation dated May 12, 1995. We also consent to the reference to our firm 
under the caption "Experts."


                                             COOPERS & LYBRAND L.L.P.



New York, New York
October 17, 1996




