
<PAGE>   1
 
                                                                    EXHIBIT 23.2
 
                         INDEPENDENT AUDITORS' CONSENT
 
The Board of Directors
Evergreen Media Corporation:
 
We consent to the incorporation by reference herein of our reports on the
following financial statements: 1) the consolidated balance sheets of Evergreen
Media Corporation as of December 31, 1995 and 1996 and the related consolidated
statements of operations, stockholders' equity and cash flows for each of the
years in the three-year period ended December 31, 1996; 2) the combined balance
sheets of WMZQ Inc. and Viacom Broadcasting East, Inc. as of December 31, 1995
and 1996 and the related combined statements of earnings and cash flows for each
of the years in the three-year period ended December 31, 1996; 3) the combined
balance sheets of Riverside Broadcasting Co., Inc. and WAXQ Inc. as of December
31, 1995 and 1996 and the related combined statements of earnings and cash flows
for each of the years in the three-year period ended December 31, 1996; 4) the
balance sheets of WLIT Inc. as of December 31, 1995 and 1996 and the related
statements of earnings and cash flows for each of the years in the three-year
period ended December 31, 1996; 5) the combined balance sheets of KYSR Inc. and
KIBB Inc. as of December 31, 1995 and 1996 and the related combined statements
of operations and cash flows for each of the years in the three-year period
ended December 31, 1996; and 6) the balance sheets of KKSF-FM/KDFC-FM and AM (A
Division of the Brown Organization) as of December 31, 1995 and 1996 and the
related statements of earnings and division equity and cash flows for the years
then ended. We also consent to the reference of our firm under the headings
"Experts" and "Evergreen Media Corporation Selected Consolidated Historical
Financial Data" in the Registration Statement.
 
                                            KPMG PEAT MARWICK LLP
 
Dallas, Texas
July 31, 1997
