
<PAGE>
 
                                                              Exhibit 23.2
                                                              ------------


                         Independent Auditors' Consent



The Board of Directors
Evergreen Media Corporation:

We consent to incorporation by reference in this Registration Statement on 
Form S-3 of Evergreen Media Corporation filed pursuant to Rule 462(b) and 
incorporating the previously effective Registration Statement on Form S-3 (No. 
333-12453) of Evergreen Media Corporation of (a) our report dated February 9, 
1996, except for note 14(b), which is as of February 14, 1996, and note l(m), 
which is as of August 8, 1996, relating to the consolidated balance sheets of 
Evergreen Media Corporation and subsidiaries as of December 31, 1994 and 1995 
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, 
1995, which report appears in the Form 8-K/A dated September 3, 1996 filed by 
Evergreen Media Corporation, (b) our report dated June 28, 1996, relating to the
balance sheet of WEDR, Inc. as of December 31, 1995 and the related statements 
of operations and retained earnings and cash flows for the year then ended, 
which report appears in the Form 8-K dated August 23, 1996 filed by Evergreen 
Media Corporation, (c) our report dated September 24, 1996, relating to the 
balance sheet of KKSF-FM/KDFC-FM and AM as of December 31, 1995, and the related
statements of operations and division equity and cash flows for the year then 
ended, which report appears in the Form 8-K dated September 30, 1996 filed by 
Evergreen Media Corporation, and (d) our report dated March 29, 1996 relating to
the balance sheet of WDAS-AM/FM as of December 31, 1995, and the related
statements of earnings and station equity and cash flows for the year then
ended, which report appears in the Form 8-K dated September 30, 1996 filed by
Evergreen Media Corporation. We also consent to the reference to our firm under
the heading "Experts" in the Prospectus.


                                /s/ KPMG Peat Marwick LLP
                                KPMG Peat Marwick LLP


Dallas, Texas
October 16, 1996


