1
                                                                 EXHIBIT 10.20.4


                                THIRD AMENDMENT
                                       TO
                             STOCKHOLDERS AGREEMENT

         This THIRD AMENDMENT TO STOCKHOLDERS AGREEMENT (this "Third
Amendment") amends that certain Stockholders Agreement, as amended, dated as of
October 16, 1996 (the "Stockholders Agreement"), between Capstar Broadcasting
Partners, Inc., a Delaware corporation (the "Company"), the securityholders
listed on the signature pages thereto, and Hicks, Muse Tate & Furst
Incorporated, a Texas corporation ("HMTF") and is entered into effective June
20, 1997, by and among the Company, HMTF, certain securityholders listed on the
signature pages hereto, and Capstar Broadcasting Corporation, a Delaware
corporation ("Capstar Broadcasting").  A copy of the Stockholders Agreement is
attached hereto as Exhibit A.

                                   RECITALS:

         WHEREAS, the stockholders of the Company have effected an exchange of
all of the outstanding shares of the Company for all of the outstanding shares
of Capstar Broadcasting;

         WHEREAS, as a result of such exchange, the Company is a wholly-owned
subsidiary of Capstar Broadcasting;

         WHEREAS, the parties to the Stockholders Agreement desire to amend the
Stockholders Agreement as provided herein pursuant to Section 10.7.2 of the
Stockholders Agreement;

         WHEREAS, among other things, the parties to the Stockholders Agreement
desire  to replace the Company with Capstar as a party to the Stockholders
Agreement for all purposes; and

         WHEREAS, any capitalized term used herein, and not otherwise defined
herein, shall have the meaning set forth in the Stockholders Agreement.


                                  AGREEMENTS:

         NOW, THEREFORE, in consideration of the foregoing and the agreements
herein contained, the parties hereto covenant and agree as follows:

         1.      From and after the date hereof, the Company shall not be a
party to the Stockholders Agreement.  All references in the Stockholders
Agreement to the Company shall hereby be deemed, from and after the date
hereof, to refer to Capstar Broadcasting for all purposes.

         2.      Capstar Broadcasting hereby assumes and agrees to perform and
discharge all of the Company's duties and obligations under the Stockholders
Agreement that are to be performed from and after the date hereof.

         3.      "Common Stock" Definition.  The definition of "Common Stock"
set forth in Section 1.1 of the Stockholders  Agreement is hereby amended and
restated to read in its entirety as follows:

         "Common Stock" means (a) shares of Class A Common Stock, $0.01 par
         value per share, of the Company, (b) shares of Class B Common Stock,
         $0.01 par value per
   2
         share, of the Company, (c) shares of Class C Common Stock, $0.01 par
         value per share, of the Company, and (d) any capital stock into which
         any such shares of common stock thereafter may be changed.

         4.      "Excluded Registration" Definition.  The definition of
"Excluded Registration" in Section 1.1 of the Stockholders Agreement is hereby
amended and restated to read in its entirety as follows:

         "Excluded Registration" means a registration under the Securities Act
         of (i) a registration to effect a Qualified IPO if such registration
         only includes equity securities to be issued by the Company and does
         not include any equity securities for the account of any other
         securityholder of the Company, (ii) securities registered on Form S-8
         or any similar successor form, (iii) securities registered to effect
         the acquisition of or combination with another Person and (iv)
         securities registered pursuant to any registration rights agreement to
         be entered into with the securityholders of Patterson Broadcasting,
         Inc., a Delaware corporation ("Patterson"), upon consummation of the
         Company's acquisition of Patterson.

         5.      Except as herein specifically amended or supplemented, the
Stockholders Agreement shall continue in full force and effect in accordance
with its terms.

         6.      This Third Amendment may be executed and delivered (including
by facsimile transmission) in one or more counterparts, all of which shall be
considered one and the same agreement and shall become effective when one or
more counterparts have been signed by each of the parties and delivered to the
other parties, it being understood that all parties need not sign the same
counterpart.

                  [Remainder of page intentionally left blank]




                                      2
   3
         IN WITNESS WHEREOF, the parties have caused this Third Amendment to be
duly executed, all as of the date first written above.

                                        CAPSTAR BROADCASTING PARTNERS, INC.



                                        By:      /S/ Paul D. Stone 
                                             -----------------------------------
                                        Name:    Paul D. Stone
                                             -----------------------------------
                                        Title:   Executive Vice President
                                              ----------------------------------

                                        HICKS, MUSE, TATE & FURST INCORPORATED



                                        By:      /S/ Eric C. Neuman
                                             -----------------------------------
                                        Name:    Eric C. Neuman 
                                             -----------------------------------
                                        Title:   Senior Vice President
                                             -----------------------------------


                                        CAPSTAR BROADCASTING PARTNERS, L.P.

                                        By:      HM3/Capstar Partners, L.P.,
                                                 its General Partner

                                        By:      HM3/Capstar, Inc.
                                                 its General Partner


                                                 By:     /S/ Eric C. Neuman 
                                                     --------------------------
                                                 Name:   Eric Neuman 
                                                      -------------------------
                                                 Title:  Senior Vice President
                                                       ------------------------


                                        /S/ R. Steven Hicks R. Steven Hicks
                                        ----------------------------------------


                                        /S/ Jason Mabry Jason Mabry
                                        ----------------------------------------


                                        /S/ Kristen Lea Hicks 
                                        ----------------------------------------
                                        Kristen Lea Hicks

   4
                                        /S/ Shelly Mabry Ellard 
                                        ----------------------------------------
                                        Shelly Mabry Ellard



                                        /S/ Larry Taylor 
                                        ----------------------------------------
                                        Larry Taylor as Custodian for Robert S.
                                        Hicks, Jr. under the Texas Uniform
                                        Gifts to Minors Act



                                        /S/ Larry Taylor 
                                        ----------------------------------------
                                        Larry Taylor as Custodian for Brandon 
                                        Vaughan Hicks under the Texas Uniform
                                        Gifts to Minors Act


                                        CAPSTAR BT PARTNERS, L.P.

                                        By:      HM3/GP Partners, L.P.,
                                                 its General Partner

                                        By:      Hicks, Muse GP Partners III,
                                                 L.P., its General Partner

                                        By:      Hicks, Muse Fund III
                                                 Incorporated, its General
                                                 Partner



                                                 By:     /S/ Eric C. Neuman 
                                                    ---------------------------
                                                 Name:   Eric C. Neuman 
                                                      -------------------------
                                                 Title:  Senior Vice President
                                                       ------------------------
   5
                                        CAPSTAR BOSTON PARTNERS, L.L.C.

                                        By:     HM3/GP Partners, L.P.,
                                                its Manager
                                               
                                        By:     Hicks, Muse GP Partners III, 
                                                L.P., its General Partner
                                               
                                        By:     Hicks, Muse Fund III
                                                Incorporated, its General
                                                Partner
                                               


                                                By:     /S/ Eric C. Neuman 
                                                   ----------------------------
                                                Name:   Eric C. Neuman 
                                                     --------------------------
                                                Title:  Senior Vice President
                                                      -------------------------

                                        CAPSTAR BROADCASTING CORPORATION



                                        By:     /S/ Paul D. Stone      
                                                ------------------------------
                                        Name:   Paul D. Stone        
                                                ------------------------------
                                        Title:  Executive Vice President
                                                ------------------------------

   6
                                   EXHIBIT A

                            (STOCKHOLDERS AGREEMENT)