
<PAGE>   1
                                                                   EXHIBIT 4.5.3

                    SECOND AMENDMENT TO AMENDED AND RESTATED
                             STOCKHOLDERS AGREEMENT


         This SECOND AMENDMENT TO AMENDED AND RESTATED STOCKHOLDERS AGREEMENT
(this "Agreement") is made and entered into as of July 13, 1999, by and among
AMFM INC. (formerly known as CHANCELLOR MEDIA CORPORATION), a Delaware
corporation (the "Company"), and each of the Holders (as defined in the
Stockholders Agreement (as hereinafter defined)) whose names are set forth on
the signature pages hereto.


         WHEREAS, the Company and the Holders are parties to that certain
Amended and Restated Stockholders Agreement, dated as of February 14, 1996, as
amended by that certain First Amendment to Amended and Restated Stockholders
Agreement, dated as September 5, 1997, a complete copy of which is attached
hereto as Annex I (as amended, the "Stockholders Agreement");

         WHEREAS, the Company is a party to that certain Amended and Restated
Agreement and Plan of Merger, dated as of August 26, 1998 and amended and
restated as of April 29, 1999, as amended on June 30, 1999, (the "Merger
Agreement"), among the Company, Capstar Broadcasting Corporation ("Capstar"), a
Delaware corporation, and CMC Merger Sub, Inc. ("Merger Sub"), a Delaware
corporation and wholly-owned subsidiary of the Company, pursuant to which Merger
Sub will be merged with and into Capstar, with Capstar surviving such merger as
a wholly-owned subsidiary of the Company; and

         WHEREAS, in connection with the closing of the transactions
contemplated by the Merger Agreement and pursuant to the terms thereof, the
Company and the Holders desire hereby to amend the Stockholders Agreement as
provided herein and to add such additional Holders (the "Additional Holders")
that agree to be bound by the terms of the Stockholders Agreement, as amended by
this Agreement.

         NOW, THEREFORE, in consideration of the mutual agreements and covenants
set forth herein, together with other good and valuable consideration, the
parties hereto agree as follows:

         SECTION 1. Amendments. The Stockholders Agreement is amended as
follows:

            (a). The definition of "Company" in the Stockholders Agreement shall
mean AMFM Inc. (formerly known as Chancellor Media Corporation), a Delaware
corporation.




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            (b). The definition of "Common Stock" set forth in Section 1 of the
Stockholders Agreement is hereby amended and restated in its entirety to read as
follows:

         "Common Stock" means the Common Stock, $0.01 par value, of the Company,
and any other class of series of capital stock issued by the Company which has
the unlimited right to participate in dividends and distributions upon
liquidation of the Company (a "Common Equity Security"), as well as any capital
stock or other securities received in exchange for, or upon conversion of, such
Common Stock or Common Equity Security, whether by merger, consolidation,
reorganization, reclassification or otherwise.

            (c). Section 3(a)(i) of the Stockholders Agreement is hereby amended
and restated in its entirety to read as follows:

         "(a) Request for Registration. (i) At any time after the date hereof, a
Holder or Holders of at least 40% of the total number of Registrable Shares held
by all Holders may request the Company, in writing (a "Demand Request"), to
effect the registration under the Securities Act of all or part of its or their
Registrable Shares (a "Demand Registration"); provided that the Registrable
Shares proposed to be sold by the Holder or Holders requesting a Demand
Registration (the "Requesting Holders," which term shall include parties deemed
"Requesting Holders" pursuant to Section 3(e) hereof) represent, in the
aggregate, Registrable Shares with a fair market value of at least $5.0 million.
For purposes of the immediately preceding sentence, fair market value in respect
of a Demand Request shall be determined as of the date on which the Demand
Request is made (or if such day is not a trading day, then as of the immediately
preceding trading day) and shall equal the product of (A) the aggregate number
of Registrable Shares proposed to be included in such Demand Registration,
multiplied by (B) (x) if the Common Stock is listed or admitted for trading on a
national securities exchange, the last reported sales price or, if no such
reported sale occurs on such day, the average of the closing bid and asked
prices regular way on such day, in each case as reported on the principal
consolidated transaction reporting system with respect to the shares of Common
Stock listed on the principal national securities exchange on which such Common
Stock is listed or admitted to trading, or (y) if the Common Stock is not listed
or admitted for trading on any national securities exchange, the last quoted
sales price, or, if not so quoted, the average of the high bid and low asked
prices in the over-the-counter market on such day as reported by The National
Association of Securities Dealers, Inc. Automated Quotation System or any
comparable system then in use or, if not so reported, as reported by any New
York Stock Exchange member firm reasonably selected by the Company for such
purpose."

            (d). Section 8(b) of the Stockholders Agreement is hereby amended
and restated in its entirety to read as follows:



                                       2
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         "(b) Amendments and Waivers. The provisions of this Agreement may be
amended or waived at any time by the written agreement of the Company and a
Holder or Holders of a majority of the Registrable Shares."

         SECTION 2. Additional Holders. Each Additional Holder hereby agrees to
be bound by the terms of the Stockholders Agreement and is deemed to be a
"Holder" for all purposes under the Stockholders Agreement.

         SECTION 3. Stockholders Agreement Otherwise Unchanged. Except as
expressly amended hereby, the Stockholders Agreement shall remain unchanged and
in full force and effect.

         SECTION 4. Counterparts. This Agreement may be executed in any number
of counterparts, each of which shall constitute one and the same instrument.

         SECTION 5. Successors and Assigns. The rights and obligations of the
parties hereunder shall be binding upon and inure to the benefit of the Company
and the Holders and each of their respective successors and assigns.

         SECTION 6. Governing Law. This Agreement shall be governed by, and
construed in accordance with, the laws of the State of New York, without giving
effect to conflict of laws principles thereof.

            [The remainder of this page is intentionally left blank.]


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         IN WITNESS WHEREOF, in accordance with the terms of the Stockholders
Agreement, the Company, a majority of the HM2 Holders (as defined in the
Stockholders Agreement), and a majority of the Holders (as defined in the
Stockholders Agreement) have executed this Agreement as of the day and year
first written above.

                                        AMFM INC.



                                        By: /s/ William S. Banowsky, Jr.
                                            -----------------------------------
                                        Name:  William S. Banowsky, Jr.
                                        Title: Executive Vice President

                                    HOLDERS:

                                        HM2/CHANCELLOR, L.P.

                                        By:    HM2/CHANCELLOR GP, L.P., its
                                               general partner

                                        By:    HM2/CHANCELLOR HOLDINGS, INC.,
                                               its general partner


                                               By: /s/ Thomas O. Hicks
                                                  -----------------------------
                                               Name:
                                               Title:

                                        HICKS, MUSE, TATE & FURST EQUITY
                                        FUND II, L.P.

                                        By:    HM2/GP PARTNERS, L.P., its
                                               general partner

                                        By:    HICKS, MUSE G.P. PARTNERS, L.P.,
                                               its general partner

                                        By:    HICKS, MUSE FUND II INCORPORATED,
                                               its general partner


                                               By: /s/ Thomas O. Hicks
                                                  -----------------------------
                                               Name:
                                               Title:


                     (SIGNATURE PAGE TO SECOND AMENDMENT TO
                  AMENDED AND RESTATED STOCKHOLDERS AGREEMENT)



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                                        HM2/HMW, L.P.

                                        By: HICKS, MUSE, TATE & FURST EQUITY
                                            FUND II, L.P., its general partner

                                        By: HM2/GP PARTNERS, L.P., its general
                                            partner

                                        By: HICKS, MUSE GP PARTNERS, L.P., its
                                            general partner

                                        By: HICKS, MUSE FUND II INCORPORATED,
                                            its general partner


                                            By: /s/ Thomas O. Hicks
                                                --------------------------------
                                                Name: Thomas O. Hicks
                                                Title:

                                        HM4/CHANCELLOR, L.P.

                                        By: HICKS, MUSE FUND IV LLC, its general
                                            partner


                                            By: /s/ Thomas O. Hicks
                                                -------------------------------
                                                Name: Thomas O. Hicks
                                                Title:

                                            /s/ Thomas O. Hicks
                                            ------------------------------------
                                            Thomas O. Hicks


                                            THOMAS O. HICKS, AS TRUSTEE OF THE
                                            WILLIAM CREE HICKS 1992 IRREVOCABLE
                                            TRUST


                                            By: /s/ Thomas O. Hicks
                                                --------------------------------
                                                Thomas O. Hicks,
                                                Trustee


                     (SIGNATURE PAGE TO SECOND AMENDMENT TO
                  AMENDED AND RESTATED STOCKHOLDERS AGREEMENT)




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                                            THOMAS O. HICKS, AS TRUSTEE OF THE
                                            CATHERINE FORGRAVE HICKS 1993
                                            IRREVOCABLE TRUST


                                            By: /s/ Thomas O. Hicks
                                                --------------------------------
                                                Thomas O. Hicks,
                                                Trustee

                                            THOMAS O. HICKS, AS TRUSTEE OF THE
                                            JOHN ALEXANDER HICKS 1984 TRUST


                                            By: /s/ Thomas O. Hicks
                                                --------------------------------
                                                Thomas O. Hicks,
                                                Trustee

                                            THOMAS O. HICKS, AS TRUSTEE OF THE
                                            MACK HARDIN HICKS 1984 TRUST


                                            By: /s/ Thomas O. Hicks
                                                -------------------------------
                                                Thomas O. Hicks,
                                                Trustee

                                            THOMAS O. HICKS, AS TRUSTEE OF THE
                                            ROBERT BRADLEY HICKS 1984 TRUST


                                            By: /s/ Thomas O. Hicks
                                                --------------------------------
                                                Thomas O. Hicks,
                                                Trustee

                                            THOMAS O. HICKS, AS TRUSTEE OF THE
                                            THOMAS O. HICKS, JR. 1984 TRUST


                                            By: /s/ Thomas O. Hicks
                                                --------------------------------
                                                Thomas O. Hicks,
                                                Trustee

                     (SIGNATURE PAGE TO SECOND AMENDMENT TO
                  AMENDED AND RESTATED STOCKHOLDERS AGREEMENT)


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                                            /s/ Steven Dinetz
                                            ------------------------------------
                                            Steven Dinetz


                                            /s/ Lawrence D. Stuart, Jr.
                                            ------------------------------------
                                            Lawrence D. Stuart, Jr.


                                            /s/ R. Scott Cohen
                                            ------------------------------------
                                            R. Scott Cohen


                                            /s/ Jerred G. Blanchard, Jr.
                                            ------------------------------------
                                            Jerred G. Blanchard, Jr.


                                            /s/ George C. Toulas
                                            ------------------------------------
                                            George C. Toulas


                                            /s/ Rick Eytcheson
                                            ------------------------------------
                                            Rick Eytcheson


                                            /s/ Matthew Leibowitz
                                            ------------------------------------
                                            Matthew Leibowitz


                                            /s/ Eric W. Neumann
                                            ------------------------------------
                                            Eric W. Neumann


                                            /s/ Matrice Ellis-Kirk
                                            ------------------------------------
                                            Matrice Ellis-Kirk






                     (SIGNATURE PAGE TO SECOND AMENDMENT TO
                  AMENDED AND RESTATED STOCKHOLDERS AGREEMENT)



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                           ADDITIONAL HOLDERS:

         The undersigned hereby agree to hold the Common Stock and Common Stock
Equivalents of the Company pursuant to the terms of the Stockholders Agreement
and agree to be bound by the terms thereby:


                                          CAPSTAR BROADCASTING
                                          PARTNERS, L.P., a Delaware limited
                                          partnership

                                          By: HM3/CAPSTAR PARTNERS, L.P., a
                                              Texas limited partnership, its
                                              general partner

                                          By: HM3/CAPSTAR, INC., a Texas
                                              corporation, its general partner



                                              By: /s/ David W. Knickel
                                                  ------------------------------
                                                  Name:  David W. Knickel
                                                  Title:


                                          BT CAPITAL PARTNERS, INC.



                                          By: /s/ Joseph T. Wood
                                              ----------------------------------
                                          Name:  Joseph T. Wood
                                          Title:



                                          /s/ R. Steven Hicks
                                          --------------------------------------
                                          R. Steven Hicks


                     (SIGNATURE PAGE TO SECOND AMENDMENT TO
                  AMENDED AND RESTATED STOCKHOLDERS AGREEMENT)



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                                          HICKS FAMILY CHARITABLE FOUNDATION


                                          By:    /s/ R. Steven Hicks
                                             -----------------------------------
                                          Name:  R. Steven Hicks
                                          Title:

                                          R. STEVEN HICKS AS CUSTODIAN FOR
                                          BRINSON ELIZABETH ELLARD UNDER THE
                                          TEXAS UNIFORM TRANSFERS TO MINORS ACT


                                          By:    /s/ R. Steven Hicks
                                             -----------------------------------
                                          Name:  R. Steven Hicks
                                          Title: Custodian


                     (SIGNATURE PAGE TO SECOND AMENDMENT TO
                  AMENDED AND RESTATED STOCKHOLDERS AGREEMENT)
