<PAGE>   1
                                                                     EXHIBIT 3.2




                              AMENDED AND RESTATED

                                     BYLAWS

                                       OF

                      CAPSTAR BROADCASTING PARTNERS, INC.







<PAGE>   2
                               TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                                                                     Page
                                                                                                                     ----
<S>                                                                                                                     <C>
ARTICLE I:  OFFICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
         Section 1.       Registered Office . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
         Section 2.       Other Offices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

ARTICLE II:  STOCKHOLDERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
         Section 1.       Place of Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
         Section 2.       Quorum; Adjournment of Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
         Section 3.       Annual Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
         Section 4.       Special Meetings  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
         Section 5.       Record Date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
         Section 6.       Notice of Meetings  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
         Section 7.       Stock List  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
         Section 8.       Proxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
         Section 9.       Voting; Elections; Inspectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
         Section 10.      Conduct of Meetings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
         Section 11.      Treasury Stock  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
         Section 12.      Action Without Meeting  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

ARTICLE III:  BOARD OF DIRECTORS  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
         Section 1.       Power; Number; Term of Office . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
         Section 2.       Quorum  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
         Section 3.       Place of Meetings; Order of Business  . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
         Section 4.       First Meeting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
         Section 5.       Regular Meetings  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
         Section 6.       Special Meetings  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
         Section 7.       Removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
         Section 8.       Vacancies; Increases in the Number of Directors . . . . . . . . . . . . . . . . . . . . . . . 6
         Section 9.       Compensation  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
         Section 10.      Action Without a Meeting; Telephone Conference Meeting  . . . . . . . . . . . . . . . . . . . 7
         Section 11.      Approval or Ratification of Acts or Contracts by Stockholders . . . . . . . . . . . . . . . . 7

ARTICLE IV:  COMMITTEES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
         Section 1.       Designation; Powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
         Section 2.       Procedure; Meetings; Quorum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
         Section 3.       Substitution of Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

ARTICLE V:  OFFICERS  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
         Section 1.       Number, Titles and Term of Office . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
         Section 2.       Salaries  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
         Section 3.       Removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
</TABLE>


                                       i
<PAGE>   3
<TABLE>
<S>                                                                                                                    <C>
         Section 4.       Vacancies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
         Section 5.       Powers and Duties of the Chief Executive Officer                                              9
         Section 6.       Powers and Duties of the Chairman of the Board  . . . . . . . . . . . . . . . . . . . . . . . 9
         Section 7.       Powers and Duties of the President  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
         Section 8.       Vice Presidents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
         Section 9.       Treasurer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  10
         Section 10.      Assistant Treasurers  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  10
         Section 11.      Secretary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  10
         Section 12.      Assistant Secretaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  10
         Section 13.      Action with Respect to Securities of Other Corporations . . . . . . . . . . . . . . . . . .  10

ARTICLE VI:  INDEMNIFICATION OF DIRECTORS, OFFICERS, EMPLOYEES
AND AGENTS  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
         Section 1.       Right to Indemnification  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
         Section 2.       Indemnification of Employees and Agents . . . . . . . . . . . . . . . . . . . . . . . . . .  11
         Section 3.       Right of Claimant to Bring Suit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  11
         Section 4.       Nonexclusivity of Rights  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12
         Section 5.       Insurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12
         Section 6.       Savings Clause  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12
         Section 7.       Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12

ARTICLE VII:  CAPITAL STOCK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  13
         Section 1.       Certificates of Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  13
         Section 2.       Transfer of Shares  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  13
         Section 3.       Ownership of Shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  13
         Section 4.       Regulations Regarding Certificates  . . . . . . . . . . . . . . . . . . . . . . . . . . . .  13
         Section 5.       Lost or Destroyed Certificates  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14

ARTICLE VIII:  MISCELLANEOUS PROVISIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14
         Section 1.       Fiscal Year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14
         Section 2.       Corporate Seal  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14
         Section 3.       Notice and Waiver of Notice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14
         Section 4.       Resignations  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14
         Section 5.       Facsimile Signatures  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  15
         Section 6.       Reliance upon Books, Reports and Records  . . . . . . . . . . . . . . . . . . . . . . . . .  15

ARTICLE IX:  AMENDMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  15
</TABLE>





                                       ii
<PAGE>   4
                              AMENDED AND RESTATED

                                     BYLAWS

                                       OF

                      CAPSTAR BROADCASTING PARTNERS, INC.



                                   ARTICLE I

                                    OFFICES

         Section 1.       Registered Office.  The registered office of the
Corporation required by the General Corporation Law of the State of Delaware to
be maintained in the State of Delaware, shall be the registered office named in
the original Certificate of Incorporation of the Corporation (as the same may
be amended and restated from time to time, the "Certificate of Incorporation"),
or such other office as may be designated from time to time by the Board of
Directors in the manner provided by law.  Should the Corporation maintain a
principal office within the State of Delaware such registered office need not
be identical to such principal office of the Corporation.

         Section 2.       Other Offices.  The Corporation may also have offices
at such other places both within and without the State of Delaware as the Board
of Directors may from time to time determine or the business of the Corporation
may require.


                                   ARTICLE II

                                  STOCKHOLDERS

         Section 1.       Place of Meetings.  All meetings of the stockholders
shall be held at the principal office of the Corporation, or at such other
place within or without the State of Delaware as shall be specified or fixed in
the notices or waivers of notice thereof.

         Section 2.       Quorum; Adjournment of Meetings.  Unless otherwise
required by law or provided in the Certificate of Incorporation or these
bylaws, the holders of a majority of the stock issued and outstanding and
entitled to vote thereat, present in person or represented by proxy, shall
constitute a quorum at any meeting of stockholders for the transaction of
business and the act of a majority of such stock so represented at any meeting
of stockholders at which a quorum is present shall constitute the act of the
meeting of stockholders.  The stockholders present at a duly organized meeting
may continue to transact business until adjournment, notwithstanding the
withdrawal of enough stockholders to leave less than a quorum.





                                       1
<PAGE>   5
         Notwithstanding the other provisions of the Certificate of
Incorporation or these bylaws, the chairman of the meeting or the holders of a
majority of the issued and outstanding stock, present in person or represented
by proxy, at any meeting of stockholders, whether or not a quorum is present,
shall have the power to adjourn such meeting from time to time, without any
notice other than announcement at the meeting of the time and place of the
holding of the adjourned meeting; provided, however, if the adjournment is for
more than thirty (30) days, or if after the adjournment a new record date is
fixed for the adjourned meeting, a notice of the adjourned meeting shall be
given to each stockholder of record entitled to vote at such meeting.  At any
such adjourned meeting at which a quorum shall be present or represented any
business may be transacted which might have been transacted at the meeting as
originally called.

         Section 3.       Annual Meetings.  An annual meeting of the
stockholders, for the election of directors to succeed those whose terms expire
and for the transaction of such other business as may properly come before the
meeting, shall be held at such place, within or without the State of Delaware,
on such date, and at such time as the Board of Directors shall fix and set
forth in the notice of the meeting, which date shall be within thirteen (13)
months subsequent to the later of the date of incorporation or the last annual
meeting of stockholders.

         Section 4.       Special Meetings.  Unless otherwise provided in the
Certificate of Incorporation, special meetings of the stockholders for any
purpose or purposes may be called at any time by the Chairman of the Board (if
any), by the President or by a majority of the Board of Directors, or by a
majority of the executive committee (if any), and shall be called by the
Chairman of the Board (if any), by the President or the Secretary upon the
written request therefor, stating the purpose or purposes of the meeting,
delivered to such officer, signed by the holder(s) of at least ten percent
(l0%) of the issued and outstanding stock entitled to vote at such meeting.

         Section 5.       Record Date.  For the purpose of determining
stockholders entitled to notice of or to vote at any meeting of stockholders,
or any adjournment thereof, or entitled to express consent to corporate action
in writing without a meeting, or entitled to receive payment of any dividend or
other distribution or allotment of any rights, or entitled to exercise any
rights in respect of any change, conversion or exchange of stock or for the
purpose of any other lawful action, the Board of Directors of the Corporation
may fix, in advance, a date as the record date for any such determination of
stockholders, which date shall not be more than sixty (60) days nor less than
ten (l0) days before the date of such meeting, nor more than sixty (60) days
prior to any other action.

         If the Board of Directors does not fix a record date for any meeting
of the stockholders, the record date for determining stockholders entitled to
notice of or to vote at such meeting shall be at the close of business on the
day next preceding the day on which notice is given, or, if in accordance with
Article VIII, Section 3 of these bylaws notice is waived, at the close of
business on the day next preceding the day on which the meeting is held.  If,
in accordance with Section 12 of this Article II, corporate action without a
meeting of stockholders is to be taken, the record date for determining
stockholders entitled to express consent to such corporate action in writing,
when no prior action by the Board of Directors is necessary, shall be the day
on which the first written consent is expressed.  The record date for
determining stockholders for any other purpose shall be at the close of
business on the day on which the Board of Directors adopts the resolution
relating thereto.





                                       2
<PAGE>   6
         A determination of stockholders of record entitled to notice of or to
vote at a meeting of stockholders shall apply to any adjournment of the
meeting; provided, however, that the Board of Directors may fix a new record
date for the adjourned meeting.

         Section 6.       Notice of Meetings.  Written notice of the place,
date and hour of all meetings, and, in case of a special meeting, the purpose
or purposes for which the meeting is called, shall be given by or at the
direction of the Chairman of the Board (if any) or the President, the Secretary
or the other person(s) calling the meeting to each stockholder entitled to vote
thereat not less than ten (10) nor more than sixty (60) days before the date of
the meeting.  Such notice may be delivered either personally or by mail.  If
mailed, notice is given when deposited in the United States mail, postage
prepaid, directed to the stockholder at his address as it appears on the
records of the Corporation.

         Section 7.       Stock List.  A complete list of stockholders entitled
to vote at any meeting of stockholders, arranged in alphabetical order for each
class of stock and showing the address of each such stockholder and the number
of shares registered in the name of such stockholder, shall be open to the
examination of any stockholder, for any purpose germane to the meeting, during
ordinary business hours, for a period of at least ten (10) days prior to the
meeting, either at a place within the city where the meeting is to be held,
which place shall be specified in the notice of the meeting, or if not so
specified, at the place where the meeting is to be held.  The stock list shall
also be produced and kept at the time and place of the meeting during the whole
time thereof, and may be inspected by any stockholder who is present.

         Section 8.       Proxies.  Each stockholder entitled to vote at a
meeting of stockholders or to express consent or dissent to a corporate action
in writing without a meeting may authorize another person or persons to act for
him by proxy.  Proxies for use at any meeting of stockholders shall be filed
with the Secretary, or such other officer as the Board of Directors may from
time to time determine by resolution, before or at the time of the meeting.
All proxies shall be received and taken charge of and all ballots shall be
received and canvassed by the secretary of the meeting who shall decide all
questions touching upon the qualification of voters, the validity of the
proxies, and the acceptance or rejection of votes, unless an inspector or
inspectors shall have been appointed by the chairman of the meeting, in which
event such inspector or inspectors shall decide all such questions.

         No proxy shall be valid after three (3) years from its date, unless
the proxy provides for a longer period.  Each proxy shall be revocable unless
expressly provided therein to be irrevocable and coupled with an interest
sufficient in law to support an irrevocable power.

         Should a proxy designate two or more persons to act as proxies, unless
such instrument shall provide the contrary, a majority of such persons present
at any meeting at which their powers thereunder are to be exercised shall have
and may exercise all the powers of voting or giving consents thereby conferred,
or if only one be present, then such powers may be exercised by that one; or,
if an even number attend and a majority do not agree on any particular issue,
each proxy so attending shall be entitled to exercise such powers in respect of
the same portion of the shares as he is of the proxies representing such
shares.





                                       3
<PAGE>   7
         Section 9.       Voting; Elections; Inspectors.  Unless otherwise
required by law or provided in the Certificate of Incorporation, each
stockholder shall have one vote for each share of stock entitled to vote which
is registered in his name on the record date for the meeting.  Shares
registered in the name of another corporation, domestic or foreign, may be
voted by such officer, agent or proxy as the bylaw (or comparable instrument)
of such corporation may prescribe, or in the absence of such provision, as the
Board of Directors (or comparable body) of such corporation may determine.
Shares registered in the name of a deceased person may be voted by his executor
or administrator, either in person or by proxy.

         All voting, except as required by the Certificate of Incorporation or
where otherwise required by law, may be by a voice vote; provided, however,
that upon demand therefor by stockholders holding a majority of the issued and
outstanding stock present in person or by proxy at any meeting a stock vote
shall be taken.  Every stock vote shall be taken by written ballots, each of
which shall state the name of the stockholder or proxy voting and such other
information as may be required under the procedure established for the meeting.
All elections of directors shall be by ballot, unless otherwise provided in the
Certificate of Incorporation.

         At any meeting at which a vote is taken by ballots, the chairman of
the meeting may appoint one or more inspectors, each of whom shall subscribe an
oath or affirmation to execute faithfully the duties of inspector at such
meeting with strict impartiality and according to the best of his ability.
Such inspector shall receive the ballots, count the votes and make and sign a
certificate of the result thereof.  The chairman of the meeting may appoint any
person to serve as inspector, except no candidate for the office of director
shall be appointed as an inspector.

         Unless otherwise provided in the Certificate of Incorporation,
cumulative voting for the election of directors shall be prohibited.

         Section 10.      Conduct of Meetings.  The meetings of the
stockholders shall be presided over by the Chairman of the Board (if any), or
if he is not present, by the President, or if neither the Chairman of the Board
(if any), nor President is present, by a chairman elected at the meeting.  The
Secretary of the Corporation, if present, shall act as secretary of such
meetings, or if he is not present, an Assistant Secretary shall so act; if
neither the Secretary nor an Assistant Secretary is present, then a secretary
shall be appointed by the chairman of the meeting.  The chairman of any meeting
of stockholders shall determine the order of business and the procedure at the
meeting, including such regulation of the manner of voting and the conduct of
discussion as seem to him in order.  Unless the chairman of the meeting of
stockholders shall otherwise determine, the order of business shall be as
follows:

         (a)     Calling of meeting to order.
         (b)     Election of a chairman and the appointment of a secretary if
                 necessary.
         (c)     Presentation of proof of the due calling of the meeting.
         (d)     Presentation and examination of proxies and determination of a
                 quorum.
         (e)     Reading and settlement of the minutes of the previous meeting.
         (f)     Reports of officers and committees.
         (g)     The election of directors if an annual meeting, or a meeting 
                 called for that purpose.





                                       4
<PAGE>   8
         (h)     Unfinished business.
         (i)     New business.
         (j)     Adjournment.

         Section 11.      Treasury Stock.  The Corporation shall not vote,
directly or indirectly, shares of its own stock owned by it and such shares
shall not be counted for quorum purposes.

         Section 12.      Action Without Meeting.  Unless otherwise provided in
the Certificate of Incorporation, any action permitted or required by law, the
Certificate of Incorporation or these bylaws to be taken at a meeting of
stockholders, may be taken without a meeting, without prior notice and without
a vote, if a consent in writing, setting forth the action so taken, shall be
signed by the holders of outstanding stock having not less than the minimum
number of votes that would be necessary to authorize or take such action at a
meeting at which all shares entitled to vote thereon were present and voted.
Prompt notice of the taking of the corporate action without a meeting by less
than a unanimous written consent shall be given by the Secretary to those
stockholders who have not consented in writing.


                                  ARTICLE III

                               BOARD OF DIRECTORS

         Section 1.       Power; Number; Term of Office.  The business and
affairs of the Corporation shall be managed by or under the direction of the
Board of Directors, and subject to the restrictions imposed by law or the
Certificate of Incorporation, they may exercise all the powers of the
Corporation.

         Unless otherwise provided in the Certificate of Incorporation, the
number of directors that shall constitute the entire Board of Directors shall
be determined from time to time by resolution of the Board of Directors
(provided that no decrease in the number of directors that would have the
effect of shortening the term of an incumbent director may be made by the Board
of Directors).  If the Board of Directors makes no such determination, the
number of directors shall be the number set forth in the Certificate of
Incorporation as the number of directors constituting the initial Board of
Directors.  Each director shall hold office for the term for which he is
elected and thereafter until his successor shall have been elected and
qualified, or until his earlier death, resignation or removal.

         Unless otherwise provided in the Certificate of Incorporation,
directors need not be stockholders nor residents of the State of Delaware.

         Section 2.       Quorum.  Unless otherwise provided in the Certificate
of Incorporation, a majority of the total number of directors shall constitute
a quorum for the transaction of business of the Board of Directors and the vote
of a majority of the directors present at a meeting at which a quorum is
present shall be the act of the Board of Directors.





                                       5
<PAGE>   9
         Section 3.       Place of Meetings; Order of Business.  The directors
may hold their meetings and may have an office and keep the books of the
Corporation, except as otherwise provided by law, in such place or places,
within or without the State of Delaware, as the Board of Directors may from
time to time determine by resolution.  At all meetings of the Board of
Directors business shall be transacted in such order as shall from time to time
be determined by the Chairman of the Board (if any), or in his absence by the
President, or by resolution of the Board of Directors.

         Section 4.       First Meeting.  Each newly elected Board of Directors
may hold its first meeting for the purpose of organization and the transaction
of business, if a quorum is present, immediately after and at the same place as
the annual meeting of the stockholders.  Notice of such meeting shall not be
required.  At the first meeting of the Board of Directors in each year at which
a quorum shall be present, held next after the annual meeting of stockholders,
the Board of Directors shall proceed to the election of the officers of the
Corporation.

         Section 5.       Regular Meetings.  Regular meetings of the Board of
Directors shall be held at such times and places as shall be designated from
time to time by resolution of the Board of Directors.  Notice of such regular
meetings shall not be required.

         Section 6.       Special Meetings.  Special meetings of the Board of
Directors may be called by the Chairman of the Board (if any), the President
or, on the written request of any two directors, by the Secretary, in each case
on at least twenty-four (24) hours personal, written, telegraphic, cable or
wireless notice to each director.  Such  notice, or any waiver thereof pursuant
to Article VIII, Section 3 hereof, need not state the purpose or purposes of
such meeting, except as may otherwise be required by law or provided for in the
Certificate of Incorporation or these bylaws.


         Section 7.       Removal.  Any director or the entire Board of
Directors may be removed, with or without cause, by the holders of a majority
of the shares then entitled to vote at an election of directors; provided that,
unless the Certificate of Incorporation otherwise provides, if the Board of
Directors is classified, then the stockholders may effect such removal only for
cause; and provided further that, if the Certificate of Incorporation expressly
grants to stockholders the right to cumulate votes for the election of
directors and if less than the entire board is to be removed, no director may
be removed without cause if the votes cast against his removal would be
sufficient to elect him if then cumulatively voted at an election of the entire
Board of Directors, or, if there be classes of directors, at an election of the
class of directors of which such director is a part.

         Section 8.       Vacancies; Increases in the Number of Directors.
Unless otherwise provided in the Certificate of Incorporation, vacancies and
newly created directorships resulting from any increase in the authorized
number of directors may be filled by a majority of the directors then in
office, although less than a quorum, or a sole remaining director; and any
director so chosen shall hold office until the next annual election and until
his successor shall be duly elected and shall qualify, unless sooner displaced.

         If the directors of the Corporation are divided into classes, any
directors elected to fill vacancies or newly created directorships shall hold
office until the next election of the class for which such directors shall have
been chosen, and until their successors shall be duly elected and shall
qualify.





                                       6
<PAGE>   10
         Section 9.       Compensation.  Unless otherwise restricted by the
Certificate of Incorporation, the Board of Directors shall have the authority
to fix the compensation of directors.

         Section 10.      Action Without a Meeting; Telephone Conference
Meeting.  Unless otherwise restricted by the Certificate of Incorporation, any
action required or permitted to be taken at any meeting of the Board of
Directors, or any committee designated by the Board of Directors, may be taken
without a meeting if all members of the Board of Directors or committee, as the
case may be consent thereto in writing, and the writing or writings are filed
with the minutes of proceedings of the Board of Directors or committee.  Such
consent shall have the same force and effect as a unanimous vote at a meeting,
and may be stated as such in any document or instrument filed with the
Secretary of State of Delaware.

         Unless otherwise restricted by the Certificate of Incorporation,
subject to the requirement for notice of meetings, members of the Board of
Directors, or members of any committee designated by the Board of Directors,
may participate in a meeting of such Board of Directors or committee, as the
case may be, by means of a conference telephone or similar communications
equipment by means of which all persons participating in the meeting can hear
each other, and participation in such a meeting shall constitute presence in
person at such meeting, except where a person participates in the meeting for
the express purpose of objecting to the transaction of any business on the
ground that the meeting is not lawfully called or convened.

         Section 11.      Approval or Ratification of Acts or Contracts by
Stockholders.  The Board of Directors in its discretion may submit any act or
contract for approval or ratification at any annual meeting of the
stockholders, or at any special meeting of the stockholders called for the
purpose of considering any such act or contract, and any act or contract that
shall be approved or be ratified by the vote of the stockholders holding a
majority of the issued and outstanding shares of stock of the Corporation
entitled to vote and present in person or by proxy at such meeting (provided
that a quorum is present), shall be as valid and as binding upon the
Corporation and upon all the stockholders as if it has been approved or
ratified by every stockholder of the Corporation.  In addition, any such act or
contract may be approved or ratified by the written consent of stockholders
holding a majority of the issued and outstanding shares of capital stock of the
Corporation entitled to vote and such consent shall be as valid and as binding
upon the Corporation and upon all the stockholders as if it had been approved
or ratified by every stockholder of the Corporation.


                                   ARTICLE IV

                                   COMMITTEES

         Section 1.       Designation; Powers.  The Board of Directors may, by
resolution passed by a majority of the whole board, designate one or more
committees, including, if they shall so determine, an executive committee, each
such committee to consist of one or more of the directors of the Corporation.
Any such designated committee shall have and may exercise such of the powers
and authority of the Board of Directors in the management of the business and
affairs of the Corporation as may be provided in such resolution, except that
no such committee shall have the power or authority





                                       7
<PAGE>   11
of the Board of Directors in reference to amending the Certificate of
Incorporation, adopting an agreement of merger or consolidation, recommending
to the stockholders the sale, lease or exchange of all or substantially all of
the Corporation's property and assets, recommending to the stockholders a
dissolution of the Corporation or a revocation of a dissolution of the
Corporation, or amending, altering or repealing the bylaws or adopting new
bylaws for the Corporation and, unless such resolution or the Certificate of
Incorporation expressly so provides, no such committee shall have the power or
authority to declare a dividend or to authorize the issuance of stock.  Any
such designated committee may authorize the seal of the Corporation to be
affixed to all papers which may require it.  In addition to the above such
committee or committees shall have such other powers and limitations of
authority as may be determined from time to time by resolution adopted by the
Board of Directors.

         Section 2.       Procedure; Meetings; Quorum.  Any committee
designated pursuant to Section 1 of this Article shall choose its own chairman,
shall keep regular minutes of its proceedings and report the same to the Board
of Directors when requested, shall fix its own rules or procedures, and shall
meet at such times and at such place or places as may be provided by such
rules, or by resolution of such committee or resolution of the Board of
Directors.  At every meeting of any such committee, the presence of a majority
of all the members thereof shall constitute a quorum and the affirmative vote
of a majority of the members present shall be necessary for the adoption by it
of any resolution.

         Section 3.       Substitution of Members.  The Board of Directors may
designate one or more directors as alternate members of any committee, who may
replace any absent or disqualified member at any meeting of such committee.  In
the absence or disqualification of a member of a committee, the member or
members present at any meeting and not disqualified from voting, whether or not
constituting a quorum, may unanimously appoint another member of the Board of
Directors to act at the meeting in the place of the absent or disqualified
member.


                                   ARTICLE V

                                    OFFICERS

         Section 1.       Number, Titles and Term of Office.  The officers of
the Corporation shall be a President, one or more Vice Presidents (any one or
more of whom may be designated Executive Vice President, Senior Vice President
or such other descriptive title, if any, as the Board of Directors shall
determine), a Treasurer, a Secretary and, if the Board of Directors so elects,
a Chairman of the Board and such other officers as the Board of Directors may
from time to time elect or appoint.  Each officer shall hold office until his
successor shall be duly elected and shall qualify or until his death or until
he shall resign or shall have been removed in the manner hereinafter provided.
Any number of offices may be held by the same person, unless the Certificate of
Incorporation provides otherwise.  Except for the Chairman of the Board, if
any, no officer need be a director.

         Section 2.       Salaries.  The salaries or other compensation of the
officers and agents of the Corporation shall be fixed from time to time by the
Board of Directors.





                                       8
<PAGE>   12
         Section 3.       Removal.  Any officer or agent elected or appointed
by the Board of Directors may be removed, either with or without cause, by the
vote of a majority of the whole Board of Directors at a special meeting called
for the purpose, or at any regular meeting of the Board of Directors, provided
the notice for such meeting shall specify that the matter of any such proposed
removal will be considered at the meeting but such removal shall be without
prejudice to the contract rights, if any, of the person so removed.  Election
or appointment of an officer or agent shall not of itself create contract
rights.

         Section 4.       Vacancies.  Any vacancy occurring in any office of
the Corporation may be filled by the Board of Directors.

         Section 5.       Powers and Duties of the Chief Executive Officer.
The President shall be the chief executive officer of the Corporation unless
the Board of Directors elects or appoints a chief executive officer or
designates the Chairman of the Board as chief executive officer.  Subject to
the control of the Board of Directors and the executive committee (if any), the
chief executive officer shall have general executive charge, management and
control of the properties, business and operations of the Corporation with all
such powers as may be reasonably incident to such responsibilities; he may
agree upon and execute all leases, contracts, evidences of indebtedness and
other obligations in the name of the Corporation and may sign all certificates
for shares of capital stock of the Corporation; unless the Board of Directors
otherwise determines, the chief executive officer shall, in the absence of the
Chairman of the Board or if there be no Chairman of the Board, preside at all
meetings of the stockholders and (should he be a director) of the Board of
Directors; and shall have such other powers and duties as designated in
accordance with these bylaws and as from time to time may be assigned to him by
the Board of Directors.

         Section 6.       Powers and Duties of the Chairman of the Board.  If
elected, the Chairman of the Board shall preside at all meetings of the
stockholders and of the Board of Directors; and he shall have such other powers
and duties as designated in these bylaws and as from time to time may be
assigned to him by the Board of Directors.

         Section 7.       Powers and Duties of the President.  Unless the Board
of Directors otherwise determines, the President shall have the authority to
agree upon and execute all leases, contracts, evidences of indebtedness and
other obligations in the name of the Corporation; and, unless the Board of
Directors otherwise determines, he shall, in the absence of the chief executive
officer and Chairman of the Board or if there be no chief executive officer or
Chairman of the Board, preside at all meetings of the stockholders and (should
he be a director) of the Board of Directors; and he shall have such other
powers and duties as designated in accordance with these bylaws and as from
time to time may be assigned to him by the Board of Directors.

         Section 8.       Vice Presidents.  In the absence of the President, or
in the event of his inability or refusal to act, a Vice President designated by
the Board of Directors shall perform the duties of the President, and when so
acting shall have all the powers of and be subject to all the restrictions upon
the President.  In the absence of a designation by the Board of Directors of a
Vice President to perform the duties of the President, or in the event of his
absence or inability or refusal to act, the Vice President who is present and
who is senior in terms of time as a Vice President of the Corporation shall





                                       9
<PAGE>   13
so act.  The Vice Presidents shall perform such other duties and have such
other powers as the Board of Directors may from time to time prescribe.

         Section 9.       Treasurer.  The Treasurer shall have responsibility
for the custody and control of all the funds and securities of the Corporation,
and he shall have such other powers and duties as designated in these bylaws
and as from time to time may be assigned to him by the Board of Directors.  He
shall perform all acts incident to the position of Treasurer, subject to the
control of the chief executive officer and the Board of Directors; and he
shall, if required by the Board of Directors, give such bond for the faithful
discharge of his duties in such form as the Board of Directors may require.

         Section 10.      Assistant Treasurers.  Each Assistant Treasurer shall
have the usual powers and duties pertaining to his office, together with such
other powers and duties as designated in these bylaws and as from time to time
may be assigned to him by the chief executive officer or the Board of
Directors.  The Assistant Treasurers shall exercise the powers of the Treasurer
during that officer's absence or inability or refusal to act.

         Section 11.      Secretary.  The Secretary shall keep the minutes of
all meetings of the Board of Directors, committees of directors and the
stockholders, in books provided for that purpose; he shall attend to the giving
and serving of all notices; he may in the name of the Corporation affix the
seal of the Corporation to all contracts of the Corporation and attest the
affixation of the seal of the Corporation thereto; he may sign with the other
appointed officers all certificates for shares of capital stock of the
Corporation; he shall have charge of the certificate books, transfer books and
stock ledgers, and such other books and papers as the Board of Directors may
direct, all of which shall at all reasonable times be open to inspection of any
director upon application at the office of the Corporation during business
hours; he shall have such other powers and duties as designated in these bylaws
and as from time to time may be assigned to him by the Board of Directors; and
he shall in general perform all acts incident to the office of Secretary,
subject to the control of the chief executive officer and the Board of
Directors.

         Section 12.      Assistant Secretaries.  Each Assistant Secretary
shall have the usual powers and duties pertaining to his office, together with
such other powers and duties as designated in these bylaws and as from time to
time may be assigned to him by the chief executive officer or the Board of
Directors.  The Assistant Secretaries shall exercise the powers of the
Secretary during that officer's absence or inability or refusal to act.

         Section 13.      Action with Respect to Securities of Other
Corporations.  Unless otherwise directed by the Board of Directors, the chief
executive officer shall have power to vote and otherwise act on behalf of the
Corporation, in person or by proxy, at any meeting of security holders of or
with respect to any action of security holders of any other corporation in
which this Corporation may hold securities and otherwise to exercise any and
all rights and powers which this Corporation may possess by reason of its
ownership of securities in such other corporation.





                                       10
<PAGE>   14
                                   ARTICLE VI

                         INDEMNIFICATION OF DIRECTORS,
                         OFFICERS, EMPLOYEES AND AGENTS

         Section 1.       Right to Indemnification.  Each person who was or is
made a party or is threatened to be made a party to or is involved in any
action, suit or proceeding, whether civil, criminal, administrative or
investigative (hereinafter a "proceeding"), by reason of the fact that he or
she or a person of whom he or she is the legal representative, is or was or has
agreed to become a director or officer of the Corporation or is or was serving
or has agreed to serve at the request of the Corporation as a director,
officer, employee or agent of another corporation or of a partnership, joint
venture, trust or other enterprise, including service with respect to employee
benefit plans, whether the basis of such proceeding is alleged action in an
official capacity as a director or officer or in any other capacity while
serving or having agreed to serve as a director or officer, shall be
indemnified and held harmless by the Corporation to the fullest extent
authorized by the Delaware General Corporation Law, as the same exists or may
hereafter be amended, (but, in the case of any such amendment, only to the
extent that such amendment permits the Corporation to provide broader
indemnification rights than said law permitted the Corporation to provide prior
to such amendment) against all expense, liability and loss (including without
limitation, attorneys' fees, judgments, fines, ERISA excise taxes or penalties
and amounts paid or to be paid in settlement) reasonably incurred or suffered
by such person in connection therewith and such indemnification shall continue
as to a person who has ceased to serve in the capacity which initially entitled
such person to indemnity hereunder and shall inure to the benefit of his or her
heirs, executors and administrators; provided, however, that the Corporation
shall indemnify any such person seeking indemnification in connection with a
proceeding (or part thereof), other than a proceeding (or part thereof) brought
under Section 3 of this Article VI, initiated by such person or his or her
heirs, executors and administrators only if such proceeding (or part thereof)
was authorized by the board of directors of the Corporation.  The right to
indemnification conferred in this Article VI shall be a contract right and
shall include the right to be paid by the Corporation the expenses incurred in
defending any such proceeding in advance of its final disposition; provided,
however, that, if the Delaware General Corporation Law requires, the payment of
such expenses incurred by a current, former or proposed director or officer in
his or her capacity as a director or officer or proposed director or officer
(and not in any other capacity in which service was or is or has been agreed to
be rendered by such person while a director or officer, including, without
limitation, service to an employee benefit plan) in advance of the final
disposition of a proceeding, shall be made only upon delivery to the
Corporation of an undertaking, by or on behalf of such indemnified person, to
repay all amounts so advanced if it shall ultimately be determined that such
indemnified person is not entitled to be indemnified under this Section or
otherwise.

         Section 2.       Indemnification of Employees and Agents.  The
Corporation may, by action of its Board of Directors, provide indemnification
to employees and agents of the Corporation, individually or as a group, with
the same scope and effect as the indemnification of directors and officers
provided for in this Article.

         Section 3.       Right of Claimant to Bring Suit.  If a written claim
received by the Corporation from or on behalf of an indemnified party under
this Article VI is not paid in full by the Corporation





                                       11
<PAGE>   15
within ninety days after such receipt, the claimant may at any time thereafter
bring suit against the Corporation to recover the unpaid amount of the claim
and, if successful in whole or in part, the claimant shall be entitled to be
paid also the expense of prosecuting such claim.  It shall be a defense to any
such action (other than an action brought to enforce a claim for expenses
incurred in defending any proceeding in advance of its final disposition where
the required undertaking, if any is required, has been tendered to the
Corporation) that the claimant has not met the standards of conduct which make
it permissible under the Delaware General Corporation Law for the Corporation
to indemnify the claimant for the amount claimed, but the burden of proving
such defense shall be on the Corporation.  Neither the failure of the
Corporation (including its Board of Directors, independent legal counsel, or
its stockholders) to have made a determination prior to the commencement of
such action that indemnification of the claimant is proper in the circumstances
because he or she has met the applicable standard of conduct set forth in the
Delaware General Corporation Law, nor an actual determination by the
Corporation (including its Board of Directors, independent legal counsel, or
its stockholders) that the claimant has not met such applicable standard of
conduct, shall be a defense to the action or create a presumption that the
claimant has not met the applicable standard of conduct.

         Section 4.       Nonexclusivity of Rights.  The right to
indemnification and the advancement and payment of expenses conferred in this
Article VI shall not be exclusive of any other right which any person may have
or hereafter acquire under any law (common or statutory), provision of the
Certificate of Incorporation of the Corporation, bylaw, agreement, vote of
stockholders or disinterested directors or otherwise.

         Section 5.       Insurance.  The Corporation may maintain insurance,
at its expense, to protect itself and any person who is or was serving as a
director, officer, employee or agent of the Corporation or is or was serving at
the request of the Corporation as a director, officer, employee or agent of
another corporation, partnership, joint venture, trust or other enterprise
against any expense, liability or loss, whether or not the Corporation would
have the power to indemnify such person against such expense, liability or loss
under the Delaware General Corporation Law.

         Section 6.       Savings Clause.  If this Article VI or any portion
hereof shall be invalidated on any ground by any court of competent
jurisdiction, then the Corporation shall nevertheless indemnify and hold
harmless each director and officer of the Corporation, as to costs, charges and
expenses (including attorneys' fees), judgments, fines, and amounts paid in
settlement with respect to any action, suit or proceeding, whether civil,
criminal, administrative or investigative to the full extent permitted by any
applicable portion of this Article VI that shall not have been invalidated and
to the fullest extent permitted by applicable law.

         Section 7.       Definitions.  For purposes of this Article, reference
to the "Corporation" shall include, in addition to the Corporation, any
constituent corporation (including any constituent of a constituent) absorbed
in a consolidation or merger prior to (or, in the case of an entity
specifically designated in a resolution of the Board of Directors, after) the
adoption hereof and which, if its separate existence had continued, would have
had the power and authority to indemnify its directors, officers and employees
or agents, so that any person who is or was a director, officer, employee or
agent of such constituent corporation, or is or was serving at the request of
such constituent corporation as a director, officer, employee or agent of
another corporation, partnership, joint venture, trust or





                                       12
<PAGE>   16
other enterprise, shall stand in the same position under the provisions of this
Article with respect to the resulting or surviving corporation as he would have
with respect to such constituent corporation if its separate existence had
continued.


                                  ARTICLE VII

                                 CAPITAL STOCK

         Section 1.       Certificates of Stock.  The certificates for shares
of the capital stock of the Corporation shall be in such form, not inconsistent
with that required by law and the Certificate of Incorporation, as shall be
approved by the Board of Directors.  The Chairman of the Board (if any),
President or a Vice President shall cause to be issued to each stockholder one
or more certificates, under the seal of the Corporation or a facsimile thereof
if the Board of Directors shall have provided for such seal, and signed by the
Chairman of the Board (if any), President or a Vice President and the Secretary
or an Assistant Secretary or the Treasurer or an Assistant Treasurer certifying
the number of shares (and, if the stock of the Corporation shall be divided
into classes or series, the class and series of such shares) owned by such
stockholder in the Corporation; provided, however, that any of or all the
signatures on the certificate may be facsimile.  The stock record books and the
blank stock certificate books shall be kept by the Secretary, or at the office
of such transfer agent or transfer agents as the Board of Directors may from
time to time by resolution determine.  In case any officer, transfer agent or
registrar who shall have signed or whose facsimile signature or signatures
shall have been placed upon any such certificate or certificates shall have
ceased to be such officer, transfer agent or registrar before such certificate
is issued by the Corporation, such certificate may nevertheless be issued by
the Corporation with the same effect as if such person were such officer,
transfer agent or registrar at the date of issue.  The stock certificates shall
be consecutively numbered and shall be entered in the books of the Corporation
as they are issued and shall exhibit the holder's name and number of shares.

         Section 2.       Transfer of Shares. The shares of stock of the
Corporation shall be transferable only on the books of the Corporation by the
holders thereof in person or by their duly authorized attorneys or legal
representatives upon surrender and cancellation of certificates for a like
number of shares.  Upon surrender to the Corporation or a transfer agent of the
Corporation of a certificate for shares duly endorsed or accompanied by proper
evidence of succession, assignment or authority to transfer, it shall be the
duty of the Corporation to issue a new certificate to the person entitled
thereto, cancel the old certificate and record the transaction upon its books.

         Section 3.       Ownership of Shares.  The Corporation shall be
entitled to treat the holder of record of any share or shares of capital stock
of the Corporation as the holder in fact thereof and, accordingly, shall not be
bound to recognize any equitable or other claim to or interest in such share or
shares on the part of any other person, whether or not it shall have express or
other notice thereof, except as otherwise provided by the laws of the State of
Delaware.

         Section 4.       Regulations Regarding Certificates.  The Board of
Directors shall have the power and authority to make all such rules and
regulations as they may deem expedient concerning





                                       13
<PAGE>   17
the issue, transfer and registration or the replacement of certificates for
shares of capital stock of the Corporation.


         Section 5.       Lost or Destroyed Certificates.  The Board of
Directors may determine the conditions upon which a new certificate of stock
may be issued in place of a certificate which is alleged to have been lost,
stolen or destroyed; and may, in their discretion, require the owner of such
certificate or his legal representative to give bond, with sufficient surety,
to indemnify the Corporation and each transfer agent and registrar against any
and all losses or claims which may arise by reason of the issue of a new
certificate in the place of the one so lost, stolen or destroyed.



                                  ARTICLE VIII

                            MISCELLANEOUS PROVISIONS

         Section 1.       Fiscal Year.  The fiscal year of the Corporation
shall be such as established from time to time by the Board of Directors.

         Section 2.       Corporate Seal.  The Board of Directors may provide a
suitable seal, containing the name of the Corporation.  The Secretary shall
have charge of the seal (if any).  If and when so directed by the Board of
Directors or a committee thereof, duplicates of the seal may be kept and used
by the Treasurer or by the Assistant Secretary or Assistant Treasurer.

         Section 3.       Notice and Waiver of Notice.  Whenever any notice is
required to be given by law, the Certificate of Incorporation or under the
provisions of these bylaws, said notice shall be deemed to be sufficient if
given (i) by telegraphic, cable or wireless transmission or (ii) by deposit of
the same in a post office box in a sealed prepaid wrapper addressed to the
person entitled thereto at his post office address, as it appears on the
records of the Corporation, and such notice shall be deemed to have been given
on the day of such transmission or mailing, as the case may be.

         Whenever notice is required to be given by law, the Certificate of
Incorporation or under any of the provisions of these bylaws, a written waiver
thereof, signed by the person entitled to notice, whether before or after the
time stated therein, shall be deemed equivalent to notice.  Attendance of a
person at a meeting shall constitute a waiver of notice of such meeting, except
when the person attends a meeting for the express purpose of objecting, at the
beginning of the meeting, to the transaction of any business because the
meeting is not lawfully called or convened.  Neither the business to be
transacted at, nor the purpose of, any regular or special meeting of the
stockholders, directors, or members of a committee of directors need be
specified in any written waiver of notice unless so required by the Certificate
of Incorporation or the bylaws.

         Section 4.       Resignations.  Any director, member of a committee or
officer may resign at any time.  Such resignation shall be made in writing and
shall take effect at the time specified therein, or if no time be specified, at
the time of its receipt by the chief executive officer or Secretary.  The
acceptance of a resignation shall not be necessary to make it effective, unless
expressly so provided in the resignation.





                                       14
<PAGE>   18
         Section 5.       Facsimile Signatures.  In addition to the provisions
for the use of facsimile signatures elsewhere specifically authorized in these
bylaws, facsimile signatures of any officer or officers of the Corporation may
be used whenever and as authorized by the Board of Directors.

         Section 6.       Reliance upon Books, Reports and Records.  Each
director and each member of any committee designated by the Board of Directors
shall, in the performance of his duties, be fully protected in relying in good
faith upon the books of account or reports made to the Corporation by any of
its officers, or by an independent certified public accountant, or by an
appraiser selected with reasonable care by the Board of Directors or by any
such committee, or in relying in good faith upon other records of the
Corporation.


                                   ARTICLE IX

                                   AMENDMENTS

         If provided in the Certificate of Incorporation of the Corporation,
the Board of Directors shall have the power to adopt, amend and repeal from
time to time bylaws of the Corporation, subject to the right of the
stockholders entitled to vote with respect thereto to amend or repeal such
bylaws as adopted or amended by the Board of Directors.


                                 CERTIFICATION

         The undersigned, being the duly elected and acting Secretary of
Capstar Broadcasting Partners, Inc. (the "Corporation"), hereby certifies that
the Bylaws of the Corporation have been repealed and the Amended and Restated
Bylaws of the Corporation have been duly adopted, effective as of September 22,
1997, by the Board of Directors.


Dated:  September 29, 1997


                                        /s/ WILLIAM S. BANOWSKY, JR.
                                        ------------------------------
                                        William S. Banowsky, Jr.





                                       15