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                                                                    EXHIBIT 4(h)

                           AGREEMENT TO ISSUE WARRANT

         Agreement dated as of June 15, 1998 by and between Regent
Communications, Inc., a Delaware corporation ("Regent") and General Electric
Capital Corporation, a New York corporation ("GE Capital").

                                   WITNESSETH:

        WHEREAS, GE Capital owns 1,000,000 shares of the 7% Series B Convertible
Preferred Stock of Regent; and 

        WHEREAS, Regent contemplates the issuance of shares of a Series F
Convertible Preferred Stock of Regent to Waller-Sutton Media Partners, L.P.
("Waller-Sutton") and certain other investors pursuant to the terms of a Stock
Purchase Agreement of even date herewith; and

         WHEREAS, in order to induce GE Capital to approve the issuance of
shares of a Series F Convertible Preferred Stock of Regent to Waller-Sutton and
certain other investors as described in the Registration Statement on Form S-4
filed by Regent with the Securities and Exchange Commission, effective May 7,
1998, and as more specifically set forth in said Stock Purchase Agreement,
Regent has agreed to issue to GE Capital, and GE Capital has agreed to accept
upon issuance of such shares, warrants to purchase 50,000 shares of Regent
Common Stock.

         NOW, THEREFORE, the parties, desiring to enter into this Agreement to
establish the specific terms and conditions of the warrants, agree as follows:

         1.        Issuance of Warrant.

                  Upon and concurrently with the issuance to Waller-Sutton of
shares of Series F Convertible Preferred Stock of Regent pursuant to the terms
of said Stock Purchase Agreement,
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Regent shall deliver to GE Capital a warrant in the form of Exhibit A hereto to
purchase 50,000 shares of Common Stock of Regent (the "Warrant").

         2.       Representations and Warranties of Regent.

                  Regent hereby represents and warrants to GE Capital as
follows:

                  (a) All corporate action on the part of Regent, its directors
and stockholders necessary for the authorization, execution, delivery and
performance of this Agreement by Regent; the authorization, sale, issuance and
delivery of (i) the Warrant and (ii) the Warrant Shares (as defined in the
Warrant), and the performance of all of Regent's obligations hereunder and
thereunder has been taken.

                  (b) This Agreement constitutes the valid and binding
obligation of Regent, enforceable in accordance with its terms, except as
enforcement may be limited by bankruptcy, insolvency, reorganization, moratorium
or similar laws affecting enforcement of creditors' rights generally and except
as enforcement is subject to general principles of equity regardless of whether
enforcement is considered in a proceeding at law or in equity.

                  (c) The Warrant, when issued in compliance with the provisions
of this Agreement, will be validly issued, will have the rights, preferences and
privileges described therein and will constitute valid and binding obligations
of Regent, enforceable in accordance with its terms, subject to the matters
described above.

                  (d) The Warrant Shares have been duly and validly reserved
and, when issued in compliance with the provisions of the Warrant, will be
validly issued, fully paid and nonassessable.

                  (e) The Warrant and the Warrant Shares will be free of any
liens or encumbrances, other than any liens or encumbrances created by or
imposed upon the holders

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thereof through no action of Regent; provided, however, that the Warrant and the
Warrant Shares will be subject to restrictions on transfer under state and/or
federal securities laws as set forth therein.

         3. Representations and Warranties of GE Capital.

                  GE Capital hereby represents and warrants to Regent, as of the
date hereof, as follows:

                  (a) Investment Intent. GE Capital is acquiring the Warrant for
its own account, for investment and not with a view to resale, distribution, or
other disposition, and GE Capital has no present plans to enter into any
contract, undertaking, agreement or arrangement for any such resale,
distribution or other disposition. GE Capital will not sell or otherwise
transfer the Warrant without registration under the Securities Act of 1933, as
amended, and applicable state securities laws, or pursuant to an exemption from
the registration requirements thereof which, in the opinion of counsel
acceptable to Regent, is available for the transaction.

                  (b) Opportunity to Review Books and Records. GE Capital has
had a reasonable opportunity to inspect all documents, books and records
pertaining to Regent and the Warrant and confirms that the Warrant is being
acquired without GE Capital's receipt of any offering literature.

                  (c) Opportunity for Questions. GE Capital has had a reasonable
opportunity to ask questions of and receive answers from a person or persons
acting on behalf of Regent concerning Regent, its business and proposed
operations, the terms of the Warrant and all other aspects of investment in
Regent, and all such questions have been answered to the full satisfaction of GE
Capital.

                  (d) No Conflict. The execution, delivery and performance of
this Agreement by GE Capital (i) will not constitute a default under or conflict
with any agreement or instrument to

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which GE Capital is a party or by which it or its assets are bound, (ii) will
not conflict with or violate any order, judgment, decree, statute, ordinance or
regulation applicable to GE Capital (including, without limitation, any
applicable laws relating to permissible legal investments) and (iii) do not
require the consent of any person or entity.

                  (e) Authority of GE Capital. This Agreement constitutes the
legal, valid and binding obligations of GE Capital, enforceable against GE
Capital in accordance with its terms, except as enforcement may be limited by
bankruptcy, insolvency, reorganization, moratorium or similar laws affecting
enforcement of creditors' rights generally and except as enforcement is subject
to general principles of equity regardless of whether enforcement is considered
in a proceeding at law or in equity.

         4.        Miscellaneous.

                  (a) Notices. Any notice, request or other document to be given
hereunder to any party shall be effective upon receipt (or refusal of receipt)
and shall be in writing and delivered personally or sent by telecopy or
certified or registered mail, postage prepaid:

                        (i)      if to Regent, addressed to:

                                 Regent Communications, Inc.
                                 50 East RiverCenter Boulevard, Suite 180
                                 Covington, Kentucky  41011
                                 Attn:  Terry S. Jacobs, Chairman of the Board
                                 Facsimile (606) 292-0352

                        (ii)     if to GE Capital, addressed to:

                                 General Electric Capital Corporation
                                 3379 Peachtree Road, N.E., Suite 600
                                 Atlanta, Georgia 30326
                                 Attn: Regent Account Manager
                                 Facsimile (408)-842-1533

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                                 with a copy to:

                                 General Electric Capital Corporation
                                 201 High Ridge Road
                                 Stanford, Connecticut 06927
                                 Attn: Region Counsel
                                 Facsimile: (203) 316-7889

or to such other address or telecopy number as any party shall have specified by
notice given to the other parties in the manner specified above.

                  (b) Entire Agreement; Amendment. This Agreement, including the
Exhibit hereto, and the other agreements, if any, expressly contemplated by this
Agreement, contain the entire agreement between the parties with respect to the
subject matter hereof and supersede all prior oral and written agreements,
memoranda, term sheets, understandings and undertakings among the parties hereto
relating to the subject matter hereof. This Agreement may be modified or amended
only by a written instrument executed by or on behalf of the parties hereto.

                  (c) Governing Law. This Agreement shall be governed by, and
construed in accordance with, the internal laws of the State of Delaware without
regard to the application of its conflicts of laws principles. The parties
hereby waive all right to trial by jury in any action, suit or proceeding
brought to enforce or defend any rights or remedies under this Agreement or the
transactions contemplated hereby.

                  (d) Severability. If any provision in this Agreement shall be
invalid, illegal or unenforceable, the validity, legality and enforceability of
the remaining provisions hereof shall not in any way be affected or impaired
thereby.

                  (e) Construction. The section and subsection headings used
herein are for convenience of reference only, are not a party of this Agreement
and are not to affect the construction of, or be taken into consideration in
interpreting, any provision of this Agreement.

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As used in this Agreement, the masculine, feminine and neuter gender each
includes the other, unless the context otherwise dictates. Any and all schedules
and exhibits referred to in this Agreement and attached hereto are and shall be
incorporated in this Agreement as if fully set forth herein.

                  (f) Counterparts. This Agreement may be executed in one or
more counterparts, each of which shall be deemed to be an original, but all of
which together shall constitute one and the same instruments.

                  (g) Specific Performance. The parties hereto acknowledge that
damages may be an inadequate remedy for any breach of the provisions of this
Agreement and agree that the obligations of the parties hereunder may be
specifically enforced, and no party will take any action to impede the other
from seeking to enforce such right of specific performance after any such
breach.

                  (h) Successors and Assigns; Assignability. Except as otherwise
provided herein, this Agreement shall be binding upon and inure to the benefit
of and be enforceable by the parties hereto and their respective successor and
permitted assigns. This Agreement shall not confer upon any person other than
the parties hereto and their respective successors and permitted assigns any
rights or remedies hereunder.

                  (i) Further Assurances. Subject to the terms and conditions
herein provided, each of the parties hereto agrees to use all reasonable efforts
to take, or cause to be taken, all action and to do, or cause to be done, all
things necessary, proper or advisable to consummate and make effective the
transactions contemplated by this Agreement.

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                  (j) Survival. The representations and warranties of the
parties contained herein shall survive execution and delivery of this Agreement
and issuance and delivery of the Warrant or Warrant Shares.

         IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed and delivered, as of the day and year first above written.

                                         REGENT COMMUNICATIONS, INC.

                                         By:/s/
                                            ------------------------------------
                                            Its:
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                                         GENERAL ELECTRIC CAPITAL
                                         CORPORATION

                                         By:/s/
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                                            Its:
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