<PAGE>
                                                                  EXHIBIT 10.5.1

                                    FIRST AMENDMENT AND WAIVER dated as of
                           January 23, 2002 (this "Amendment"), to the Amended
                           and Restated Credit Agreement dated as of June 29,
                           2001 (the "Credit Agreement"), among LIN HOLDINGS
                           CORP., a Delaware corporation ("Holdings"), LIN
                           TELEVISION CORPORATION, a Delaware corporation (the
                           "Borrower"), the Lenders, JPMORGAN CHASE BANK
                           (formerly known as The Chase Manhattan Bank), as
                           Administrative Agent, Swingline Lender and Issuing
                           Lender, and the other parties party thereto.

                  A. Pursuant to the Credit Agreement, the Lenders, the
Swingline Lender and the Issuing Lender have extended credit to the Borrower and
have agreed to extend credit to the Borrower, in each case pursuant to the terms
and subject to the conditions set forth therein.

                  B. The Borrower has informed the Administrative Agent that it
has entered into the Management Services Agreement, dated January 7, 2002, among
the Borrower, Sunrise Television Corp., STC Broadcasting, Inc. and STC License
Company.

                  C. The Borrower and Holdings have requested that the
Administrative Agent, the Swingline Lender, the Issuing Lender and the Required
Lenders grant a limited waiver of and amend the Credit Agreement, as set forth
herein.

                  D. The Administrative Agent, the Swingline Lender, the Issuing
Lender and the Required Lenders are willing to grant such limited waiver of, and
to so amend, the Credit Agreement, in each case pursuant to the terms and
subject to the conditions set forth herein.

                  E. Capitalized terms used and not otherwise defined herein
shall have the meanings assigned to them in the Credit Agreement (as amended by
this Amendment).

                  Accordingly, in consideration of the mutual agreements herein
contained and other good and valuable consideration, the sufficiency and receipt
of which are hereby acknowledged, the parties hereto agree as follows:

                  SECTION 1. (a) Amendments to Section 1.1 of the Credit
Agreement (Defined Terms). Section 1.1 of the Credit Agreement is hereby amended
by: (i) inserting the following at the end of the text of the definition of the
term "Subsidiary":

                  "Notwithstanding the foregoing, neither Sunrise Television
                  Corp., a Delaware corporation, nor any of its Subsidiaries
                  shall be considered a Subsidiary of the Borrower or Holdings
                  solely as a result of (a) the existence of, or the
                  performance by any party thereto of its obligations under,
                  the Management Services Agreement or (b) one or more
                  individuals' serving as officers or directors of both (i)
                  Holdings or the Borrower, on the one hand, and (ii) Sunrise
                  Television Corp. or any of its Subsidiaries, on the other
                  hand."; and


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                  (ii) inserting the following new defined term in proper
                  alphabetical order:

                  "`Management Services Agreement': the Management Services
                  Agreement, dated January 7, 2002, among the Borrower,
                  Sunrise Television Corp., STC Broadcasting, Inc. and STC
                  License Company, as the same may be amended, restated,
                  supplemented or otherwise modified from time to time in
                  compliance with the terms hereof."

                  (b) Amendment to Section 6 of the Credit Agreement
(Affirmative Covenants). Section 6 of the Credit Agreement is hereby amended by
inserting the following new subsections at the end of such Section:

                  "6.14 Control of Sunrise Television Corp. and its
                  Subsidiaries. Manage, direct or otherwise control, directly
                  or indirectly, the business or affairs of Sunrise Television
                  Corp. or any of its Subsidiaries solely to the extent
                  contemplated by the Management Services Agreement."; and

                  "6.15 Amendments to the Management Services Agreement. Furnish
                  any amendment, restatement, supplement or other modification
                  to or waiver of the Management Services Agreement to the
                  Administrative Agent (which shall in turn be promptly
                  distributed by the Administrative Agent to the Lenders) prior
                  to or promptly after the entering into or effectiveness
                  thereof but in no event later than the fifth Business Day
                  after the earlier of the entering into or effectiveness
                  thereof."

                  (c) Amendment to Section 7 of the Credit Agreement (Negative
Covenants). Section 7 of the Credit Agreement is hereby amended by: (i) deleting
the word "and" at the end of the text of clause (ii) of Section 7.10(b) and
inserting the following immediately prior to the period at the end of the text
of Section 7.10(b)(iii):

                  "; and

                  (iv) the Management Services Agreement"; and

                  (ii) inserting the following new subsection at the end of
                  Section 7:

                  "7.20 Limitation on Amendments to the Management Services
                  Agreement. Effect any amendment, restatement, supplement or
                  other modification to or waiver of the Management Services
                  Agreement that could reasonably be expected to materially and
                  adversely affect the interests of the Lenders without the
                  prior written consent of the Required Lenders."

                  SECTION 2. Limited Waiver of the Credit Agreement. The Lenders
hereby grant a limited waiver of compliance with Section 7.10(a) of the Credit
Agreement to the extent, but only to the extent, necessary to permit the
Borrower to enter into the Management Services Agreement and perform its
obligations and exercise its rights under the Management Services Agreement.


                                       2

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                  SECTION 3. Representations and Warranties. Each of Holdings
and the Borrower represents and warrants to the Administrative Agent, the
Swingline Lender, the Issuing Lender and each of the Lenders that:

                  (a) This Amendment has been duly authorized, executed and
delivered by it and constitutes its legal, valid and binding obligation,
enforceable in accordance with its terms, subject to applicable bankruptcy,
insolvency, reorganization, moratorium or other laws affecting creditors' rights
generally and subject to general principles of equity, regardless of whether
considered in a proceeding in equity or at law, and an implied covenant of good
faith and fair dealing.

                  (b) After giving effect to this Amendment, the representations
and warranties set forth in Section 4 of the Credit Agreement are true and
correct in all material respects on and as of the Effective Date (as defined in
Section 4 hereof), except to the extent such representations and warranties
expressly relate to an earlier date, in which case such representations and
warranties are, to such extent, true and correct in all material respects as of
such earlier date.

                  (c) After giving effect to this Amendment, no Default or Event
of Default has occurred and is continuing.

                  SECTION 4. Conditions to Effectiveness. This Amendment shall
become effective on the date (the "Effective Date") that (a) the representations
and warranties set forth in Section 3 hereof are true and correct and (b) the
Administrative Agent shall have received counterparts of this Amendment that,
when taken together, bear the signatures of Holdings, the Borrower and the
Required Lenders.

                  SECTION 5. Effect of this Amendment. Except as expressly set
forth herein, this Amendment shall not by implication or otherwise limit,
impair, constitute a waiver of or otherwise affect the rights and remedies of
the Lenders, the Swingline Lender, the Issuing Lender or the Administrative
Agent under the Credit Agreement or any other Loan Document and shall not alter,
modify, amend or in any way affect any of the terms, conditions, obligations,
covenants or agreements contained in the Credit Agreement or any other Loan
Document, all of which are ratified and affirmed in all respects and shall
continue in full force and effect. Nothing herein shall be deemed to entitle the
Borrower or Holdings to a consent to, or a waiver, amendment, modification or
other change of, any of the terms, conditions, obligations, covenants or
agreements contained in the Credit Agreement or any other Loan Document in
similar or different circumstances. After the date hereof, any reference to the
Credit Agreement shall mean the Credit Agreement as amended hereby. This
Amendment shall constitute a Loan Document for all purposes under the Credit
Agreement and the other Loan Documents.

                  SECTION 6. APPLICABLE LAW. THIS AMENDMENT SHALL BE GOVERNED
BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

                  SECTION 7. Counterparts. This Amendment may be executed in any
number of counterparts and by different parties hereto in separate counterparts,
each of which when so

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executed and delivered shall be deemed an original, but all such counterparts
together shall constitute but one and the same instrument. Delivery of any
executed counterpart of a signature page of this Amendment by facsimile
transmission shall be as effective as delivery of a manually executed
counterpart hereof.

                                    IN WITNESS WHEREOF, the parties hereto have
caused this Amendment to be duly executed by their respective authorized
officers as of the day and year first above written.


                                      LIN HOLDINGS CORP.,

                                         by /s/ Deborah R. Jacobson
                                            ------------------------------------
                                            Name:  Deborah R. Jacobson
                                            Title: Vice President, Corporate
                                                   Development & Treasurer

                                      LIN TELEVISION CORPORATION,

                                         by /s/ Deborah R. Jacobson
                                            ------------------------------------
                                            Name:  Deborah R. Jacobson
                                            Title: Vice President, Corporate
                                                   Development & Treasurer

                                      JPMORGAN CHASE BANK,
                                      individually and as Administrative Agent,
                                      Swingline Lender and Issuing Lender,

                                         by  /s/ Tracey Navin Ewing
                                             -----------------------------------
                                             Name:  Tracey Navin Ewing
                                             Title: Vice President

                                      THE BANK OF NEW YORK,
                                      individually and as Co-Syndication Agent,

                                         by: /s/ John R. Ciulla
                                             -----------------------------------
                                             Name:  John R. Ciulla
                                             Title: Vice President


                                       4
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                                      THE BANK OF NOVA SCOTIA,
                                      individually and as Co-Documentation
                                      Agent,

                                         by: /s/ P. A. Weissenberger
                                             -----------------------------------
                                             Name:  P.A. Weissenberger
                                             Title: Authorized Signatory


                                      BALANCED HIGH-YIELD FUND I, LTD.
                                         By: ING Capital Advisors LLC, as
                                             Asset Manager,

                                             by: /s/ Michael D. Hatley
                                                 -------------------------------
                                                 Name:  Michael D. Hatley
                                                 Title: Managing Director


                                      BANKERS TRUST COMPANY,

                                         by: /s/ Gregory Shefrin
                                             -----------------------------------
                                             Name:   Gregory Shefrin
                                             Title:  Director

                                      THE DAI-ICHI KANGYO BANK, LTD.,

                                         by: /s/ Yudesh Sohan
                                             -----------------------------------
                                             Name:  Yudesh Sohan
                                             Title: Credit Officer


                                      DRESDNER BANK AG, NEW YORK AND GRAND
                                      CAYMAN BRANCHES,

                                         by: /s/ Brian K. Schneider
                                             -----------------------------------
                                             Name:  Brian K. Schneider
                                             Title: Associate

                                         by: /s/ Michael S. Greenberg
                                             -----------------------------------
                                             Name:  Michael S. Greenberg
                                             Title: Associate


                                       5

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                                      EATON VANCE CDO III, LTD.,
                                         By: Eaton Vance Management, as
                                             Investment Advisor,

                                             by: /s/ Scott H. Page
                                                 -------------------------------
                                                 Name:  Scott H. Page
                                                 Title: Vice President


                                      EATON VANCE CDO IV, LTD.,
                                         By: Eaton Vance Management, as
                                             Investment Advisor,

                                             by: /s/ Scott H. Page
                                                 -------------------------------
                                                 Name:  Scott H. Page
                                                 Title: Vice President


                                      EATON VANCE INSTITUTIONAL SENIOR LOAN
                                      FUND,
                                         By: Eaton Vance Management, as
                                             Investment Advisor,

                                             by: /s/ Scott H. Page
                                                 -------------------------------
                                                 Name:  Scott H. Page
                                                 Title: Vice President


                                      EATON VANCE SENIOR INCOME TRUST,
                                         By: Eaton Vance Management, as
                                             Investment Advisor,

                                             by: /s/ Scott H. Page
                                                 -------------------------------
                                                 Name:  Scott H. Page
                                                 Title: Vice President


                                      FIRST HAWAIIAN BANK,

                                         by: /s/ Shannon Sansevero
                                             -----------------------------------
                                             Name:  Shannon Sansevero
                                             Title: Media Finance Officer


                                       6

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                                      FLEET NATIONAL BANK,

                                         by: /s/ Laura Neenan
                                             -----------------------------------
                                             Name:  Laura Neenan
                                             Title: Vice President


                                      GE CAPITAL CORPORATION,

                                         by: /s/ Karl Kieffer
                                             -----------------------------------
                                             Name:  Karl Kieffer
                                             Title: Duly Authorized Signatory


                                      GRAYSON & CO,
                                         By: Boston Management and Research, as
                                             Investment Advisor,

                                             by: /s/ Scott H. Page
                                                 -------------------------------
                                                 Name:  Scott H. Page
                                                 Title: Vice President


                                      THE MITSUBISHI TRUST AND BANKING
                                      CORPORATION,

                                         by: /s/ Hiroyuki Tsuru
                                             -----------------------------------
                                             Name:  Hiroyuki Tsuru
                                             Title: Deputy General Manager


                                      OXFORD STRATEGIC INCOME FUND,
                                         By: Eaton Vance Management, as
                                             Investment Advisor,

                                             by: /s/ Scott H. Page
                                                 -------------------------------
                                                 Name:  Scott H. Page
                                                 Title: Vice President


                                      SENIOR DEBT PORTFOLIO
                                         By: Boston Management and Research, as
                                             Investment Advisor,
                                             by: /s/ Scott H. Page
                                                 -------------------------------
                                                 Name:  Scott H. Page
                                                 Title: Vice President

                                       7

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                                      SOCIETE GENERALE,

                                         by: /s/ Elaine Khalil
                                             -----------------------------------
                                             Name:  Elaine Khalil
                                             Title: Director

                                      VAN KAMPEN PRIME RATE INCOME TRUST,
                                         By: Van Kampen Investment Advisory
                                             Corp.,

                                             by: /s/ Darvin D. Pierce
                                                 -------------------------------
                                                 Name:  Darvin D. Pierce
                                                 Title: Executive Director


                                      WINGED FOOT FUNDING TRUST,

                                         by: /s/ Ann E. Morris
                                             -----------------------------------
                                             Name:  Ann E. Morris
                                             Title: Authorized Agent




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