<PAGE>   1
                                                                    Exhibit 99.1


                                                                  EXECUTION COPY


                                    AMENDMENT


            AMENDMENT, dated as of March 17, 1998 (this "Amendment"), to the
Fifth Amended and Restated Credit Agreement, dated as of August 15, 1997 (as
amended, supplemented or otherwise modified from time to time, the "Credit
Agreement"), among OUTDOOR SYSTEMS, INC. (the "Company"), MEDIACOM, INC. (the
"Canadian Borrower"; together with the Company, the "Borrowers"), the several
banks and other financial institutions from time to time parties thereto (the
"Lenders"), CANADIAN IMPERIAL BANK OF COMMERCE, as Canadian Administrative
Agent, and CANADIAN IMPERIAL BANK OF COMMERCE, NEW YORK AGENCY, as US
Administrative Agent (in such capacity, the "US Administrative Agent"; together
with the Canadian Administrative Agent, the "Agents").


                              W I T N E S S E T H:

            WHEREAS, the Borrowers, the Lenders and the Agents are parties to
the Credit Agreement;

            WHEREAS, the Borrowers have requested that the Lenders agree to
amend certain provisions of the Credit Agreement, and the Lenders are agreeable
to such request upon the terms and subject to the conditions set forth herein;

            NOW, THEREFORE, in consideration of the premises and mutual
agreements contained herein, and for other valuable consideration the receipt of
which is hereby acknowledged, the Borrowers, the Lenders and the Agents hereby
agree as follows:

            1. Definitions. All terms defined in the Credit Agreement shall have
such defined meanings when used herein unless otherwise defined herein.

            2. Amendment of Subsection 9(j). Subsection 9(j) of the Credit
Agreement is hereby amended by replacing it with the following new clause (j):

            "(j) (i) Except for the Designated Holders, any Person or "group"
(within the meaning of Section 13(d) or 14(d) of the Securities Exchange Act of
1934, as amended) (A) shall have acquired beneficial ownership of 20% or more of
any outstanding class of Capital Stock having ordinary voting power in the
election of directors of the Company or (B) shall obtain the power (whether or
not exercised) to elect a majority of the Company's directors, or (ii) the
aggregate amount of Capital Stock having ordinary voting power in the election
of directors of the Company held by the Designated Holders (on a fully diluted
basis) shall not constitute at least 25% of the issued and outstanding Capital
Stock having such voting power, or (iii) either of the Designated Holders shall
own fewer than 60% of the number of shares of Capital Stock of the Company of
any class held by them on the Closing Date (without giving effect to any stock
split or distribution of additional shares in respect thereof), or (iv) a
"Change of Control" (as
<PAGE>   2
                                                                               2

defined in the Senior Subordinated 1996 Indenture or the Senior Subordinated
1997 Indenture) shall have occurred, or (v) the Board of Directors of the
Company shall not consist of a majority of Continuing Directors; as used in this
paragraph "Continuing Directors" shall mean the directors of the Company on the
Closing Date and each other director, if such other director's nomination for
election to the Board of Directors of the Company is recommended by a majority
of the then Continuing Directors; or"

            3. Waiver. The Lenders hereby waive any Event of Default which may
have occurred prior to the date hereof under Section 9(j) of the Credit
Agreement as in effect before giving effect to this Amendment.

            4. Conditions to Effectiveness. This Amendment shall become
effective on and as of the date that the US Administrative Agent shall have
received counterparts of this Amendment, duly executed and delivered by a duly
authorized officer of each of the Borrowers, and the Majority Lenders and
consented to by each Guarantor.

            5. Limited Amendment. Except as expressly amended herein, the Credit
Agreement shall continue to be, and shall remain, in full force and effect. This
Amendment shall not be deemed to be a waiver of, or consent to, or a
modification or amendment of, any other term or condition of the Credit
Agreement (including, without limitation, the financial covenants set forth in
subsection 8.1) or any other Loan Document or to prejudice any other right or
rights which the Lenders may now have or may have in the future under or in
connection with the Credit Agreement or any of the instruments or agreements
referred to therein, as the same may be amended from time to time.

            6. Counterparts. This Amendment may be executed by one or more of
the parties hereto in any number of separate counterparts, and all of said
counterparts taken together shall be deemed to constitute one and the same
instrument.

            7. GOVERNING LAW. THIS AMENDMENT SHALL BE GOVERNED BY, AND CONSTRUED
AND INTERPRETED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.
<PAGE>   3
                                                                               3

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

                                    OUTDOOR SYSTEMS, INC.


                                    By: /s/
                                        -----------------------------------
                                        Title:


                                    MEDIACOM, INC.

                                    By: /s/
                                        -----------------------------------
                                        Title:

                                    CANADIAN IMPERIAL BANK OF COMMERCE, as
                                    Canadian Administrative Agent and as a
                                    Lender

                                    By: /s/
                                        -----------------------------------
                                        Title:


                                    CIBC INC., as a Lender

                                    By:  /s/
                                        -----------------------------------
                                        Title:


                                    CANADIAN IMPERIAL BANK OF COMMERCE, NEW
                                    YORK AGENCY, as US Administrative Agent
                                    and as a Lender

                                    By: /s/
                                        -----------------------------------
                                        Title:
<PAGE>   4
                                    ALLSTATE INSURANCE COMPANY



                                    By:  /s/
                                        -----------------------------------
                                        Title:


                                    ALLSTATE LIFE INSURANCE COMPANY

                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    ARCHIMEDES FUNDING, L.L.C.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    BANK OF AMERICA NATIONAL TRUST
                                      & SAVINGS ASSOCIATION

                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    BANK OF AMERICA CANADA

                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    BANK OF HAWAII

                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    THE BANK OF MONTREAL, CHICAGO
                                      BRANCH


                                    By:  /s/
                                        -----------------------------------
                                         Title:
<PAGE>   5
                                    THE BANK OF NEW YORK


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    THE BANK OF NOVA SCOTIA

                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    The BANK OF NOVA SCOTIA - CANADA

                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    BANK ONE, ARIZONA, NA

                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    BANKBOSTON, N.A.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    BANQUE PARIBAS


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    BAYERISCHE VEREINSBANK A.G.


                                    By:  /s/
                                        -----------------------------------
                                         Title:
<PAGE>   6
                                    BEAR STEARNS INVESTMENT PRODUCTS, INC.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    CAPTIVA FINANCE LTD.

                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    CARILLON HOLDING, LTD.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    CITY NATIONAL BANK


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    COMPAGNIE FINANCIERE DE CIC
                                      ET DE L'UNION EUROPEENNE


                                    By:  /s/
                                        -----------------------------------
                                         Title:

                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    CONTINENTAL ASSURANCE COMPANY


                                    By:  /s/
                                        -----------------------------------
                                         Title:
<PAGE>   7
                                    CORESTATES BANK, N.A.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    CREDIT LYONNAIS, LOS ANGELES BRANCH


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    CREDIT LYONNAIS CANADA


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    CREDITANSTALT CORPORATE
                                      FINANCE, INC.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    DEEPROCK & COMPANY


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    DRESDNER BANK AG NEW YORK &
                                      GRAND CAYMAN BRANCHES


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    DRESDNER BANK CANADA

                                    By:  /s/
                                        -----------------------------------
                                         Title:
<PAGE>   8
                                    FIRST HAWAIIAN BANK


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    FIRST NATIONAL BANK OF MARYLAND


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    FIRST UNION NATIONAL BANK
                                      (f/k/a FIRST UNION BANK OF NORTH
                                      CAROLINA


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    FLEET NATIONAL BANK


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    FLOATING RATE PORTFOLIO

                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    THE FUJI BANK LIMITED, LOS
                                      ANGELES AGENCY


                                    By:  /s/
                                        -----------------------------------
                                         Title:
<PAGE>   9
                                    GENERAL ELECTRIC CAPITAL
                                      CORPORATION


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    IMPERIAL BANK, A CALIFORNIA
                                      BANKING CORPORATION


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    INDOSUEZ CAPITAL FUNDING II, LIMITED
                                    BY: INDOSUEZ CAPITAL, AS PORTFOLIO
                                      ADVISOR


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    INDUSTRIAL BANK OF JAPAN, LTD.,
                                      LOS ANGELES AGENCY


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    KZH-CRESCENT CORPORATION


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    KZH HOLDING CORPORATION III


                                    By:  /s/
                                        -----------------------------------
                                         Title:
<PAGE>   10
                                    KZH-ING HOLDING CORPORATION


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    KZH-SOLEIL CORPORATION


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    LEHMAN COMMERCIAL PAPER INC.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    THE LONG TERM CREDIT BANK OF
                                      JAPAN, LTD.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    MASSACHUSETTS MUTUAL LIFE
                                      INSURANCE COMPANY


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    MELLON BANK, N.A.


                                    By:  /s/
                                        -----------------------------------
                                         Title:
<PAGE>   11
                                    MERITA BANK LTD. - NEW YORK BRANCH


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    MERRILL LYNCH PRIME RATE PORTFOLIO
                                    BY: MERRILL LYNCH ASSET MANAGEMENT,
                                       L.P., AS INVESTMENT ADVISOR


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    MERRILL LYNCH SENIOR FLOATING
                                      RATE FUND, INC.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    METROPOLITAN LIFE INSURANCE
                                      COMPANY


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    MICHIGAN NATIONAL BANK


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    THE MITSUBISHI TRUST AND BANKING
                                      CORPORATION, LOS ANGELES AGENCY


                                    By:  /s/
                                        -----------------------------------
                                         Title:
<PAGE>   12
                                    NATIONAL CITY BANK

                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    NORWEST BANK ARIZONA, N.A.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    PARIBAS BANK OF CANADA


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    PARIBAS CAPITAL FUNDING L.L.C.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    ROYALTON COMPANY


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    SENIOR DEBT PORTFOLIO


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    SOUTHERN PACIFIC BANK


                                    By:  /s/
                                        -----------------------------------
                                         Title:
<PAGE>   13
                                    STRATA FUNDING LTD.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    THE SUMITOMO BANK, LIMITED, NEW
                                      YORK BRANCH


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    THE SUMITOMO BANK OF CANADA


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    TCW LEVERAGED INCOME TRUST, L.P.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    THE TRAVELERS INSURANCE COMPANY


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    UNION BANK OF CALIFORNIA NA


                                    By:  /s/
                                        -----------------------------------
                                         Title:
<PAGE>   14
                                    VAN KAMPEN AMERICAN CAPITAL
                                      PRIME RATE INCOME TRUST


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    VAN KAMPEN CLO I, LIMITED


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    The undersigned hereby consent and agree
                                    to the foregoing amendment.


                                    OUTDOOR SYSTEMS PAINTING, INC.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    OS ADVERTISING OF TEXAS
                                      PAINTING, INC.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    OS BASELINE, INC.

                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    DECADE COMMUNICATIONS GROUP, INC.

                                    By:  /s/
                                        -----------------------------------
                                         Title:
<PAGE>   15
                                    BENCH ADVERTISING COMPANY OF
                                    COLORADO, INC.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    NEW YORK SUBWAYS ADVERTISING
                                      CO., INC.


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    OUTDOOR SYSTEMS, INC.

                                    By:  /s/
                                        -----------------------------------
                                    Title:


                                    OUTDOOR SYSTEMS (NEW YORK), INC.

                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    OS BUS, INC.

                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    NATIONAL ADVERTISING COMPANY


                                    By:  /s/
                                        -----------------------------------
                                         Title:


                                    PACIFIC CONNECTION, INC.


                                    By:  /s/
                                        -----------------------------------
                                         Title: