<PAGE>
 
                                                                 Exhibit 10.6(c)

                                                         [EXECUTION COUNTERPART]



                      AMENDMENT NO. 2 TO CREDIT AGREEMENT

          AMENDMENT NO. 2 TO CREDIT AGREEMENT dated as of July 1, 1998, between
MEDIACOM SOUTHEAST LLC, a Delaware limited liability company (the "Borrower");
                                                                   --------
each of the lenders that is a signatory hereto identified under the caption
"LENDERS" on the signature pages hereto (each, individually, a "Lender" and,
 -------                                                        ------
collectively, the "Lenders"); and THE CHASE MANHATTAN BANK, as administrative
                   -------
agent for the Lenders (in such capacity, the "Administrative Agent").
                                              --------------------

          The Borrower, the Lenders and the Administrative Agent are party to a
Credit Agreement dated as of January 23, 1998 (as heretofore modified and
supplemented and in effect on the date hereof, the "Credit Agreement"),
                                                    ----------------
providing, subject to the terms and conditions thereof, for extensions of credit
in an aggregate principal amount up to but not exceeding $225,000,000 (which
may, in certain circumstances, be increased to $275,000,000). The Borrower, the
Lenders and the Administrative wish to amend the Credit Agreement in certain
respects, and accordingly, the parties hereto hereby agree as follows:

          Section 1.  Definitions.  Except as otherwise defined in this
                      -----------
Amendment No. 2, terms defined in the Credit Agreement are used herein as
defined therein.

          Section 2.  Amendments.  Upon execution and delivery of this Amendment
                      ----------
No. 2 by the Borrower and Majority Lenders, but effective as of the date hereof,
the Credit Agreement shall be amended as follows:

          2.01.  References in the Credit Agreement (including references to the
Credit Agreement as amended hereby) to "this Agreement" (and indirect references
such as "hereunder", "hereby", "herein" and "hereof") shall be deemed to be
references to the Credit Agreement as amended hereby.

          2.02.  Section 8.09(e) of the Credit Agreement is hereby amended by
deleting clause (iii) thereof, inserting the word "and" at the end of clause (i)
thereof and replacing "; and" at the end of clause (ii) thereof with a period.



                      Amendment No. 2 to Credit Agreement
                      -----------------------------------
<PAGE>
 
                                      -2-



          Section 3. Miscellaneous. Except as herein provided, the Credit
                     -------------
Agreement shall remain unchanged and in full force and effect. This Amendment
No. 2 may be executed in any number of counterparts, all of which taken together
shall constitute one and the same amendatory instrument and any of the parties
hereto may execute this Amendment No. 2 by signing any such counterpart. This
Amendment No. 2 shall be governed by, and construed in accordance with, the law
of the State of New York.
<PAGE>
 
                                      -3-

          IN WITNESS WHEREOF, the parties hereto have caused this Amendment No.
2 to be duly executed and delivered as of the day and year first above written.


                                     MEDIACOM SOUTHEAST LLC



                                     By /s/ MARK E. STEPHAN
                                       --------------------------------------
                                     Title:  CHIEF FINANCIAL OFFICER


                                    LENDERS
                                    -------
                                        

                                     THE CHASE MANHATTAN BANK



                                     By /s/ [SIGNATURE ILLEGIBLE]
                                       --------------------------------------
                                     Title:  VICE PRESIDENT



                                     BANK OF MONTREAL



                                     By   /s/ ALLEGRA GRIFFITHS
                                       --------------------------------------
                                     Title:   DIRECTOR


                                     CREDIT SUISSE FIRST BOSTON


                                     By   /s/ CHRIS T HORGAN
                                       --------------------------------------
                                     Title:   VICE PRESIDENT


                                     By   /s/ THOMAS G MUOIO
                                       --------------------------------------
                                     Title:   VICE PRESIDENT 
<PAGE>
 
                                      -4-




                                     CIBC INC.


                                     By /s/  TEFTA GHILAGA
                                      ---------------------------------------
                                      Title: EXECUTIVE DIRECTOR
                                             CIBC Oppenheimer Corp., AS AGENT



                                     FIRST UNION NATIONAL BANK


                                     By /s/  [SIGNATURE ILLEGIBLE]
                                      ---------------------------------------
                                      Title: VICE PRESIDENT



                                     THE FIRST NATIONAL BANK OF CHICAGO


                                     By /s/  [SIGNATURE ILLEGIBLE]
                                      ---------------------------------------
                                      Title:  CORPORATE BANKING OFFICER



                                     MELLON BANK, N.A.


                                     By /s/  [SIGNATURE ILLEGIBLE]
                                      ---------------------------------------
                                      Title:  VICE PRESIDENT



                                     ABN AMRO BANK N.V.


                                     By /s/  LARRY KELLEY
                                      ---------------------------------------
                                      Title: GROUP VICE PRESIDENT


                                     By ROBERT BUDNEK

                                      ---------------------------------------
                                      Title: ASSISTANT VICE PRESIDENT
<PAGE>
 
                                      -5-

                                     FLEET NATIONAL BANK



                                     By /s/  ERIC S MEYER
                                      ---------------------------------------
                                      Title: VICE PRESIDENT


                                     DRESDNER BANK AG, NEW YORK AND
                                      GRAND CAYMAN BRANCHES


                                     By /s/  WILLIAM E. LAMBERT
                                      ---------------------------------------
                                      Title: ASSISTANT VICE PRESIDENT


                                     By /s/  ROBERT GRELLA 
                                      ---------------------------------------
                                      Title: VICE PRESIDENT



                                     PNC BANK, NATIONAL ASSOCIATION


                                     By /s/  JOHN T. WILDEN
                                      ---------------------------------------
                                      Title: VICE PRESIDENT       



                                     SUNTRUST BANK, CENTRAL FLORIDA,
                                      N.A.


                                     By /s/  JANET P. SAMMONS
                                      ---------------------------------------
                                      Title: VICE PRESIDENT
                                             
<PAGE>
 
                                      -6-

                             ADMINISTRATIVE AGENT
                             --------------------
                                        

                                     THE CHASE MANHATTAN BANK, as
                                        Administrative Agent


                                     By /s/  [SIGNATURE ILLEGIBLE]
                                      ---------------------------------------
                                      Title: VICE PRESIDENT