<PAGE>

                                  EXHIBIT 3.8

                          OLYMPUS COMMUNICATIONS, L.P.

                             THIRD AMENDMENT TO THE
                          SECOND AMENDED AND RESTATED
                         LIMITED PARTNERSHIP AGREEMENT

          This Third Amendment dated as of October 1, 1999 to the Second Amended
and Restated Limited Partnership Agreement of Olympus Communications, L.P.
entered into as of February 28, 1995, by and among ACP Holdings, Inc., a
Delaware corporation ("ACP Holdings"), as the managing general partner (the
"Managing General Partner"), ACP Holdings, Inc., as a preferred limited partner
(a "Preferred Limited Partner"), Cable GP, Inc. a Florida corporation ("Cable
GP"), as the general partner (the "General Partner"), Cable GP, as the limited
partner (the "Limited Partner"), Cable GP, as a senior limited partner (the
"Senior Limited Partner"), Cable GP, as a special limited partner (a "Special
Limited Partner") and Cable GP, as a preferred limited partner (a "Preferred
Limited Partner" and together with the other Preferred Limited Partner, the
"Preferred Limited Partners").  The Managing General Partner, the General
Partner, the Limited Partner, the Special Limited Partner, the Preferred Limited
Partners and the Senior Limited Partner shall collectively be referred to as the
"Partners."

                                  WITNESSETH:

          WHEREAS, the ACP Holdings, Cable GP and Cable LP III, Inc. entered
into the Second Amended and Restated Limited Partnership Agreement as of
February 28, 1995 which Partnership Agreement has been amended (the "Partnership
Agreement") and agreed to be governed by the provisions of the Delaware Revised
Uniform Limited Partnership Act and the Partnership Agreement;

<PAGE>

          WHEREAS, the Partners desire to execute this Third Amendment to the
Second Amended and Restated Limited Partnership Agreement to reflect the
amendment of certain provisions of the Partnership Agreement; and

          WHEREAS, each of the capitalized terms not defined herein shall have
the meaning ascribed to them in the Partnership Agreement.

          NOW, THEREFORE, in consideration of the mutual promises and covenants
herein and intending to be legally bound, the Partners agree as follows:

          1. The Partnership Agreement is hereby amended by adding the
following new Section 12.12:

               Redemption of Partnership Interests.  Notwithstanding the
               -----------------------------------
          provisions of Section 17-702(d) of the Delaware Revised Uniform
          Partnership Act, upon the Partnership's acquisition of an interest in
          the Partnership by purchase, redemption or otherwise, the Managing
          General Partner may determine that any such partnership interests will
          not be cancelled.

          2. This Third Amendment may be executed in one or more counterparts,
each of which shall be deemed an original, but all of which taken together
shall constitute one and the same instrument. Delivery of executed signature
pages hereof by facsimile transmission shall constitute effective and binding
execution and delivery hereof.

                                      -2-
<PAGE>

          IN WITNESS WHEREOF, the undersigned have executed this Third Amendment
to the Second Amended and Restated Limited Partnership Agreement as of the date
first above written.
                             MANAGING GENERAL PARTNER:

                             ACP HOLDINGS, INC.


                              By:   /s/  Michael C. Mulcahey
                                   -------------------------
                              Name: Michael C. Mulcahey
                              Title: Assistant Treasurer



                             GENERAL PARTNER:

                             CABLE GP, INC.


                             By:  /s/  Dennis P. Coyle
                                  --------------------
                             Name:  Dennis P. Coyle
                             Title:  President


                             LIMITED PARTNER:

                             CABLE GP, INC.


                             By:  /s/  Dennis P. Coyle
                                  --------------------
                             Name:  Dennis P. Coyle
                             Title:  President


                             PREFERRED LIMITED PARTNERS:

                             ACP HOLDINGS, INC.


                              By:   /s/  Michael C. Mulcahey
                                   -------------------------
                              Name: Michael C. Mulcahey
                              Title: Assistant Treasurer

                                      -3-
<PAGE>

                             CABLE GP, INC.


                             By:  /s/  Dennis P. Coyle
                                  --------------------
                             Name:  Dennis P. Coyle
                             Title:  President


                             SPECIAL LIMITED PARTNER:

                             CABLE GP, INC.

                             By:  /s/  Dennis P. Coyle
                                  --------------------
                             Name:  Dennis P. Coyle
                             Title:  President


                             SENIOR LIMITED PARTNER:

                             CABLE GP, INC.


                             By:  /s/  Dennis P. Coyle
                                  --------------------
                             Name:  Dennis P. Coyle
                             Title:  President

                                      -4-