
<PAGE>   1
                                                                 Exhibit 10.2(b)


                       SECOND AMENDED MANAGEMENT AGREEMENT


                  THIS SECOND AMENDED MANAGEMENT AGREEMENT (this "Agreement") is
made as of the ____day of ___________, 1999 by and among Charter Investment,
Inc., a Delaware corporation (formerly known as Charter Communications, Inc.)
("Investment"), Charter Communications, Inc., a Delaware Corporation ("CCI"),
and Charter Communications Operating, LLC, a Delaware limited liability company
("Charter Operating").

                                    RECITALS

         A.       Investment and Charter Operating entered into an Amended and
Restated Management Agreement dated as of March 17, 1999 (the "Management
Agreement").

         B.       In connection with an initial public offering of CCI common
stock, the parties wish to amend the Management Agreement and CCI wishes to
acquire all of Investment's right, title and interest under the Management
Agreement and to assume all of Investment's obligations and liabilities under
the Management Agreement.

                  NOW, THEREFORE, in consideration of the mutual covenants and
agreements contained herein, and for other good and valuable consideration, the
receipt and sufficiency of which is hereby acknowledged, the parties hereto
hereby agree as follows:

         1.       Amendment. Upon the Effective Date (as defined below), the
first paragraph of Section 3(a) of the Management Agreement shall be amended to
read as follows:

                  "All expenses, costs, losses, liabilities or damages incurred
         with respect to the ownership or operation of the Cable Systems,
         including, without limitation, wages, salaries and other labor costs
         incurred in the construction, maintenance, expansion or operation of
         the Cable Systems, or personnel working on special projects or services
         for the Company, will be paid by the Company and, to the extent that
         the Manager pays or incurs any obligation for any such expenses, costs,
         losses, liabilities or damages, the Company, subject to the limitations
         set forth in Section 5, will pay or reimburse the Manager therefor, as
         well as for any reasonable out-of-pocket expenses incurred by the
         Manager in the performance of its obligations under this Agreement.
         Subject to the payment priority provisions of this Section 3, the
         Company agrees to pay the Manager such costs and expenses, which shall
         include all the costs, expenses, liabilities and damages incurred by
         the Manager in performing its obligations hereunder and any payments
         that the Manager may become obligated to pay pursuant to the Mutual
         Services Agreement (the "Management Expenses") monthly in arrears,
         provided, that in no event shall the aggregate Management Expenses paid
         during any fiscal quarter exceed three percent (3.0%) of the Gross
         Revenue (as determined in accordance with generally accepted accounting
         principles) of the Company for that quarter. "Gross Revenue" will
         include all revenues from the operation of the Cable Systems including,
         without limitation, subscriber payments, advertising revenues and


                                       1
<PAGE>   2
         revenues from other services provided by the Cable Systems, but not
         including interest income or income from investments unrelated to the
         Cable Systems. Accrual of such Management Expenses shall commence upon
         the Effective Date (as defined below) of this Agreement. The Management
         Expenses payable pursuant to this paragraph for any month shall be
         reduced by the amount of any management fees and expenses with respect
         to Gross Revenue of a subsidiary of the Company and separately paid to
         the Manager for such month pursuant to a separate management agreement
         between the Manager and a subsidiary of the Company."

         2.       Assignment and Assumption of Management Agreement.

                  (a)      Upon the Effective Date, Investment hereby fully and
                           completely assigns to CCI all of Investment's right,
                           title and interest in and to, and its obligations
                           under, the Management Agreement.

                  (b)      Upon the Effective Date, CCI hereby fully and
                           completely assumes all of Investment's right, title
                           and interest in and to, and agrees to perform when
                           due, all obligations of Investment under, the
                           Management Agreement.

         3.       Mutual Services Agreement. Nothing contained herein shall
affect Investment's obligations under the Mutual Services Agreement dated as of
the date hereof.

         4.       Effective Date. This Agreement shall become effective only
upon the closing (the "Effective Date") of the initial public offering of CCI as
contemplated by its Registration Statement on Form S-1 filed with the Securities
and Exchange Commission. If such closing does not occur for any reason, or has
not occurred by January 1, 2000, this Agreement shall be of no force or effect
and none of Investment, CCI or Charter Operating shall have any rights,
obligations or liabilities under or arising out of this Agreement.

         5.       Amendments. This Agreement cannot be amended, waived, or
terminated except by a writing signed by all parties.

         6.       Counterparts. This Agreement may be executed in two or more
separately executed counterparts, which may include faxed signature pages, each
of which counterparts shall be deemed an original, but all of which together
shall constitute one and the same instrument.


                                       2
<PAGE>   3
                  IN WITNESS WHEREOF, the parties hereto have caused this Second
Amended Management Agreement to be duly executed and delivered as of the date
first above written and effective as of the Effective Date.


                                       CHARTER INVESTMENT, INC.,
                                       a Delaware corporation



                                       By:__________________________________
                                          Name:
                                          Title:


                                       CHARTER COMMUNICATIONS, INC.,
                                       a Delaware corporation



                                       By:__________________________________
                                          Name:
                                          Title:



                                       CHARTER COMMUNICATIONS OPERATING, LLC,
                                       a Delaware limited liability company



                                       By:__________________________________
                                          Name:
                                          Title:


                                       3
