<PAGE>
                                                                    EXHIBIT 10.4



                                    SECOND AMENDMENT (this "Amendment") dated as
                           of June 28, 2002 in respect of the FIVE-YEAR CREDIT
                           AGREEMENT dated as of September 26, 2000 (the "Credit
                           Agreement"), among Cox Communications, Inc., the
                           banks party thereto (the "Banks"), JPMorgan Chase
                           Bank, as administrative agent, The Bank of New York
                           and Wachovia Bank, National Association, as
                           co-documentation agents (the "Documentation Agents")
                           and Bank of America, N.A., as syndication agent (the
                           "Syndication Agent").

                  A.       The parties hereto have agreed, subject to the terms
and conditions hereof, to amend the Credit Agreement as set forth herein on the
terms and subject to the conditions provided herein.

                  B.       Capitalized terms used and not otherwise defined
herein shall have the meanings assigned to such terms in the Credit Agreement.

                  SECTION 1. (a) Amendment to Section 1.01. Section 1.01 is
hereby amended by (i) deleting the definition of "Consolidated Annualized
Operating Cash Flow" in its entirety, and substituting therefor the following:

                  "'Consolidated Annualized Operating Cash Flow' shall mean the
sum of (i) four times operating income of the Company and its Restricted
Subsidiaries for the most recently completed fiscal quarter (less cash dividends
and other cash distributions to the holders of minority interests in the
Company's Restricted Subsidiaries), before giving effect to depreciation,
amortization, equity in earnings (losses) of unconsolidated investees on a
consolidated basis determined in accordance with GAAP and nonrecurring one-time
charges and (ii) cash dividends and cash distributions paid (other than
extraordinary distributions) to the Company and its Restricted Subsidiaries
during the most recently completed fiscal quarter and the three immediately
preceding fiscal quarters by unconsolidated investees of the Company and its
Restricted Subsidiaries, on a consolidated basis determined in accordance with
GAAP." and


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                  (ii) in the definition of "364-Day Agreement", replacing the
date "September 26, 2000" with the date "June 28, 2002".

                  (b) Amendment to Section 4.01(b). Section 4.01(b) is hereby
amended by replacing the percentage "50%" with the percentage "33 1/3%", and by
replacing the phrase "shall accrue at the rate of .10% per annum" with the
phrase "shall accrue at the rate of .25% per annum".

                  (c) Amendment to Section 7.01. Section 7.01 is hereby amended
by deleting the entire section and substituting therefor the following:

                  "Section 7.01.  [Intentionally Omitted]."

                  (d) Amendment to Section 7.04. Section 7.04 is hereby amended
by deleting the entire section and substituting therefor the following:

                  "Section 7.04.  [Intentionally Omitted]."

                  (e) Amendment to Section 8.02. The final paragraph of Section
8.02 is hereby amended by deleting the third sentence thereof and substituting
therefor the following:

                  "Together with each delivery of financial statements required
by clause (a) above, the Company will deliver to each Bank a written statement
of said accountants that, in conducting the audit necessary to the issuance of
an opinion on such financial statements, nothing came to their attention that
caused them to believe that an Event of Default or Default relating to financial
and accounting matters (an "Accounting Event of Default or Default") had
occurred, or, if such accountants shall have obtained knowledge of any such
Accounting Event of Default or Default, such statement shall specify the nature
and period of existence thereof; provided that such accountants shall not be
liable directly or indirectly to any Bank for failure to obtain knowledge of any
such Accounting Event of Default or Default; and provided further that in
issuing such statement, such accountants shall not be required to go beyond
those auditing procedures conducted in connection with their issuance of the
opinion referred to above."

                  (f) Amendment to Section 10.03. Section 10.03 is hereby
amended by inserting the following text at the end of clause (i) therein:

                  "provided that a default under other Debt of the Company or
any Restricted Subsidiary as described in this clause (i) shall not constitute
an Event of Default under

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                                                                               3


this agreement unless (x) the Company or such Restricted Subsidiary is aware of
the default under such other Debt and, if no grace period of at least 3 days is
provided for under the other Debt, 3 days have passed since the Company or
Restricted Subsidiary became aware of such default, without the curing of the
default or (y) such other Debt has become due prior to the maturity thereof; and
provided further that, during the continuance of any applicable grace period or
such 3 day period, any such failure to pay such other Debt when due shall
constitute a Default (but not an Event of Default) hereunder;"

                  SECTION 2. Representations and Warranties. The Company hereby
represents and warrants to the Administrative Agent and the Banks that:

         (a)      This Amendment has been duly authorized, executed and
delivered by it and constitutes its legal, valid and binding obligations
enforceable in accordance with its terms.

         (b)      As of the date hereof, and after giving effect to this
Amendment, no Default or Event of Default has occurred and is continuing and the
representations and warranties contained in the Credit Agreement, as amended by
this Amendment, are true and correct in all material respects as if made on the
date hereof.

                  SECTION 3. Effectiveness. The effectiveness of this Amendment
is subject to the satisfaction on the date hereof of the following conditions:

                  (a) the Administrative Agent shall have received executed
         counterparts of this Amendment which, when taken together, bear the
         signatures of the Company and the Majority Banks; and

                  (b) the Administrative Agent shall have received all fees and
         other amounts payable in connection with this Amendment on or prior to
         the date hereof, including, to the extent invoiced, reimbursement or
         payment of all out-of-pocket expenses required to be reimbursed or paid
         by the Company hereunder.

         Following the satisfaction on the date hereof of the conditions set
forth above, the Administrative Agent shall


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                                                                               4


inform the Company in writing that this Amendment has become effective.

                  SECTION 4. Counterparts. This Amendment may be signed in any
number of counterparts, each of which shall constitute an original but all of
which when taken together shall constitute but one contract. Delivery of an
executed counterpart of a signature page by facsimile transmission shall be
effective as delivery of a manually executed counterpart of this Amendment.

                  SECTION 5. APPLICABLE LAW. THIS AMENDMENT SHALL BE DEEMED TO
BE AN AGREEMENT EXECUTED UNDER THE LAWS OF THE STATE OF NEW YORK AND OF THE
UNITED STATES AND FOR ALL PURPOSES SHALL BE CONSTRUED IN ACCORDANCE WITH, AND
GOVERNED BY, THE LAWS OF SAID STATE AND OF THE UNITED STATES.

                  SECTION 6. Credit Agreement. As used in the Credit Agreement
and the Exhibits thereto, the terms "Agreement", "herein", "hereinafter",
"hereunder", "hereto", and words of similar import shall mean, from and after
the date hereof, the Credit Agreement as amended by this Amendment.

                  SECTION 7. Expenses. The Company shall, in accordance with the
provisions of Section 13.01 of the Credit Agreement, pay all reasonable
out-of-pocket expenses incurred by the Administrative Agent and the Banks in
connection with the preparation, negotiation, execution, delivery and
enforcement of this Amendment, including, but not limited to, the reasonable
fees and disbursements of Cravath, Swaine & Moore. The agreement set forth in
this Section 7 shall survive the termination of this Amendment.

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                                                                               5


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


                                         COX COMMUNICATIONS, INC.,

                                            by
                                                 /s/   Susan W. Coker
                                             -----------------------------------
                                             Name:  Susan W. Coker
                                             Title: Treasurer


                                         JPMORGAN CHASE BANK, individually
                                         and as Administrative Agent,

                                            by
                                              /s/ Constance M. Coleman
                                             -----------------------------------
                                             Name:  Constance M. Coleman
                                             Title: Vice President


                                         BANK OF AMERICA, N.A., Individually
                                         and as Co-Syndication Agent

                                            by
                                               /s/ Pamela S. Kurtzman
                                             -----------------------------------
                                             Name:  Pamela S. Kurtzman
                                             Title: Principal


                                         CITIBANK, N.A.

                                            by
                                             /s/ Elizabeth H. Minnella
                                             -----------------------------------
                                             Name:  Elizabeth H. Minnella
                                             Title: Director


                                         THE BANK OF NEW YORK

                                           by
                                              /s/   Cynthia L. Rogers
                                             -----------------------------------
                                             Name:  Cynthia L. Rogers
                                             Title: Vice President

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                                       FLEET NATIONAL BANK

                                         by
                                            /s/   William Weiss
                                           ----------------------------------
                                           Name:  William Weiss
                                           Title: Vice President


                                       SUNTRUST BANK

                                         by
                                            /s/   Thomas C. Palmer
                                           ----------------------------------
                                           Name:  Thomas C. Palmer
                                           Title: Managing Director


                                       BANK OF TOKYO-MITSUBISHI TRUST COMPANY

                                         by
                                            /s/   Spencer Hughes
                                           ----------------------------------
                                           Name:  Spencer Hughes
                                           Title: VP & Manager


                                       COMMERZBANK NEW YORK AND GRAND
                                       CAYMAN BRANCHES

                                         by
                                            /s/   Brian Campbell
                                           ----------------------------------
                                           Name:  Brian Campbell
                                           Title: Senior Vice President

                                         by
                                            /s/   Subash Viswanathan
                                           ----------------------------------
                                           Name:  Subash Viswanathan
                                           Title: Senior Vice President

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                                       CREDIT SUISSE FIRST BOSTON


                                           by
                                               /s/   Jay Chall
                                              -------------------------------
                                           Name:  Jay Chall
                                           Title: Director

                                           by
                                               /s/   Jeffrey Bernstein
                                              -------------------------------
                                           Name:  Jeffrey Bernstein
                                           Title: Vice President



                                       DRESDNER BANK AG, NEW YORK AND GRAND
                                       CAYMAN BRANCHES

                                         by
                                            /s/   Michael S. Greenberg
                                           ----------------------------------
                                           Name:  Michael S. Greenberg
                                           Title: Vice President

                                         by
                                            /s/   William E. Lambert
                                           ----------------------------------
                                           Name:  William E. Lambert
                                           Title: Vice President


                                       WESTDEUTSCHE LANDESBANK GIROZENTRALE

                                         by
                                            /s/   Pascal Kabemba
                                           ----------------------------------
                                           Name:  Pascal Kabemba
                                           Title: Associate Director

                                         by
                                            /s/   Lisa Walker
                                           ----------------------------------
                                           Name:  Lisa Walker
                                           Title: Associate Director


                                       BANK OF OKLAHOMA, N.A.

                                         by
                                            /s/   Mark A. Fish
                                           ----------------------------------
                                           Name:  Mark A. Fish
                                           Title: Senior Vice President


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                                       THE BANK OF NOVA SCOTIA

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


                                       ABN AMRO BANK N.V.

                                           by
                                               /s/   David C. Carrington
                                              -------------------------------
                                           Name:  David C. Carrington
                                           Title: Group Vice President

                                           by
                                               /s/   Craig Shirey
                                              -------------------------------
                                           Name:  Craig Shirey
                                           Title: Corporate Banking Officer


                                       FIRST HAWAIIAN BANK

                                         by
                                            /s/   Seydou Diallo
                                           ----------------------------------
                                           Name:  Seydou Diallo
                                           Title: Media Finance Officer