<PAGE>
                                                                   EXHIBIT 10.1

                     JOINDER AGREEMENT AND ACKNOWLEDGEMENT

         This Joinder Agreement and Acknowledgement of Rights and Obligations
(this "Agreement and Acknowledgement") is made and entered into as of August
31, 2002, by and among Cox Communications, Inc., a Delaware corporation (the
"Company"), G.C. Investments, A Limited Liability Company ("Assignor"), Barbara
J. Greenspun as Trustee of the Unified Credit Trust created under a Declaration
of Trust dated December 6, 1988, being all of the parties to that certain
Registration Rights Agreement dated as of October 1, 1998 (the "Registration
Rights Agreement") and that certain First Offer Agreement dated as of October
1, 1998 (the "First Offer Agreement"), Greenspun Legacy Limited Partnership
("Legacy") and 3G Capital, LLC ("3G Capital"). Capitalized terms used but not
defined herein have the meanings ascribed to them in the Registration Rights
Agreement.

                                    RECITALS

         WHEREAS, in 1999, Assignor transferred to Legacy 345,572 shares of
Common Stock (the "Legacy Common Shares") and 1,382,290 shares of Series A
Preferred Stock (the "Legacy Preferred Shares" and with the Legacy Common
Shares, the "Legacy Shares"), which Legacy Shares were acquired by Assignor
pursuant to the Merger Agreement;

         WHEREAS, Assignor desires to transfer to 3G Capital 3,430,964 shares
of Common Stock (the "3G Common Shares") and 628,931 shares of Series A
Preferred Stock (the "3G Preferred Shares" and with the 3G Common Shares, the
"3G Shares"), which 3G Shares were acquired by the Assignor pursuant to the
Merger Agreement; and

         WHEREAS, Legacy and 3G Capital desire to become parties to the
Registration Rights Agreement in accordance with Section 13 thereof, and to
acknowledge the Company's rights and their respective obligations under the
First Offer Agreement in accordance with Section 4(d) thereof.

                                   AGREEMENTS

         NOW, THEREFORE, in consideration of the foregoing, and for other good
and valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, the parties hereto, intending to be legally bound, agree as
follows:

         1.       Joinder. By executing this Agreement and Acknowledgement,
Legacy and 3G Capital shall become, and shall be deemed for all purposes to be,
signatories to the Registration Rights Agreement as Stockholders, with the same
force and effect as if Legacy and 3G Capital had been original signatories
thereto, and Legacy and 3G Capital acknowledge, accept and agree to, and shall
be bound by, all of the terms and conditions of the Registration Rights
Agreement.

         2.       Assumption. Legacy and 3G Capital hereby assume and agree to
perform all liabilities and obligations of Assignor with ---------- respect to
the Legacy Shares and the 3G Shares, respectively, under the Registration
Rights Agreement.

         3.       Acknowledgement of Rights and Obligations. As of the
respective dates of transfer of the Legacy Preferred Shares and the 3G
Preferred Shares, each of Legacy and 3G


<PAGE>

Capital (a) acknowledges (i) the rights of the Company with respect to the
Legacy Preferred Shares and the 3G Preferred Shares as set forth in Section 4
of the First Offer Agreement and (ii) in accordance with Section 4(d)
thereunder, its respective obligations thereunder as a Greenspun Affiliate
transferee, (b) accepts and agrees to, and shall be bound by, all of the terms
and conditions of the First Offer Agreement and (c) assumes and agrees to
perform all liabilities and obligations of Assignor thereunder with respect to
the Legacy Preferred Shares and the 3G Preferred Shares, respectively.

         4.       Representations and Warranties of Legacy and 3G Capital.
Legacy and 3G Capital hereby severally represent and warrant that:

                  (a)      Legacy and 3G Capital are duly authorized, and have
         the power and authority, to execute and deliver this Agreement and
         Acknowledgement and to perform all obligations (i) with respect to the
         Legacy Shares and 3G Shares, respectively, under the Registration
         Rights Agreement, and (ii) with respect to the Legacy Preferred Shares
         and 3G Preferred Shares, respectively, under the First Offer
         Agreement;

                  (b)      The execution, delivery and performance by Legacy and
         3G Capital of this Agreement and Acknowledgement, and the performance
         by Legacy and 3G Capital of the Registration Rights Agreement and the
         First Offer Agreement do not require the consent, approval or
         authorization of, notice to or filing with any person or any federal,
         state, or local governmental authority;

                  (c)      The Registration Rights Agreement and any rights or
         obligations of Legacy and 3G Capital thereunder or under the First
         Offer Agreement will not conflict with, result in a breach or
         violation of, or result in the imposition of any lien upon any
         property or assets of Legacy or 3G Capital pursuant to (i) the terms
         of any indenture, contract, lease, mortgage, deed of trust, note
         agreement, loan agreement or other agreement, obligation, condition,
         covenant or instrument to which Legacy or 3G Capital is a party or to
         which any of their respective assets or property is subject, (ii) any
         provision of the applicable organizational documents of Legacy or 3G
         Capital or (iii) any statute, law, rule, regulation, judgment, order
         or decree applicable to Legacy or 3G Capital of any court, regulatory
         body, administrative agency, governmental body, arbitrator or other
         authority having jurisdiction over Legacy or 3G Capital or any of
         their respective assets or properties; and

                  (d)      Each of Legacy and 3G Capital is a "Greenspun
         Affiliate," as such term is defined in the Certificate of Designations
         for the Series A Preferred Stock.

         5.       Consent of Parties. Pursuant to Section 13 of the Registration
Rights Agreement, by executing this Agreement and Acknowledgement the parties
hereto expressly consent to the assignment of the rights and obligations of
Assignor with respect to the Legacy Shares and the 3G Shares to Legacy and 3G
Capital, respectively. Other than with respect to the Legacy Shares and the 3G
Shares, the rights and obligations of the Assignor under the Registration
Rights Agreement remain the same.


                                      -2-
<PAGE>

         6.       Governing Law. This Agreement and Acknowledgement and all
disputes hereunder shall be governed by, and construed and enforced, in
accordance with the laws of the State of Delaware, without giving effect to any
choice or conflict of laws provision or rule that would cause the application
of the laws of any other jurisdiction.

         7.       Name, Captions. The name assigned this Agreement and
Acknowledgement and the section captions used herein are for convenience of
reference only and shall not affect the interpretation or construction hereof.

         8.       Further Assurances. Assignor, Legacy and 3G Capital agree to
perform any further acts and execute and deliver any additional documents and
instruments reasonably requested by the Company that may be necessary to carry
out the provisions of this Agreement and Acknowledgement.

         9.       Counterparts. This Agreement and Acknowledgement may be
executed in any number of counterparts, each of which shall be deemed an
original, but all of which together shall constitute one instrument. Each
counterpart may consist of a number of copies each signed by less than all, but
together signed by all, the parties hereto.

                            [Signature Page Follows]


                                      -3-
<PAGE>

         IN WITNESS WHEREOF, the parties have duly executed this Agreement and
Acknowledgement as of the date first above written.


                            COX COMMUNICATIONS, INC.




                            By:  /s/  John M. Dyer
                                -----------------------------------------------
                                Name:     John M. Dyer
                                Title:    Senior Vice President


                            GREENSPUN LEGACY LIMITED PARTNERSHIP




                            By:  /s/  Brian L. Greenspun
                                -----------------------------------------------
                                Name:  Brian L. Greenspun


                            3G CAPITAL, LLC




                            By:  /s/  Brian L. Greenspun
                                -----------------------------------------------
                                Brian L. Greenspun, Manager


                            G.C. INVESTMENTS, A LIMITED LIABILITY COMPANY




                            By:  /s/  Brian L. Greenspun
                                -----------------------------------------------
                                Brian L. Greenspun, Manager


                            UNIFIED CREDIT TRUST, created under a Declaration of
                            Trust dated December 6, 1988




                            By:  /s/  Barbara J. Greenspun
                                -----------------------------------------------
                                Barbara J. Greenspun, Trustee