<PAGE>   1
                                                                     EXHIBIT 4.2

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                               GUARANTEE AGREEMENT


                COX COMMUNICATIONS, INC. and THE BANK OF NEW YORK


            Relating to the Preferred Securities of Cox RHINOS Trust


                           Dated as of October 6, 1999


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<PAGE>   2



                             CROSS REFERENCE TABLE(1)

<TABLE>
<CAPTION>

Section of Trust                                                                         Section of
Indenture Act Of                                                                          Guarantee
1939, as amended                                                                          Agreement


<S>                                                                                   <C>
310(a)......................................................................................4.01(a)
310(b) ...............................................................................4.01(c), 2.08
310(c).................................................................................Inapplicable
311(a)......................................................................................2.02(b)
311(b)......................................................................................2.02(b)
311(c).................................................................................Inapplicable
312(a)......................................................................................2.02(a)
312(b)......................................................................................2.02(b)
313............................................................................................2.03
314 (a)........................................................................................2.04
314(b).................................................................................Inapplicable
314(c).........................................................................................2.05
314(d).................................................................................Inapplicable
314(e).............................................................................1.01, 2.03, 3.02
314(f).........................................................................................3.02
315(a)......................................................................................3.01(d)
315(b).........................................................................................2.07
315(c).........................................................................................3.01
315(d)......................................................................................3.01(d)
316(a).............................................................................1.01, 2.06, 5.04
316(b).........................................................................................5.03
317(a).................................................................................Inapplicable
317(b).................................................................................Inapplicable
318(a)......................................................................................2.01(b)
318(b).........................................................................................2.01
318(c)......................................................................................2.01(a)

</TABLE>

--------
         (1) This Cross-Reference Table does not constitute part of this
Guarantee Agreement and shall not affect the interpretation of any of its terms
or provisions.


                                        2

<PAGE>   3


                                TABLE OF CONTENTS

<TABLE>
<CAPTION>

                                                                                               PAGE
                                                                                               ----

                                             ARTICLE 1
                                            DEFINITIONS

<S>            <C>                                                                               <C>
SECTION 1.01.  Definitions........................................................................2

                                             ARTICLE 2
                                        TRUST INDENTURE ACT

SECTION 2.01.  Trust Indenture Act; Application...................................................4
SECTION 2.02.  List of Holders....................................................................5
SECTION 2.03.  Reports by the Guarantee Trustee...................................................5
SECTION 2.04.  Periodic Reports to Guarantee Trustee..............................................5
SECTION 2.05.  Evidence of Compliance with Conditions Precedent...................................5
SECTION 2.06.  Events of Default; Waiver..........................................................6
SECTION 2.07.  Events of Default; Notice..........................................................6
SECTION 2.08.  Conflicting Interests..............................................................6

                                             ARTICLE 3
                        POWERS, DUTIES AND RIGHTS OF THE GUARANTEE TRUSTEE

SECTION 3.01.  Powers and Duties of the Guarantee Trustee.........................................7
SECTION 3.02.  Certain Rights of Guarantee Trustee................................................8
SECTION 3.03.  Indemnity.........................................................................10

                                             ARTICLE 4
                                         GUARANTEE TRUSTEE

SECTION 4.01.  Guarantee Trustee; Eligibility....................................................11
SECTION 4.02.  Appointment, Removal and Resignation of the Guarantee
         Trustee.................................................................................11

                                             ARTICLE 5
                                             GUARANTEE

SECTION 5.01.  Guarantee.........................................................................12
SECTION 5.02.  Waiver of Notice and Demand.......................................................12
SECTION 5.03.  Obligations Not Affected..........................................................12
SECTION 5.04.  Rights of Holders.................................................................13
SECTION 5.05.  Guarantee of Payment..............................................................14

SECTION 5.06.  Subrogation.......................................................................14
SECTION 5.07.  Independent Obligations...........................................................14

                                             ARTICLE 6
                                       COVENANTS AND STATUS

SECTION 6.01.  Status of this Guarantee Agreement................................................15
SECTION 6.02.  Certain Covenants of the Guarantor................................................15

</TABLE>


<PAGE>   4

<TABLE>
<CAPTION>

                                                                                               PAGE
                                                                                               ----

                                             ARTICLE 7
                                            TERMINATION

<S>            <C>                                                                               <C>
SECTION 7.01.  Termination.......................................................................16

                                             ARTICLE 8
                                           MISCELLANEOUS

SECTION 8.01.  Successors and Assigns............................................................16
SECTION 8.02.  Amendments........................................................................17
SECTION 8.03.  Notices...........................................................................17
SECTION 8.04.  Benefit...........................................................................18
SECTION 8.05.  Interpretation....................................................................18
SECTION 8.06.  Governing Law.....................................................................19
SECTION 8.07.  Counterparts......................................................................19

</TABLE>


                                       ii

<PAGE>   5



                               GUARANTEE AGREEMENT


         This GUARANTEE AGREEMENT dated as of October 6, 1999 is executed and
delivered by COX COMMUNICATIONS, INC., a Delaware corporation (the "GUARANTOR"),
and THE BANK OF NEW YORK, a New York banking corporation, as trustee (the
"GUARANTEE TRUSTEE"), for the benefit of the holders from time to time of the
Preferred Securities (as defined herein) of COX RHINOS TRUST, a Delaware
statutory business trust (the "ISSUER").

         WHEREAS, pursuant to the Amended and Restated Trust Agreement (the
"TRUST AGREEMENT"), dated as of October 6, 1999 among the Trustees named
therein, the Guarantor, as Sponsor, and the holders from time to time of
undivided beneficial interests in the assets of the Issuer, the Issuer is
issuing 500,000 of its Auction Rate Reset Preferred Securities (liquidation
preference $1,000 per preferred security) (the "PREFERRED SECURITIES")
representing preferred undivided beneficial interests in the assets of the
Issuer and having the terms set forth in the Trust Agreement;

         WHEREAS, the Preferred Securities will be issued by the Issuer and the
proceeds thereof, together with the proceeds from the issuance by the Issuer of
the Common Securities (as defined herein), will be used to purchase the Senior
Notes (as defined in the Trust Agreement) of the Guarantor, which will be
deposited with The Bank of New York, as Property Trustee under the Trust
Agreement, as trust assets;

         WHEREAS, as incentive for Holders (as defined herein) to purchase
Preferred Securities, the Guarantor desires irrevocably and unconditionally to
agree, to the extent set forth herein, to pay the Guarantee Payments (as defined
herein) to the Holders and to make certain other payments on the terms and condi
tions set forth herein; and

         WHEREAS, the Guarantor is executing and delivering for the benefit of
the holders of the Common Securities a guarantee agreement (the "COMMON
SECURITIES GUARANTEE") with terms substantially identical to those of this
Guarantee Agreement, except that if an Event of Default (as defined in the
Indenture (as defined herein)) has occurred and is continuing, the rights of
holders of the Common Securities to receive payments under the Common Securities
Guarantee shall be subordinated to the rights of Holders to receive Guarantee
Payments (as defined herein) under this Guarantee Agreement;

         NOW, THEREFORE, in consideration of the purchase by each Holder, which
purchase the Guarantor hereby agrees shall benefit the Guarantor, the Guarantor
executes and delivers this Guarantee Agreement for the benefit of the
Holders.


<PAGE>   6


                                    ARTICLE 1
                                   DEFINITIONS

         SECTION 1.01. Definitions. As used in this Guarantee Agreement, the
terms set forth below shall, unless the context otherwise requires, have the
following meanings. Capitalized or otherwise defined terms used but not
otherwise defined herein shall have the meanings assigned to such terms in the
Trust Agreement as in effect on the date hereof.

         "AFFILIATE" of any specified Person means any other Person directly or
indirectly controlling or controlled by or under direct common control with such
specified Person, provided, however, that an Affiliate of the Guarantor shall
not be deemed to include the Issuer. For the purposes of this definition,
"CONTROL" when used with respect to any specified Person means the power to
direct the management and policies of such Person, directly or indirectly,
whether through the ownership of voting securities, by contract or otherwise;
and the terms "CONTROLLING" and "CONTROLLED" have meanings correlative to the
foregoing.

         "COMMON SECURITIES" means the securities representing common beneficial
interests in the assets of the Issuer.

         "EVENT OF DEFAULT" means a default by the Guarantor on any of its
payment or other obligations under this Guarantee Agreement; provided that,
except with respect to a default in payment of any Guarantee Payments, the
Guarantor shall have received written notice of default and shall not have cured
such default within 60 days after receipt of such notice.

         "GUARANTEE PAYMENTS" means the following payments or distributions,
without duplication, with respect to the Preferred Securities, to the extent not
paid or made by or on behalf of the Issuer: (i) any accrued and unpaid
Distributions (as defined in the Trust Agreement) required to be paid on the
Preferred Securities to the extent the Issuer shall have funds available
therefor, (ii) the redemption price, including all accrued and unpaid
Distributions to the date of redemption (the "REDEMPTION PRICE"), to the extent
the Issuer shall have funds available therefor, with respect to the Preferred
Securities called for redemption by the Issuer and (iii) upon a voluntary or
involuntary dissolution, winding-up or liquidation of the Issuer, unless the
Senior Notes are distributed to Holders, the lesser of (a) the aggregate of the
liquidation amount and all accrued and unpaid Distributions on the Preferred
Securities to the date of payment, to the extent the Issuer shall have funds
available therefor and (b) the amount of assets of the Issuer remaining
available for distribution to Holders in liquidation of the Issuer (in either
case, the "LIQUIDATION DISTRIBUTION").


                                        2

<PAGE>   7


         "GUARANTEE TRUSTEE" means The Bank of New York, until a Successor
Guarantee Trustee has been appointed and has accepted such appointment pursuant
to the terms of this Guarantee Agreement and thereafter means each such
Successor Guarantee Trustee.

         "HOLDER" means any holder, as registered on the books and records of
the Issuer, of any Preferred Securities; provided that in determining whether
the holders of the requisite percentage of Preferred Securities have given any
request, notice, consent or waiver hereunder, "HOLDER" shall not include the
Guarantor or any Affiliate of the Guarantor.

         "INDENTURE" means the Indenture dated as of June 27, 1995 between the
Guarantor and The Bank of New York, as trustee (the "INDENTURE TRUSTEE"), as
supplemented by the Second Supplemental Indenture dated as of October 6, 1999
between the Guarantor and the Indenture Trustee and as further amended,
supplemented, modified or superseded from time to time.

         "LIST OF HOLDERS" has the meaning specified in Section 2.02(a).

         "MAJORITY IN LIQUIDATION AMOUNT OF THE PREFERRED SECURITIES" means,
except as provided by the Trust Indenture Act, a vote by the Holder(s), voting
separately as a class, of more than 50% of the aggregate liquidation amount of
all the outstanding Preferred Securities issued by the Issuer.

         "OFFICER'S CERTIFICATE" means, with respect to any Person, a
certificate signed by the Chairman, Chief Executive Officer, President or a Vice
President and delivered to the Guarantee Trustee. Any Officer's Certificate
delivered with respect to compliance with a condition or covenant provided for
in this Guarantee Agreement shall include:

         (a) a statement that the officer signing the Officer's Certificate has
read or has caused someone under the officer's supervision to read the covenant
or condition and the definitions relating thereto;

         (b) a brief statement of the nature and scope of the examination or
investigation undertaken by such officer in rendering the Officer's Certificate;

         (c) a statement that such officer has made such examination or
investigation as, in such officer's opinion, is necessary to enable such officer
to express an informed opinion as to whether or not such covenant or condition
has been complied with; and

         (d) a statement as to whether, in the opinion of such officer, such
condition or covenant has been complied with.


                                        3

<PAGE>   8


         "PERSON" means a legal person, including any individual, corporation,
estate, partnership, joint venture, association, joint stock company, limited
liability company, trust, unincorporated association, or government or any
agency or political subdivision thereof, or any other entity of whatever nature.

         "RESPONSIBLE OFFICER" means, with respect to the Guarantee Trustee, any
Executive Vice President, Senior Vice President, any First Vice President, any
Vice President, any Assistant Vice President, the Secretary, any Assistant
Secretary, the Treasurer, any Assistant Treasurer, any Trust Officer or
Assistant Trust Officer or any other officer of the Corporate Trust Services
Division of the Guarantee Trustee customarily performing functions similar to
those performed by any of the above designated officers and also means, with
respect to a particular corporate trust matter, any other officer to whom such
matter is referred because of that officer's knowledge of and familiarity with
the particular subject.

         "SUCCESSOR GUARANTEE TRUSTEE" means a successor Guarantee Trustee
possessing the qualifications to act as Guarantee Trustee under Section 4.01.

         "TRUST INDENTURE ACT" means the Trust Indenture Act of 1939, as
amended.



                                    ARTICLE 2
                               TRUST INDENTURE ACT

         SECTION 2.01. Trust Indenture Act; Application. (a) This Guarantee
Agreement is subject to the provisions of the Trust Indenture Act that would be
required to be part of this Guarantee Agreement in order for this Guarantee
Agreement to be a qualified indenture under the Trust Indenture Act and shall,
to the extent applicable, be governed by such provisions.

          (b) If and to the extent that any provision of this Guarantee
Agreement limits, qualifies or conflicts with the duties imposed by Sections 310
to 317, inclusive, of the Trust Indenture Act, such imposed duties shall
control.

         SECTION 2.02. List of Holders. (a) The Guarantor shall shall provide,
or cause to be provided to the Guarantee Trustee (unless the Guarantee Trustee
is acting as the Registrar (as defined in the Trust Agreement), a list, in such
form as the Guarantee Trustee may reasonably require, of the names and addresses
of the Holders of the Securities (a "LIST OF HOLDERS") (i) within 14 days after
each record date for payment of Distributions, as of such record date; provided
that the Sponsor shall not be obligated to provide such List of Holders at any
time the List of Holders does not differ from the most recent List of Holders
given to the


                                        4

<PAGE>   9


Guarantee Trustee by the Sponsor, and (ii) at any other time, within 30 days of
receipt by the Trust of a written request from the Guarantee Trustee for a List
of Holders as of a date no more than 14 days before such List of Holders is
given to the Guarantee Trustee. The Guarantee Trustee shall preserve, in as
current a form as is reasonably practicable, all information contained in Lists
of Holders given to it; provided that the Guarantee Trustee may destroy any List
of Holders previously given to it on receipt of a new List of Holders.
Notwithstanding the foregoing, the Guarantor shall not be obligated to provide
such List of Holders at any time the Preferred Securities are represented by one
or more Global Certificates (as defined in the Trust Agreement).

          (b) The Guarantee Trustee shall comply with its obligations under
Section 311(a), Section 311(b) and Section 312(b) of the Trust Indenture Act.

         SECTION 2.03. Reports by the Guarantee Trustee. On or before July 15,
of each calendar year, the Guarantee Trustee shall provide to the Holders such
reports as are required by Section 313 of the Trust Indenture Act, if any, in
the form and in the manner provided by Section 313 of the Trust Indenture Act.
The Guarantee Trustee shall also comply with the requirements of Section 313(d)
of the Trust Indenture Act.

         SECTION 2.04. Periodic Reports to Guarantee Trustee. The Guarantor
shall provide to the Guarantee Trustee, the Securities and Exchange Commission
and the Holders such documents, reports and information, if any, as may be
required by Section 314 of the Trust Indenture Act or the rules and regulations
thereunder and the compliance certificate required by Section 314 of the Trust
Indenture Act in the form, in the manner and at the times required by Section
314 of the Trust Indenture Act.

         SECTION 2.05.  Evidence of Compliance with Conditions Precedent.  The
Guarantor shall provide to the Guarantee Trustee such evidence of compliance

with such conditions precedent, if any, provided for in this Guarantee Agreement
that relate to any of the matters set forth in Section 314(c) of the Trust
Indenture Act. Any certificate or opinion required to be given by an officer
pursuant to Section 314(c)(1) may be given in the form of an Officer's
Certificate.

         SECTION 2.06. Events of Default; Waiver. The Holders of a Majority in
Liquidation Amount of the Preferred Securities may, by vote, on behalf of the
Holders, waive any past Event of Default and its consequences. Upon such waiver,
any such Event of Default shall cease to exist, and any Event of Default arising
therefrom shall be deemed to have been cured, for every purpose of this
Guarantee Agreement, but no such waiver shall extend to any subsequent or other
default or Event of Default or impair any right consequent therefrom.


                                        5

<PAGE>   10


         SECTION 2.07. Events of Default; Notice. (a) The Guarantee Trustee
shall, within 10 days after a Responsible Officer of the Guarantee Trustee
obtains knowledge of the occurrence of an Event of Default with respect to this
Guarantee Agreement, deliver by overnight courier to the Guarantor notices of
all defaults known to a Responsible Officer of the Guarantee Trustee.

         (b) The Guarantee Trustee shall, not sooner than 60 days and not more
than 90 days after the notice required by Section 2.07(a) is sent to the
Guarantor, transmit by mail, first class postage prepaid, to the Holders,
notices of all such Events of Default, unless such defaults have been cured
before the giving of such notice, provided, that, except in the case of a
default in the payment of a Guarantee Payment, the Guarantee Trustee shall be
protected in withholding such notice if and so long as the Board of Directors,
the executive committee or a trust committee of directors and/or Responsible
Officers of the Guarantee Trustee in good faith determines that the withholding
of such notice is in the interests of the Holders.

          (c) The Guarantee Trustee shall not be deemed to have knowledge of any
Event of Default unless the Guarantee Trustee shall have received written
notice, or a Responsible Officer charged with the administration of the Trust
Agreement shall have obtained written notice, of such Event of Default.

         SECTION 2.08. Conflicting Interests. The (i) Trust Agreement and (ii)
the Indenture shall be deemed to be specifically described in this Guarantee
Agreement for the purposes of clause (i) of the first proviso contained in
Section 310(b) of the Trust Indenture Act.



                                    ARTICLE 3
               POWERS, DUTIES AND RIGHTS OF THE GUARANTEE TRUSTEE

         SECTION 3.01. Powers and Duties of the Guarantee Trustee. (a) This
Guarantee Agreement shall be held by the Guarantee Trustee for the benefit of
the Holders, and the Guarantee Trustee shall not transfer this Guarantee
Agreement to any Person except a Holder exercising his or her rights pursuant to
Section 5.04(d) or to a Successor Guarantee Trustee on acceptance by such
Successor Guarantee Trustee of its appointment to act as Successor Guarantee
Trustee. The right, title and interest of the Guarantee Trustee shall
automatically vest in any Successor Guarantee Trustee, upon acceptance by such
Successor Guarantee Trustee of its appointment hereunder, and such vesting and
cessation of title shall be effective whether or not conveyancing documents have
been executed and delivered pursuant to the appointment of such Successor
Guarantee Trustee.


                                        6

<PAGE>   11


          (b) If an Event of Default actually known to the Responsible Officer
of the Guarantee Trustee has occurred and is continuing, the Guarantee Trustee
shall enforce this Guarantee Agreement for the benefit of the Holders.

          (c) The Guarantee Trustee, before the occurrence of any Event of
Default and after the curing of all Events of Default that may have occurred,
shall undertake to perform only such duties as are specifically set forth in
this Guarantee Agreement, and no implied covenants shall be read into this
Guarantee Agreement against the Guarantee Trustee. In case an Event of Default
has occurred (that has not been cured or waived pursuant to Section 2.06) and is
actually known to the Responsible Officer of the Guarantee Trustee, the
Guarantee Trustee shall exercise such of the rights and powers vested in it by
this Guarantee Agreement, and use the same degree of care and skill in its
exercise thereof, as a prudent person would exercise or use under the
circumstances in the conduct of his or her own affairs.

          (d) No provision of this Guarantee Agreement shall be construed to
relieve the Guarantee Trustee from liability for its own negligent action, its
own negligent failure to act, its own bad faith or its own willful misconduct,
except that:

                  (i) prior to the occurrence of any Event of Default and after
         the curing or waiving of all such Events of Default that may have
         occurred;

                       (A) the duties and obligations of the Guarantee Trustee
                  shall be determined solely by the express provisions of this
                  Guarantee Agreement, and the Guarantee Trustee shall not be
                  liable except for the performance of such duties and
                  obligations as are specifically set forth in this Guarantee
                  Agreement; and

                       (B) in the absence of bad faith on the part of the
                  Guarantee Trustee, the Guarantee Trustee may conclusively
                  rely, as to the truth of the statements and the correctness of
                  the opinions expressed therein, upon any certificates or
                  opinions furnished to the Guarantee Trustee and conforming to
                  the requirements of this Guarantee Agreement; but in the case
                  of any such certificates or opinions that by any provision
                  hereof or of the Trust Indenture Act are specifically required
                  to be furnished to the Guarantee Trustee, the Guarantee
                  Trustee shall be under a duty to examine the same to determine
                  whether or not they conform to the requirements of this
                  Guarantee Agreement;

                  (ii) the Guarantee Trustee shall not be liable for any error
         of judgment made in good faith by a Responsible Officer of the
         Guarantee


                                        7

<PAGE>   12


         Trustee, unless it shall be proved that the Guarantee Trustee was
         negligent in ascertaining the pertinent facts upon which such judgment
         was made;

                  (iii) the Guarantee Trustee shall not be liable with respect
         to any action taken or omitted to be taken by it in good faith in
         accordance with the direction of the Holders of not less than a
         Majority in Liquidation Amount of the Preferred Securities relating to
         the time, method and place of conducting any proceeding for any remedy
         available to the Guarantee Trustee, or exercising any trust or power
         conferred upon the Guarantee Trustee under this Guarantee Agreement;
         and

                  (iv) no provision of this Guarantee Agreement shall require
         the Guarantee Trustee to expend or risk its own funds or otherwise
         incur personal financial liability in the performance of any of its
         duties or in the exercise of any of its rights or powers, if the
         Guarantee Trustee shall have reasonable grounds for believing that the
         repayment of such funds or liability is not reasonably assured to it
         under the terms of this Guarantee Agreement or if reasonable indemnity
         against such risk or liability is not reasonably assured to it.

         SECTION 3.02.  Certain Rights of Guarantee Trustee.  (a) Subject to the
provisions of Section 3.01:

                  (i) The Guarantee Trustee may rely and shall be fully
         protected in acting or refraining from acting upon any resolution,
         certificate, statement, proxy, instrument, opinion, report, notice,
         request, direction, consent, order, bond, debenture, note, other
         evidence of indebtedness or other paper or document believed by it to
         be genuine and to have been signed, sent or presented by the proper
         party or parties.

                  (ii) Any direction or act of the Guarantor contemplated by
         this Guarantee Agreement shall be sufficiently evidenced by an
         Officer's Certificate unless otherwise prescribed herein.

                  (iii) Whenever, in the administration of this Guarantee
         Agreement, the Guarantee Trustee shall deem it desirable that a matter
         be proved or established before taking, suffering or omitting to take
         any action hereunder, the Guarantee Trustee (unless other evidence is
         herein specifically prescribed) may, in the absence of negligence, bad
         faith or willful misconduct on its part, request and rely upon an
         Officer's Certificate which, upon receipt of such request from the
         Guarantee Trustee, shall be promptly delivered by the Guarantor.

                  (iv) The Guarantee Trustee may consult with legal counsel, and
         the advice or written opinion of such legal counsel with respect to
         legal


                                        8

<PAGE>   13



         matters shall be full and complete authorization and protection in
         respect of any action taken, suffered or omitted to be taken by it
         hereunder in good faith and in accordance with such advice or opinion.
         Such legal counsel may be legal counsel to the Guarantor or any of its
         Affiliates and may be one of its employees. The Guarantee Trustee shall
         have the right at any time to seek instructions concerning the
         administration of this Guarantee Agreement from any court of competent
         jurisdiction.

                  (v) The Guarantee Trustee shall be under no obligation to
         exercise any of the rights or powers vested in it by this Guarantee
         Agreement at the request or direction of any Holder, unless such Holder
         shall have provided to the Guarantee Trustee such adequate security and
         indemnity as would satisfy a reasonable person in the position of the
         Guarantee Trustee, against the reasonable costs, expenses (including
         reasonable attorneys' fees and expenses) and liabilities that might be
         incurred by it in complying with such request or direction, including
         such reasonable advances as may be requested by the Guarantee Trustee;
         provided that nothing contained in this Section 3.02(a)(v) shall be
         taken to relieve the Guarantee Trustee, upon the occurrence of an Event
         of Default, of its obligation to exercise the rights and powers vested
         in it by this Guarantee Agreement and use the same degree of care and
         skill in the exercise thereof as a prudent person would exercise or use
         under the circumstances in the conduct of his or her own affairs.

                  (vi) The Guarantee Trustee shall not be bound to make any
         investigation into the facts or matters stated in any resolution,
         certificate, statement, instrument, opinion, report, notice, request,
         direction, consent, order, bond, debenture, note, other evidence of
         indebtedness or other paper or document, but the Guarantee Trustee, in
         its discretion, may make such further inquiry or investigation into
         such facts or matters as it may see fit.

                  (vii) The Guarantee Trustee may execute any of the trusts or
         powers hereunder or perform any duties hereunder either directly or by
         or through its agents or attorneys or any Affiliate, and the Guarantee
         Trustee shall not be responsible for any misconduct or negligence on
         the part of any such agent or attorney appointed with due care by it
         hereunder.

                  (viii) Whenever in the administration of this Guarantee
         Agreement the Guarantee Trustee shall deem it desirable to receive
         instructions with respect to enforcing any remedy or right or taking
         any other action hereunder, the Guarantee Trustee (A) may request
         instructions from the Holders of a Majority in Liquidation Amount of
         the Preferred Securities, (B) may refrain from enforcing such remedy or
         right or taking such other action until such instructions are received,
         and (C) shall be protected in acting in accordance with such
         instructions.


                                        9

<PAGE>   14




          (b) No provision of this Guarantee Agreement shall be deemed to impose
any duty or obligation on the Guarantee Trustee to perform any act or acts or
exercise any right, power, duty or obligation conferred or imposed on it in any
jurisdiction in which it shall be illegal, or in which the Guarantee Trustee
shall be unqualified or incompetent in accordance with applicable law, to
perform any such act or acts or to exercise any such right, power, duty or
obligation. No permissive power or authority available to the Guarantee Trustee
shall be construed to be a duty to act in accordance with such power and
authority.

         SECTION 3.03. Indemnity. The Guarantor agrees to indemnify the
Guarantee Trustee for, and to hold it harmless against, any loss, liability or
expense incurred without negligence or bad faith on the part of the Guarantee
Trustee, arising out of or in connection with the acceptance or administration
of this Guarantee Agreement, including the reasonable costs and expenses of
defending itself against any claim or liability in connection with the exercise
or performance of any of its powers or duties hereunder. The Guarantee Trustee
will not claim or exact any lien or charge on any Guarantee Payment as a result
of any amount due to it under this Guarantee Agreement.



                                    ARTICLE 4
                                GUARANTEE TRUSTEE

         SECTION 4.01. Guarantee Trustee; Eligibility. (a) There shall at all
times be a Guarantee Trustee which shall:

                  (i) not be an Affiliate of the Guarantor; and

                  (ii) be a Person that is eligible pursuant to the Trust
         Indenture Act to act as such and has a combined capital and surplus of
         at least $50,000,000, and shall be a corporation meeting the
         requirements of Section 310(a) of the Trust Indenture Act. If such
         corporation publishes reports of condition at least annually, pursuant
         to law or to the requirements of the supervising or examining
         authority, then, for the purposes of this Section and to the extent
         permitted by the Trust Indenture Act, the combined capital and surplus
         of such corporation shall be deemed to be its combined capital and
         surplus as set forth in its most recent report of condition so
         published.

          (b) If at any time the Guarantee Trustee shall cease to be eligible to
so act under Section 4.01(a), the Guarantee Trustee shall immediately resign in
the manner and with the effect set out in Section 4.02(c).


                                       10

<PAGE>   15


          (c) If the Guarantee Trustee has or shall acquire any "conflicting
interest" within the meaning of Section 310(b) of the Trust Indenture Act, the
Guarantee Trustee and Guarantor shall in all respects comply with the provisions
of Section 310(b) of the Trust Indenture Act.

         SECTION 4.02.  Appointment, Removal and Resignation of the Guarantee
Trustee.  (a)  Subject to Section 4.01(b) the Guarantee Trustee may be appointed
or removed without cause at any time by the Guarantor.

          (b) The Guarantee Trustee shall not be removed until a Successor
Guarantee Trustee has been appointed and has accepted such appointment by
written instrument executed by such Successor Guarantee Trustee and delivered to
the Guarantor.

          (c) The Guarantee Trustee appointed hereunder shall hold office until
a Successor Guarantee Trustee shall have been appointed or until its removal or
resignation. The Guarantee Trustee may resign from office (without need for
prior or subsequent accounting) by an instrument in writing executed by the
Guarantee Trustee and delivered to the Guarantor, which resignation shall not
take effect until a Successor Guarantee Trustee has been appointed and has
accepted such appointment by an instrument in writing executed by such Successor
Guarantee Trustee and delivered to the Guarantor and the resigning Guarantee
Trustee.

          (d) If no Successor Guarantee Trustee shall have been appointed and
accepted appointment as provided in this Section 4.02 within 60 days after
delivery to the Guarantor of an instrument of resignation, the resigning
Guarantee Trustee may petition, at the expense of the Guarantor, any court of
competent jurisdiction for appointment of a Successor Guarantee Trustee. Such
court may thereupon after prescribing such notice, if any, as it may deem
proper, appoint a Successor Guarantee Trustee.



                                    ARTICLE 5
                                    GUARANTEE

         SECTION 5.01. Guarantee. The Guarantor irrevocably and unconditionally
agrees to pay in full to the Holders the Guarantee Payments (without duplication
of amounts theretofore paid by or on behalf of the Issuer), as and when due,
regardless of any defense, right of set-off or counterclaim which the Issuer may
have or assert, other than the defense of payment. The Guarantor's obligation to
make a Guarantee Payment may be satisfied by direct payment of


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<PAGE>   16


the required amounts by the Guarantor to the Holders or by causing the Issuer to
pay such amounts to the Holders.

         SECTION 5.02. Waiver of Notice and Demand. The Guarantor hereby waives
notice of acceptance of the Guarantee Agreement and of any liability to which it
applies or may apply, presentment, demand for payment, any right to require a
proceeding first against the Guarantee Trustee, Issuer or any other Person
before proceeding against the Guarantor, protest, notice of nonpayment, notice
of dishonor, notice of redemption and all other notices and demands.

         SECTION 5.03. Obligations Not Affected. The obligations, covenants,
agreements and duties of the Guarantor under this Guarantee Agreement shall in
no way be affected or impaired by reason of the happening from time to time of
any of the following:

          (a) the release or waiver, by operation of law or otherwise, of the
performance or observance by the Issuer of any express or implied agreement,
covenant, term or condition relating to the Preferred Securities to be performed
or observed by the Issuer;

          (b) the extension of time for the payment by the Issuer of all or any
portion of the Distributions, Redemption Price, Liquidation Distribution or any
other sums payable under the terms of the Preferred Securities or the extension
of time for the performance of any other obligation under, arising out of, or in
connection with, the Preferred Securities (other than an extension of time for
payment of Distributions that results from the extension of any interest payment
period on the Senior Notes or any extension of the maturity date of the Senior
Notes permitted by the Indenture);

          (c) any failure, omission, delay or lack of diligence on the part of
the Holders to enforce, assert or exercise any right, privilege, power or remedy
conferred on the Holders pursuant to the terms of the Preferred Securities, or
any action on the part of the Issuer granting indulgence or extension of any
kind;

          (d) the voluntary or involuntary liquidation, dissolution, sale of any
collateral, receivership, insolvency, bankruptcy, assignment for the benefit of
creditors, reorganization, arrangement, composition or readjustment of debt of,
or other similar proceedings affecting, the Issuer or any of the assets of the
Issuer;

          (e) any invalidity of, or defect or deficiency in, the Preferred
Securities;

          (f) the settlement or compromise of any obligation guaranteed hereby
or hereby incurred; or


                                       12

<PAGE>   17


          (g) any other circumstance whatsoever that might otherwise constitute
a legal or equitable discharge or defense of a guarantor, it being the intent of
this Section 5.03 that the obligations of the Guarantor hereunder shall be
absolute and unconditional under any and all circumstances.

         There shall be no obligation of the Holders or the Guarantee Trustee to
give notice to, or obtain the consent of, the Guarantor with respect to the
happening of any of the foregoing.

         SECTION 5.04. Rights of Holders. The Guarantor expressly acknowledges
that: (a) this Guarantee Agreement will be deposited with the Guarantee Trustee
to be held for the benefit of the Holders; (b) the Guarantee Trustee has the
right to enforce this Guarantee Agreement on behalf of the Holders; (c) the
Holders of a Majority in Liquidation Amount of the Preferred Securities have the
right to direct the time, method and place of conducting any proceeding for any
remedy available to the Guarantee Trustee in respect of this Guarantee Agreement
or to direct the exercise of any trust or power conferred upon the Guarantee
Trustee under this Guarantee Agreement; (d) any Holder may institute a legal
proceeding directly against the Guarantor to enforce its rights under this
Guarantee Agreement, without first instituting a legal proceeding against the
Guarantee Trustee, the Issuer or any other Person; and (e) if an Event of
Default with respect to the Senior Notes constituting the failure to pay
interest or principal on the Senior Notes on the date such interest or principal
is otherwise payable has occurred and is continuing, then any Holder shall have
the right, which is absolute and unconditional, to proceed directly against the
Guarantor to obtain Guarantee Payments without first waiting to determine if the
Guarantee Trustee has enforced this Guarantee Agreement or instituting a legal
proceeding against the Issuer, the Guarantee Trustee or any other Person.

         SECTION 5.05.  Guarantee of Payment.  This Guarantee Agreement creates
a guarantee of payment and not of collection.

         SECTION 5.06. Subrogation. The Guarantor shall be subrogated to all (if
any) rights of the Holders against the Issuer in respect of any amounts paid to
the Holders by the Guarantor under this Guarantee Agreement and shall have the
right to waive payment by the Issuer pursuant to Section 5.01; provided that the
Guarantor shall not (except to the extent required by applicable law) be
entitled to enforce or exercise any rights which it may acquire by way of
subrogation or any indemnity, reimbursement or other agreement, in all cases as
a result of payment under this Guarantee Agreement, if, at the time of any such
payment, any amounts are due and unpaid under this Guarantee Agreement. If any
amount shall be paid to the Guarantor in violation of the preceding sentence,
the Guarantor agrees to hold such amount in trust for the Holders and to pay
over such amount to the Holders.


                                       13

<PAGE>   18


         SECTION 5.07. Independent Obligations. The Guarantor acknowledges that
its obligations hereunder are independent of the obligations of the Issuer with
respect to the Preferred Securities and that the Guarantor shall be liable as
principal and as debtor hereunder to make Guarantee Payments pursuant to the
terms of this Guarantee Agreement notwithstanding the occurrence of any event
referred to in subsections (a) through (g), inclusive, of Section 5.03.


                                       14

<PAGE>   19


                                    ARTICLE 6
                              COVENANTS AND STATUS

         SECTION 6.01. Status of this Guarantee Agreement. This Guarantee
Agreement shall constitute a senior unsecured obligation of the Guarantor and
shall rank equally with all of the Guarantor's other senior unsecured
obligations. If an Event of Default (as defined in the Indenture) has occurred
and is continuing, the rights of holders of the Common Securities to receive
payments under the Common Securities Guarantee shall be subordinated to the
rights of Holders to receive Guarantee Payments.

         SECTION 6.02.  Certain Covenants of the Guarantor.

          (a) The Guarantor covenants and agrees that it will not, and will not
permit any subsidiary of the Guarantor to (i) declare or pay any dividends or
distributions on, or redeem, purchase, acquire, or make a liquidation payment
with respect to, any of the Guarantor's capital stock or (ii) make any payment
of principal of, interest or premium, if any, on or repay, repurchase or redeem
any debt securities (including guarantees of indebtedness for money borrowed) of
the Guarantor that by their terms permit deferral at the option of the Guarantor
of scheduled payments of interest or principal (other than (A) any dividend,
redemption, liquidation, interest, principal or guarantee payment by Guarantor
where the payment is made by way of securities (including capital stock) that
rank pari passu with or junior to the securities on which such dividend,
redemption, interest, principal or guarantee payment is being made, (B)
purchases of the Guarantor's capital stock related to the issuance of the
Guarantor's capital stock under any of the Guarantor's benefit plans for its
directors, officers or employees, (C) as a result of a reclassification of the
Guarantor's capital stock or the ex change or conversion of one series or class
of the Guarantor's capital stock for another series or class of the Guarantor's
capital stock, including, without limitation, the conversion of the Guarantor's
Class C common stock and its Series A convertible preferred stock into shares of
the Guarantor's Class A common stock, and (D) the purchase of fractional
interests in shares of the Guarantor's capital stock pursuant to the conversion
or exchange provisions of such capital stock or the security being converted or
exchanged) if at such time (1) there shall have occurred any event of which the
Guarantor has actual knowledge that (x) with the giving of notice or the lapse
of time, or both, would constitute an Event of Default (as defined in the
Indenture) with respect to the Senior Notes and (y) the Guarantor shall not have
taken reasonable steps to cure, (2) the Guarantor shall be in default with
respect to its payment of any obligations under the Guarantee or (3) the
Guarantor shall have given notice of its selection of an Extension Period (as
defined in the Indenture) with respect to the Senior Notes


                                       15

<PAGE>   20


and shall not have rescinded such notice, or such Extension Period, or any
extension thereof, shall be continuing.

          (b) The Guarantor covenants and agrees (i) to maintain directly or
indirectly 100% ownership of the Common Securities, provided that certain
successors which are permitted by the Indenture may succeed to the Guarantor's
ownership of the Common Securities, (ii) not to voluntarily terminate, wind-up
or liquidate the Issuer, except (A) in connection with a distribution of the
Senior Notes to Holders in the event of the liquidation of the Issuer, (B) in
connection with the redemption of all of the Preferred Securities or (C) in
connection with certain mergers, consolidations or amalgamations permitted by
the Trust Agreement and (iii) to use its reasonable efforts, consistent with the
terms and provisions of the Trust Agreement, to cause the Issuer to remain
classified as a grantor trust and not as an association or publicly traded
partnership taxable as a corporation for United States Federal income tax
purposes.



                                    ARTICLE 7
                                   TERMINATION

         SECTION 7.01. Termination. This Guarantee Agreement shall terminate and
be of no further force and effect upon (a) full payment of the Redemption Price
of all Preferred Securities, (b) the distribution of Senior Notes to the Holders
in exchange for all outstanding Preferred Securities and Common Securities or
(c) full payment of the amounts payable in accordance with the Trust Agreement
upon liquidation of the Issuer. Notwithstanding the foregoing, this Guarantee
Agreement will continue to be effective or will be reinstated, as the case may
be, if at any time any Holder must restore payment of any sums paid with respect
to Preferred Securities or this Guarantee Agreement.



                                    ARTICLE 8
                                  MISCELLANEOUS

         SECTION 8.01.  Successors and Assigns.  All guarantees and agreements
contained in this Guarantee Agreement shall bind the successors, assigns,
receivers, trustees and representatives of the Guarantor and shall inure to the
benefit of the Holders of the Preferred Securities then outstanding. Except in
connection with a consolidation, merger or sale involving the Guarantor with or
into another entity that is permitted under the Indenture and pursuant to which
the assignee agrees in writing to perform the Guarantor's obligations hereunder,
the Guarantor shall not assign its obligations hereunder.


                                       16

<PAGE>   21


         SECTION 8.02. Amendments. Except with respect to any changes which do
not materially and adversely affect the rights of the Holders (in which case no
consent of the Holders will be required), this Guarantee Agreement may only be
amended with the prior approval of the Holders of not less than a Majority in
Liquidation Amount of the Preferred Securities. The provisions of Section 12.02
of the Trust Agreement concerning meetings of the Holders shall apply to the
giving of such approval. The Guarantor shall furnish the Guarantee Trustee with
an Officer's Certificate and an Opinion of Counsel to the effect that any
amendment of this Agreement is authorized and permitted.

         SECTION 8.03. Notices. Any notice, request or other communication
required or permitted to be given hereunder shall be in writing, duly signed by
the party giving such notice, and delivered, telecopied or mailed by first class
mail as follows: (a) if given to the Guarantor, to the address set forth below
or such other address as the Guarantor may give notice of to the Holders:

                       Cox Communications, Inc.
                       1400 Lake Hearn Drive
                       Atlanta, Georgia 30319
                       Telephone: (404) 843-5000
                       Telecopier: (404) 847-6336
                       Attention: Dallas S. Clement

                       with a copy to:

                       Dow, Lohnes & Albertson, PLLC
                       1200 New Hampshire Ave., N.W.
                       Suite 800
                       Washington, D.C.  20036
                       Telecopier: 202-776-2222
                       Attention: Stuart A. Sheldon

        (b) if given to the Issuer, in care of the Guarantee Trustee, at the
Issuer's (and the Guarantee Trustee's) address set forth below or such other
address as the Guarantee Trustee on behalf of the Issuer may give notice of to
the Holders:

                       Cox RHINOS Trust
                       c/o Cox Communications, Inc.
                       1400 Lake Hearn Drive
                       Atlanta, Georgia 30319
                       Telephone: (404) 843-5000
                       Telecopier: (404) 847-6336
                       Attention: Dallas S. Clement



                                       17

<PAGE>   22
        with a copy to:

                       Dow, Lohnes & Albertson, PLLC
                       1200 New Hampshire Ave., N.W.
                       Suite 800
                       Washington, D.C.  20036
                       Telecopier: 202-776-2222
                       Attention: Stuart A. Sheldon

        and with a copy to:

                       The Bank of New York
                       101 Barclay Street, Floor 21 West
                       New York, New York 10286
                       Phone No.: 212-815-5092
                       Facsimile No.: 212-815-5915
                       Attention: Corporate Trust Administration

        (c) if given to any Holder, at the address set forth on the books and
records of the Issuer.

        All notices hereunder shall be deemed to have been given when received
in person, telecopied with receipt confirmed, or mailed by first class mail,
postage prepaid, except that if a notice or other document is refused delivery
or cannot be delivered because of a changed address of which no notice was
given, such notice or other document shall be deemed to have been delivered on
the date of such refusal or inability to deliver.

        SECTION 8.04.  Benefit.  This Guarantee Agreement is solely for the
benefit of the Holders and is not separately transferable from the Preferred
Securities.

        SECTION 8.05.  Interpretation.  In this Guarantee Agreement, unless the
context otherwise requires:

        (a) capitalized terms used in this Guarantee Agreement but not defined
in the preambles hereto have the respective meanings assigned to them in Section
1.01;

        (b) a term defined anywhere in this Guarantee Agreement has the same
meaning throughout;

        (c) all references to "the Guarantee Agreement" or "this Guarantee
Agreement" are to this Guarantee Agreement as modified, supplemented or amended
from time to time;


                                       18

<PAGE>   23


        (d) all references in this Guarantee Agreement to Articles and Sections
are to Articles and Sections of this Guarantee Agreement unless otherwise
specified;

        (e) a term defined in the Trust Indenture Act has the same meaning when
used in this Guarantee Agreement unless otherwise defined in this Guarantee
Agreement or unless the context otherwise requires;

        (f) a reference to the singular includes the plural and vice versa; and

        (g) the masculine, feminine or neuter genders used herein shall include
the masculine, feminine and neuter genders.

        SECTION 8.06. Governing Law. THIS GUARANTEE AGREEMENT SHALL BE GOVERNED
BY AND CONSTRUED AND INTERPRETED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW
YORK WITHOUT REGARD TO THE CONFLICT OF LAW PRINCIPLES THEREOF.

        SECTION 8.07.  Counterparts.  This instrument may be executed in any
number of counterparts, each of which so executed shall be deemed to be an
original, but all such counterparts shall together constitute one and the same
instrument.


                                       19

<PAGE>   24


        THIS GUARANTEE AGREEMENT is executed as of the day and year first above
written.

                                             COX COMMUNICATIONS, INC.



                                             By: /s/ Dallas S. Clement
                                                --------------------------------
                                                Name: Dallas S. Clement
                                                Title: Vice President and
                                                         Treasurer



                                             THE BANK OF NEW YORK, as
                                                 Guarantee Trustee



                                             By: /s/ Marie E. Trimboli
                                                --------------------------------
                                                Name: Marie E. Trimboli
                                                Title: Assistant Treasurer