<PAGE>
 
                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM 10-Q
                                        
(Mark One)
  [ X ]    QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE
           SECURITIES EXCHANGE ACT OF 1934
           For the quarterly period ended June 30, 1998

  [   ]    TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE
           SECURITIES EXCHANGE ACT OF 1934
           For the transition period from __________ to __________

                         Commission File Number 1-13576


                            COX COMMUNICATIONS, INC.
             (Exact name of registrant as specified in its charter)


             Delaware                                   58-2112281
  (State or other jurisdiction of          (I.R.S. Employer Identification No.) 
   incorporation or organization)


  1400 Lake Hearn Drive, Atlanta, Georgia                    30319
  (Address of principal executive offices)                 (Zip Code)


       Registrant's telephone number, including area code: (404) 843-5000
                                _______________

          Indicate by check mark whether the registrant (1) has filed all
reports required to be filed by Section 13 or 15(d) of the Securities Exchange
Act of 1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.    Yes [X]   No [ ]

                                _______________

          Indicate the number of shares outstanding of each of the issuer's
classes of Common Stock, as of the latest practicable date.

            There were 257,607,609 shares of Cox Class A Common Stock
outstanding as of August 1, 1998.

            There were 13,798,896 shares of Cox Class C Common Stock outstanding
as of August 1, 1998.
<PAGE>
 
                           COX COMMUNICATIONS, INC.
                                   FORM 10-Q
                      FOR THE QUARTER ENDED JUNE 30, 1998
 

                               TABLE OF CONTENTS
 
                                                                           PAGE
                                                                           ----

                        PART I - FINANCIAL INFORMATION
 
ITEM 1.  FINANCIAL STATEMENTS.............................................    2
 
ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
         CONDITION AND RESULTS OF OPERATIONS..............................   12

ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK.......   16
 

                          PART II - OTHER INFORMATION
 
ITEM 1.  LEGAL PROCEEDINGS................................................   16

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K.................................   17
 
SIGNATURES................................................................   18

                                        
<PAGE>
<TABLE>
<CAPTION>
                           Part I - Financial Information

Item 1.     Financial Statements

                              Cox Communications, Inc.
                            Consolidated Balance Sheets
                                                                                          June 30     December 31
                                                                                           1998          1997
                                                                                       ------------   ------------
<S>                                                                                 <C>            <C> 
                                                                                               (unaudited)
                                                                                         (Thousands of Dollars)
Assets
Cash................................................................................ $      20,648  $     28,259
Restricted Cash.....................................................................            --       204,210
Accounts and notes receivable, less allowance for doubtful
  accounts of $6,930 and $6,955.....................................................       138,311       144,073
Net plant and equipment.............................................................     2,117,980     1,979,063
Investments.........................................................................     2,037,857     1,598,273
Intangible assets...................................................................     2,620,866     2,458,717
Amounts due from Cox Enterprises, Inc ("CEI").......................................            --        50,856
Other assets........................................................................        87,166        93,150
                                                                                       ------------   ------------
     Total assets................................................................... $   7,022,828  $  6,556,601
                                                                                       ============   ============
Liabilities and shareholders' equity
Accounts payable and accrued expenses............................................... $     255,918  $    217,984
Deferred income.....................................................................        27,377        26,698
Deferred income taxes...............................................................       941,247       721,594
Other liabilities...................................................................        73,359        84,179
Debt................................................................................     3,071,280     3,148,834
Amounts due to CEI..................................................................        49,689            --
                                                                                       ------------   ------------
     Total liabilities..............................................................     4,418,870     4,199,289
                                                                                       ------------   ------------
Shareholders' equity
  Preferred Stock, $1 par value; 5,000,000 shares authorized;
     none issued....................................................................           --            --
  Class A Common Stock, $1 par value; 316,000,000 shares
     authorized; shares issued and outstanding: 257,562,179
     and 257,276,414................................................................       257,562       257,276
  Class C Common Stock, $1 par value; 14,000,000 shares
     authorized; shares issued and outstanding: 13,798,896..........................        13,799        13,799
  Additional paid-in capital........................................................     1,796,291     1,790,833
  Retained earnings (deficit).......................................................       (34,560)       79,605
  Foreign currency translation adjustment...........................................        15,332        13,510
  Net unrealized gain on securities.................................................       555,534       202,289
                                                                                       ------------   ------------
     Total shareholders' equity.....................................................     2,603,958     2,357,312
                                                                                       ------------   ------------
     Total liabilities and shareholders' equity..................................... $   7,022,828  $  6,556,601
                                                                                       ============   ============

See notes to consolidated financial statements.


                                                                                                 2


</TABLE>
<PAGE>
                           COX COMMUNICATIONS, INC.
                     CONSOLIDATED STATEMENTS OF OPERATIONS
<TABLE>
<CAPTION>
                                                                      THREE MONTHS                       SIX MONTHS
                                                                     ENDED JUNE 30                      ENDED JUNE 30
                                                             -----------------------------       -----------------------------
                                                                1998              1997              1998              1997
                                                             -----------       -----------       -----------       -----------
                                                                                       (UNAUDITED)
                                                                     (THOUSANDS OF DOLLARS, EXCLUDING PER SHARE DATA)
<S>                                                          <C>               <C>                <C>               <C>
Revenues
   Complete basic.........................................  $   291,016        $   270,448       $   575,384       $   538,337
   Premium service........................................       46,548             47,289            92,195            93,035
   Pay-per-view...........................................        7,990             15,703            18,350            26,675
   Advertising............................................       33,432             25,809            58,394            47,082
   Data...................................................        4,003                321             6,778               349
   Telephony..............................................        6,607              3,176            11,579             5,761
   Satellite..............................................           --             29,884            33,492            55,750
   Other..................................................        8,699              8,468            17,915            17,219
                                                            -----------        -----------       -----------       -----------
     Total revenues.......................................      398,295            401,098           814,087           784,208
Costs and expenses
   Programming costs......................................       95,692             92,203           190,664           180,732
   Plant operations.......................................       30,789             38,190            63,540            76,301
   Marketing..............................................       25,005             17,989            47,115            35,809
   General and administrative.............................       94,848             77,213           182,259           151,951
   Satellite operating and administrative.................           --             28,264            29,403            52,613
   Depreciation...........................................       80,405             85,296           167,445           158,143
   Amortization...........................................       17,794             18,977            36,351            36,027
                                                            -----------        -----------       -----------       -----------
Operating income..........................................       53,762             42,966            97,310            92,632
Interest expense..........................................      (51,004)           (50,170)         (104,128)          (96,986)
Equity in net losses of affiliated companies..............     (128,907)           (81,827)         (270,685)         (163,108)
Gain on exchanges of cable television systems.............           --                 --                --            24,642
Gain on sale of affiliated companies......................       77,150            190,844            77,150           193,780
Gain on sale of businesses................................       37,274                 --            37,274                --
Other, net................................................        3,501               (907)            4,784             3,093
                                                            -----------        -----------       -----------       -----------
Income (loss) before income taxes.........................       (8,224)           100,906          (158,295)           54,053
Income taxes..............................................        4,022             39,742           (44,130)           30,711
                                                            -----------        -----------       -----------       -----------
Net income (loss).........................................  $   (12,246)       $    61,164       $  (114,165)      $    23,342
                                                            ===========        ===========       ===========       ===========

Per share data
  Basic and diluted net income (loss) per share...........  $     (0.05)       $      0.23       $     (0.42)      $      0.09
  Basic weighted-average shares outstanding...............  271,345,485        270,335,907       271,268,152       270,324,395
  Diluted weighted-average shares outstanding.............  268,680,816        269,244,961       268,716,498       269,257,497
</TABLE>

See notes to consolidated financial statements.

                                       3
<PAGE>
                           COX COMMUNICATIONS, INC.
                CONSOLIDATED STATEMENTS OF SHAREHOLDERS' EQUITY
<TABLE>
<CAPTION>
                                                                                              Foreign         Net                  
                                                 Common Stock       Additional  Retained      currency     unrealized              
                                 Preferred  ---------------------    paid-in    earnings     translation    gain on                
                                  Stock     Class A     Class C      capital    (deficit)    adjustment    securities      Total   
                                 --------   ---------  ----------  -----------  ----------  ------------   ----------   ------------
                                                                      (unaudited)                                        
                                                                 (Thousands of Dollars)                                  
<S>                                     <C>        <C>     <C>         <C>            <C>     <C>              <C>        <C>
Balance at December 31, 1997....       --   $257,276    $13,799    $1,790,833   $  79,605      $13,510      $202,289     $2,357,312
  Net loss......................                                                 (114,165)                                 (114,165)
  Issuance of stock related to                                                                                            
     stock compensation plans...                 286                   5,458                                                  5,744
  Foreign currency translation                                                                                             
    adjustment..................                                                                 1,822                        1,822
  Change in net unrealized gain                                                                                               
    on securities...............                                                                              353,245       353,245
                                  -------   --------  -------     ----------    ---------      -------       --------    ----------
Balance at June 30, 1998........      --    $257,562  $13,799     $1,796,291    $ (34,560)     $15,332       $555,534    $2,603,958
                                  =======   ========  =======     ==========    =========      =======       ========    ========== 
</TABLE>
                                          
See notes to consolidated financial statements.

                                       4
<PAGE>
                          Cox Communications, Inc.
                    Consolidated Statements of Cash Flows
<TABLE> 
<CAPTION> 
                                                                                             Six Months
                                                                                            Ended June 30
                                                                                     ----------------------------
                                                                                        1998              1997
                                                                                     ----------        ----------
                                                                                             (unaudited)
                                                                                        (Thousands of Dollars)
<S>                                                                                <C>               <C> 
Cash flows from operating activities
Net income (loss)............................................................      $  (114,165)      $    23,342
Adjustments to reconcile net income to net cash provided
  by operating activities, net of effects of acquisitions:
  Depreciation...............................................................          167,445           158,143
  Amortization...............................................................           36,351            36,027
  Equity in net losses of affiliated companies...............................          270,685           163,108
  Deferred income taxes......................................................           14,939           (19,219)
  Gain on exchanges of cable television systems..............................              --            (24,642)
  Gain on sale of affiliated companies.......................................          (77,150)         (193,780)
  Gain on sale of businesses.................................................          (37,274)              --
(Increase) decrease in accounts and notes receivable.........................            6,534            (1,672)
Increase (decrease) in accounts payable and accrued expenses.................            6,314           (36,811)
Increase (decrease) in taxes payable.........................................           (1,767)           85,032
Other, net...................................................................           (7,577)          (11,249)
                                                                                    ----------        ----------
       Net cash provided by operating activities.............................          264,335           178,279
                                                                                    ----------        ----------

Cash flows from investing activities
Capital expenditures.........................................................         (357,035)         (361,855)
Investments in affiliated companies..........................................          (35,036)         (251,494)
Proceeds from sale of affiliated companies...................................           63,183             6,983
Proceeds from sale of businesses.............................................           73,957               --
Restricted cash invested.....................................................          204,210               --
Payments for purchases of cable television systems...........................         (258,067)              --
Payments for exchanges of cable television systems...........................              --            (53,442)
Decrease in amounts due from CEI.............................................           50,856               --
Other, net...................................................................           (4,486)           (4,058)
                                                                                    ----------        ----------   
       Net cash used in investing activities.................................         (262,418)         (663,866)
                                                                                    ----------        ----------

Cash flows from financing activities
Short-term debt borrowings (repayments), net.................................         (800,000)          400,000
Commercial paper borrowings (repayments), net................................          522,009           (20,239)
Proceeds from issuance of debt...............................................          199,337           150,000
Repayment of debt............................................................           (9,825)           (7,113)
Proceeds from exercise of stock options......................................            5,744             1,311
Increase (decrease) in amounts due to CEI....................................           49,689           (35,120)
Increase in book overdrafts..................................................           23,518            32,843
                                                                                    ----------        ----------
       Net cash provided by (used in) financing activities...................           (9,528)          521,682
                                                                                    ----------        ----------

Net increase (decrease) in cash..............................................           (7,611)           36,095
Cash at beginning of period..................................................           28,259            42,349
                                                                                    ----------        ----------
Cash at end of period........................................................      $    20,648       $    78,444
                                                                                     =========         =========

See notes to consolidated financial statements.

                                                                 5

</TABLE>
<PAGE>
                           COX COMMUNICATIONS, INC.
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                                  (CONTINUED)
<TABLE> 
<CAPTION> 
                                                                  SIX MONTHS
                                                                 ENDED JUNE 30
                                                            ------------------------
                                                               1998          1997
                                                            ----------    ----------
                                                                  (UNAUDITED)
                                                             (THOUSANDS OF DOLLARS)
<S>                                                         <C>           <C>
Significant noncash transactions
     Transfer of PCS license...............................  $    --      $ 251,918
     Flextech merger stock exchange........................       --        203,119
     Gemstar merger stock exchange.........................       --         19,373
     Value of PrimeStar, Inc. shares received..............    94,696            --

Additional cash flow information
     Interest paid.........................................  $ 99,252     $ 102,403
     Income taxes refunded.................................   (57,302)      (35,101)
</TABLE> 


See notes to consolidated financial statements.


                                       6

<PAGE>
 
                            COX COMMUNICATIONS, INC.
             NOTES TO CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

                                 JUNE 30, 1998
                                        
 1.  BASIS OF PRESENTATION AND OTHER INFORMATION

     The accompanying unaudited consolidated financial statements have been
prepared in accordance with generally accepted accounting principles for interim
financial information and with the instructions to Form 10-Q and Article 10 of
Regulation S-X. Accordingly, they do not include all of the information and
footnote disclosures required by generally accepted accounting principles for
complete financial statements. In the opinion of management, the financial
statements reflect all adjustments considered necessary for a fair statement of
the results of operations and financial position for the interim periods
presented. All such adjustments are of a normal recurring nature. These
unaudited interim financial statements should be read in conjunction with the
audited consolidated financial statements and notes thereto contained in Cox
Communications, Inc.'s ("Cox") Annual Report on Form 10-K for the year ended
December 31, 1997.

     The preparation of financial statements in conformity with generally
accepted accounting principles requires management to make estimates and
assumptions that effect the reported amounts of assets and liabilities and
disclosure of contingent assets and liabilities at the date of the financial
statements and the reported amounts of revenues and expenses during the
reporting period.  Actual results could differ from those estimates.  The
results of operations for the six months ended June 30, 1998 are not necessarily
indicative of the results to be expected for the year ending December 31, 1998
or any interim period.

 2.  SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

     Comprehensive Income

     During the first quarter of 1998, Cox adopted Statement of Financial
Accounting Standards No. 130, "Reporting Comprehensive Income," which requires
prominent disclosure of comprehensive income. Comprehensive income (loss) was
$220.0 million and $(48.7) million for the three months ended June 30, 1998 and
1997, respectively, and $240.9 million and $50.3 million for the six months
ended June 30, 1998 and 1997, respectively. Comprehensive income (loss) includes
consolidated net income (loss) and the change in the foreign currency
translation adjustment and net unrealized gain (loss) on securities for the
periods presented.

     Recently Issued Accounting Pronouncements
 
     In June 1997, Statement of Financial Accounting Standards No. 131
("SFAS No. 131"), "Disclosure about Segments of an Enterprise and Related
Information," was issued.  This Statement requires that a public company report
segment profit or loss, certain specific revenue and expense items, segment
assets, and certain descriptive information about the determination of business
segments.  SFAS No. 131 is effective for Cox's annual 1998 financial statements
and interim 1999 financial statements.  Management has determined there will be
no effect on Cox's financial statements as a result of the adoption of SFAS No.
131.

     In June 1998, Statement of Financial Accounting Standards No. 133
("SFAS No. 133"), "Accounting for Derivative Instruments and Hedging
Activities," was issued. This Statement requires that all derivatives be
recognized in the statement of financial position as either assets or
liabilities and measured at fair value. In addition, all hedging relationships
must be designated, reassessed and documented pursuant to the provisions of SFAS
No. 133. SFAS No. 133 is effective for fiscal years beginning after June 15,
1999. The effect on the financial statements upon adoption of SFAS No. 133 has
not been determined.

                                       7
<PAGE>
 
     Reclassifications

     Certain amounts in the 1997 financial statements have been reclassified 
for comparative purposes.

 3.  ACQUISITIONS AND DISPOSALS OF BUSINESS

     In June 1998, Cox acquired a cable television system serving approximately
115,000 customers in Tucson, Sierra Vista and portions of Pima County, Arizona
from TCI Communications, Inc. ("TCIC"), part of Tele-Communications, Inc.'s TCI
Group, for approximately $250.0 million.

     In May 1998, Cox acquired a cable television system serving approximately
14,000 customers in Douglas County, Nebraska from Advance/Newhouse Partnership
for approximately $8.0 million. Cox operates this system as part of its cluster
of systems in the Omaha area.

     In April 1998, Cox contributed its partnership interests and net assets in
and operations of  PrimeStar Partners, L.P. to a new subsidiary of TCI Satellite
Entertainment, Inc., PrimeStar, Inc., in exchange for $74.0 million and
18,939,217 shares of common stock of PrimeStar, Inc. The transaction resulted in
recording a 9.43% equity interest in PrimeStar, Inc. and a pre-tax gain of $37.3
million.

     In May 1998, Cox signed a definitive agreement to acquire Prime South
Diversified, Inc. ("PSDI") for a combination of Cox stock and cash. The
transaction values all of the businesses of PSDI, comprised of 319,000
residential cable television customers, 105,000 hotel units and interests in
various other non-consolidated operations in the greater Las Vegas area, at $1.3
billion. The closing of this transaction is subject to necessary government and
regulatory approvals and is expected to occur in fourth quarter 1998.

     In April 1998, Cox and TCIC signed a non-binding agreement to form a joint
venture serving approximately 270,000 customers in several key Oklahoma
communities. The partnership will operate TCIC's system serving approximately
150,000 customers in Tulsa and surrounding communities, along with Cox's system
in the Oklahoma City area, which serves approximately 120,000 customers. The
partnership will be managed by Cox.

 4.  INVESTMENTS

     The summarized unaudited financial information presented below for
significant equity method investments served as the basis for which Cox recorded
its share of equity in net losses:

<TABLE>
<CAPTION>

THREE MONTHS ENDED
-----------------------
(Thousands of Dollars)
                                                                             OUTDOOR                            GEMS
                              SPRINT PCS        COX PCS         TCGI          LIFE         SPEEDVISION       TELEVISION
                             ------------------------------------------------------------------------------------------
<S>                          <C>               <C>            <C>            <C>           <C>               <C>
JUNE 30, 1998
-------------
REVENUES                       $ 192,294       $ 24,060       $295,300       $ 5,484           $ 6,729         $ 3,102
OPERATING LOSS                  (387,457)       (54,500)       (28,300)       (3,870)           (9,326)         (1,264)
NET LOSS                        (542,205)       (80,344)       (55,900)       (3,743)           (9,215)         (2,440)
 
JUNE 30, 1997
-------------
REVENUES                          25,386          1,793        115,700         2,841             1,880           2,560
OPERATING LOSS                  (277,712)       (31,217)       (28,600)       (4,798)           (8,113)         (1,794)
NET LOSS                        (331,332)       (47,512)       (51,400)       (5,056)           (8,454)         (2,803)
</TABLE>

                                       8
<PAGE>
 
<TABLE>
<CAPTION>
 
SIX MONTHS ENDED
-----------------------
(THOUSANDS OF DOLLARS)
                                                                              OUTDOOR                            GEMS
                               SPRINT PCS        COX PCS         TCGI          LIFE         SPEEDVISION       TELEVISION
                              ------------------------------------------------------------------------------------------
<S>                          <C>               <C>            <C>            <C>           <C>               <C>
JUNE 30, 1998
REVENUES                     $   336,104       $  45,648      $ 455,400       $10,271          $ 11,630         $ 6,314
OPERATING LOSS                  (752,901)        (96,685)       (64,600)       (6,852)          (13,889)         (1,961)
NET LOSS                      (1,040,868)       (152,391)      (118,100)       (8,947)          (15,924)         (3,941)
 
JUNE 30, 1997
REVENUES                          34,853           2,872        212,500         5,358             3,360           5,019
OPERATING LOSS                  (468,526)        (72,488)       (52,200)       (9,510)          (15,186)         (3,663)
NET LOSS                        (546,835)       (103,157)       (96,400)       (9,919)          (15,732)         (5,683)
</TABLE>

     In July 1998, Cox's equity ownership in Teleport Communications Group
("TCG") was converted into shares of AT&T Corp. ("AT&T") common stock as a
result of the consummation of the merger between AT&T and TCG.  TCG agreed to a
merger with AT&T in January 1998 under which TCG shareholders exchanged each
share of TCG for 0.943 of a share of AT&T common stock. Cox will recognize a
gain on this transaction during the third quarter.

     In June 1998, Cox exercised its option to put 20% of its interest in Cox
PCS to Sprint PCS, which resulted in a pre-tax gain of $62.2 million.

     During March 1998, FOX/Liberty Networks acquired a one-third ownership
interest in each Speedvision and Outdoor Life Networks. Cox, whose ownership
interest was 51.4% and 49.3% as of December 31, 1997, respectively, retained a
one-third ownership stake in each network. Cox recognized a minimal gain on this
transaction during the second quarter.

 5.  DEBT

<TABLE>
<CAPTION>
                                                                            JUNE 30            DECEMBER 31
                                                                              1998                1997
                                                                     -----------------------------------------
                                                                              (THOUSANDS OF DOLLARS)
<S>                                                                       <C>                 <C>
Revolving credit facilities......................................          $       --           $  799,999 

Commercial Paper, net of unamortized discount of $8,966
and $2,191.......................................................           1,198,534              683,300 

Medium-term notes, net of unamortized discount of $1,252
and $1,201.......................................................             463,301              263,352 

Floating Rate Reset Notes, due June 15, 2009, net
of unamortized discount of $2,698 and $2,820.....................             147,302              147,180

6.375% Notes, due June 15, 2000, net of unamortized
discount of $469 and $587........................................             424,531              424,414 

6.5% Notes, due November 15, 2002, net of unamortized
discount of $386 and $430........................................             199,614              199,570 

6.875% Notes, due June 15, 2005, net of unamortized
discount and hedging of $11,833 and $12,462......................             363,167              362,538 

7.25% Debentures, due November 15, 2015, net of
unamortized discount of $817 and $840............................              99,183               99,160 

7.625% Debentures, due June 15, 2025, net of unamortized
discount and hedging of $17,861 and $17,953......................             132,139              132,047 

Capitalized Lease Obligations....................................              43,509               37,274 
                                                                           -------------------------------
    Total Debt...................................................          $3,071,280           $3,148,834 
                                                                           ===============================
</TABLE>

                                       9
<PAGE>
 
     In July 1998, Cox filed a Form S-3 Registration Statement (The "1998
Shelf Registration") with the Securities and Exchange Commission under which Cox
may from time to time offer and issue debentures, notes, bonds or other evidence
of indebtedness for a maximum aggregate amount of $1 billion. During July 1998,
Cox issued $200 million of 6.4% Notes under the 1998 Shelf Registration maturing
August 1, 2008 and $200 million of 6.8% Debentures maturing August 1, 2028.  The
net proceeds to Cox were approximately $395.4 million.

     In addition, during July 1998, Cox issued $250 million of 6.15% Reset Put
Securities due August 1, 2033 ("REPS") under the 1998 Shelf Registration. The
REPS are subject to mandatory redemption from the existing holders on August 1,
2003 through either (i) the exercise by the Remarketing Dealer of its right to
purchase the REPS for remarketing, or (ii) the repurchase of the REPS by Cox. If
remarketed, the Remarketing Dealer will, based on Cox's then current credit
spreads, determine the interest to be paid on the REPS.  Upon issuance of the
REPS, the Remarketing Dealer paid Cox a premium of $11.4 million for the right
to serve as the Remarketing Dealer. Amortization of the premium will be
reflected as adjustments to interest expense. The net proceeds to Cox were
approximately $259.4 million.

     In anticipation of the issuance of these debt securities, Cox had entered
into a series of transactions under a forward treasury lock agreement in order
to hedge its interest rate exposure. Such hedging transactions totaled a
notional amount of $50 million for the Notes due August 1, 2008, $50 million for
the Debentures due August 1, 2028 and $50 million for the REPS due August 1,
2033. The hedging transactions were settled at a minimal cost which will be
reflected as adjustments to interest expense over the life of the debt
securities.

     On January 22, 1998, Cox sold $100 million in medium term notes pursuant to
a Form S-3 Registration Statement filed April 1996 (the "1996 Shelf
Registration"). The notes are due January 15, 2018 with interest at a fixed rate
of 6.85%. The net proceeds to Cox were approximately $98.8 million. In addition,
on January 22, 1998 Cox sold a second series of $100 million medium term notes
under the 1996 Shelf Registration. The notes are due January 15, 2028 with
interest at a fixed rate of 6.95%. The net proceeds to Cox from the second
series of notes were approximately $98.8 million.

 6.  TRANSACTIONS WITH AFFILIATED COMPANIES

     Cash requirements are funded by internally generated funds, by various
external financing transactions and, as needed, through intercompany loans from
CEI. CEI performs day-to-day cash management services for Cox, with settlements
of credit or debit balances between Cox and CEI occurring periodically with
interest at market rates (6.34% at June 30, 1998). Included in the amounts due
(to)/from CEI are the following transactions:

                                                         (THOUSANDS OF DOLLARS)
     Balance, December 31, 1997..........................     $   50,856 
     Cash transferred from CEI...........................       (121,518)
     Net operating expense allocations and reimbursement.         20,973 
                                                              ----------
     Balance, June 30, 1998..............................     $  (49,689) 
                                                              ==========

 7.  SHAREHOLDERS EQUITY

     The following table reconciles the numerator and the denominator of the
basic and diluted per-share computations for income from operations for the
three and six months ended June 30, 1998 and 1997:

                                       10
<PAGE>
 
<TABLE>
<CAPTION>
                                                Three months ended June 30, 1998
                                  ----------------------------------------------------------
                                     Income/(loss)            Shares             Per-share
                                      (Numerator)          (Denominator)           Amount
                                  -----------------     ----------------     --------------- 
        <S>                       <C>                   <C>                  <C>
        Net loss                       $(12,246,000)
                                  -----------------
        BASIC EPS                       (12,246,000)         271,345,485              $(0.05)
                                                                             ===============
        EFFECT OF DILUTIVE
        SECURITIES
          Options                                --           (1,657,853)
          ESPP                                   --           (1,006,816)
                                  -----------------     ----------------     
        DILUTED EPS                    $(12,246,000)         268,680,816              $(0.05)
                                  =================     ================     ===============
</TABLE>

<TABLE>
<CAPTION>
                                                Three months ended June 30, 1997
                                  ----------------------------------------------------------
                                     Income/(loss)            Shares             Per-share
                                      (Numerator)          (Denominator)          Amount
                                  -----------------     ----------------     ---------------
        <S>                       <C>                   <C>                  <C>
        Net income                      $61,164,000
                                  -----------------
        BASIC EPS                        61,164,000          270,335,907               $0.23
                                                                             ===============
        EFFECT OF DILUTIVE
        SECURITIES
          Options                                --             (381,000)
          ESPP                                   --             (709,946)
                                  -----------------     ----------------     
        DILUTED EPS                     $61,164,000          269,244,961               $0.23
                                  =================     ================     ===============
</TABLE>

<TABLE>
<CAPTION>
                                                 Six months ended June 30, 1998
                                  ----------------------------------------------------------
                                     Income/(loss)            Shares             Per-share
                                      (Numerator)          (Denominator)           Amount
                                  -----------------     ----------------     ---------------
        <S>                       <C>                   <C>                  <C>
        Net loss                      $(114,165,000)
                                  -----------------
        BASIC EPS                      (114,165,000)         271,268,152              $(0.42)
                                                                             ===============
        EFFECT OF DILUTIVE
        SECURITIES
          Options                                --           (1,563,616)
          ESPP                                   --             (988,038)
                                  -----------------     ----------------   
        DILUTED EPS                   $(114,165,000)         268,716,498              $(0.42)
                                  =================     ================     ===============
</TABLE>
<PAGE>
<TABLE>
<CAPTION>
                                                 Six months ended June 30, 1997
                                  ----------------------------------------------------------
                                     Income/(loss)            Shares             Per-share
                                      (Numerator)          (Denominator)          Amount
                                  -----------------     ----------------     ---------------
        <S>                       <C>                   <C>                  <C>
        Net income                      $23,342,000
                                  -----------------
        BASIC EPS                        23,342,000          270,324,395               $0.09
                                                                             ===============
        EFFECT OF DILUTIVE
        SECURITIES
          Options                                --             (357,467)
          ESPP                                   --             (709,431)
                                  -----------------     ----------------   
        DILUTED EPS                     $23,342,000          269,257,497               $0.09
                                  =================     ================     ===============
</TABLE>


 8.  COMMITMENTS AND CONTINGENCIES

     Cox is a party to various legal proceedings that are ordinary and
incidental to its business. Management does not expect that any legal
proceedings currently pending will have a material adverse impact on Cox's

                                       11
<PAGE>
 
consolidated financial position or consolidated results of operations. See 
"--Part II - Other Information -- Item 1. Legal Proceedings."


ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
        RESULTS OF OPERATIONS

     The following discussion should be read in conjunction with the
accompanying historical Consolidated Statements of Income for the three-month
period ended June 30, 1998 and 1997.

RECENT ACQUISITIONS AND EXCHANGES

     In July 1998, Cox's equity ownership in Teleport Communications Group
("TCG") was converted into shares of AT&T Corp. ("AT&T") common stock  as a
result of the consummation of the merger between AT&T and TCG.  TCG agreed to a
merger with AT&T in January 1998 under which TCG shareholders exchanged each
share of TCG for 0.943 of a share of AT&T common stock. Cox will recognize a
gain on this transaction during the third quarter.

     In June 1998, Cox acquired a cable television system serving approximately
115,000 customers in Tucson, Sierra Vista and portions of Pima County, Arizona
from TCI Communications, Inc. ("TCIC"), part of Tele-Communications, Inc.'s TCI
Group, for approximately $250.0 million.

     In May 1998, Cox acquired a cable television system serving approximately
14,000 customers in Douglas County, Nebraska from Advance/Newhouse Partnership
for approximately $8.0 million. Cox operates this system as part of its cluster
of systems in the Omaha area.

     In April 1998, Cox contributed its partnership interests and net assets in
and operations of  PrimeStar Partners, L.P. to a new subsidiary of TCI Satellite
Entertainment, Inc., PrimeStar, Inc., in exchange for $74.0 million and
18,939,217 shares of common stock of PrimeStar, Inc. The transaction resulted in
recording a 9.43% equity interest in PrimeStar, Inc. and a pre-tax gain of $37.3
million.

     In May 1998, Cox signed a definitive agreement to acquire Prime South
Diversified, Inc. ("PSDI") for a combination of Cox stock and cash. The
transaction values all of the businesses of PSDI, comprised of 319,000
residential cable television customers, 105,000 hotel units and interests in
various other non-consolidated operations in the greater Las Vegas area, at $1.3
billion. The closing of this transaction is subject to necessary government and
regulatory approvals.

     In April 1998, Cox and TCIC signed a non-binding agreement to form a joint
venture serving approximately 270,000 customers in several key Oklahoma
communities. The partnership will operate TCIC's system serving approximately
150,000 customers in Tulsa and surrounding communities, along with Cox's system
in the Oklahoma City area, which serves approximately 120,000 customers. The
partnership will be managed by Cox.

THREE MONTHS ENDED JUNE 30, 1998 COMPARED WITH THREE MONTHS ENDED JUNE 30, 1997

     Revenues for the three months ended June 30, 1998 were $398.3 million, down
1% from revenues of $401.1 million for the three months ended June 30, 1997.
Basic customers were 3,378,749 at June 30, 1998. Excluding the effect of the
June 15, 1998 acquisition of the Tucson and Sierra Vista, Arizona cable
television systems serving approximately 115,000 customers, customer growth was
2.3% compared to the prior year after adjusting for the cable television system
transactions during 1997 and 1998.

     Complete basic revenues for the second quarter of 1998 increased 8% over
the comparable period in 1997 to $291.0 million primarily due to customer growth
and average rate increases of 6% implemented primarily during the fourth quarter

                                       12
<PAGE>
 
of 1997. These increases are the result of new channel additions, increased
programming costs and the pass-through of inflation adjustments.

     Pay-per-view revenues for the second quarter of 1998 were $8.0 million,
down 49% from the same period in 1997 primarily as a result of the
Tyson/Holyfield boxing event in 1997. Advertising revenues increased 30% to
$33.4 million due to growth in local, national and political advertising sales
during 1998.

     Data revenues for the second quarter of 1998 were $4.0 million primarily as
a result of Cox's residential data service, Cox@Home, which as of June 30, 1998,
had launched in seven markets with 1,759,182 "data ready" homes passed and had
34,263 customers. Telephony revenues for the second quarter of 1998 increased to
$6.6 million from $3.2 million primarily due to growth in the commercial
telephony business. Telephony revenues also included revenues from Cox's
residential telephone offering, which had launched in four markets as of June
30, 1998.

     Programming costs were $95.7 million for the second quarter of 1998, an
increase of 4% over the same period in 1997 due to customer growth, programming
rate increases and new channel additions. Plant operations expenses decreased
19% to $30.8 million and included the effect of a revised cost component factor
used to capitalize indirect costs relating to network construction activity.
Marketing costs increased by 39% to $25.0 million for the current quarter due in
part to costs associated with the rollout of high-speed data and telephony
services. General and administrative expenses for the second quarter of 1998
increased 23% to $94.8 million due primarily to direct costs associated with
high-speed data and telephony services.

     Operating income before depreciation and amortization ("EBITDA") is a
commonly used financial analysis tool for measuring and comparing cable
television companies in several areas, such as liquidity, operating performance
and leverage. EBITDA increased 3% to $152.0 million for the second quarter of
1998.

     The EBITDA margin (EBITDA as a percentage of revenues) for the current
quarter was 38.2%, an increase from 36.7% for the second quarter of 1997
primarily due to the contribution of the partnership interests, net assets and
operations in PrimeStar Partners, L.P. to PrimeStar, Inc., partially offset by a
continued increase in data and telephony direct costs.

     Depreciation was $80.4 million for the second quarter of 1998, a 6%
decrease compared to the same period in 1997 due to the contribution of the
partnership interests, net assets and operations in PrimeStar Partners, L.P. to
PrimeStar, Inc.  Operating income for the second quarter of 1998 was $53.8
million, an increase of 25% compared to the same period in 1997.

     Interest expense increased $.8 million to $51.0 million for the second
quarter of 1998 primarily due to the increase in total debt outstanding. Equity
in net losses of affiliated companies was $128.9 million primarily due to losses
of $79.0 million, $26.5 million and $12.4 million associated with Sprint PCS,
Cox PCS and Teleport, respectively.

     In the second quarter of 1998, Cox exercised its option to put 20% of its
interest in Cox PCS to Sprint PCS, which resulted in a pre-tax gain of $62.2
million. Also in the second quarter of 1998, Cox contributed its partnership
interests, net assets and operations in PrimeStar Partners, L.P. to PrimeStar,
Inc. in exchange for $74.0 million and 18,939,217 shares of common stock of
PrimeStar, Inc. The transaction resulted in recording a 9.43% equity interest in
PrimeStar, Inc. and a pre-tax gain of $37.3 million.

     Net loss for the current quarter was $12.2 million as compared to net
income of $61.2 million for the second quarter of 1997.

                                       13
<PAGE>
 
SIX MONTHS ENDED JUNE 30, 1998 COMPARED WITH SIX MONTHS ENDED JUNE 30, 1997

     Revenues for the six months ended June 30, 1998 were $814.1 million, a 4%
increase over revenues of $784.2 million for the six months ended June 30, 1997.
Basic customers were 3,378,749 at June 30, 1998. Excluding the effect of the
June 15, 1998 acquisition of the Tucson and Sierra Vista, Arizona cable
television systems serving approximately 115,000 customers, customer growth was
2.3% compared to the prior year after adjusting for the cable television system
transactions during 1997 and 1998.

     Complete basic revenues for the six months ended June 30, 1998 increased 7%
over the same period in 1997 to $575.4 million due primarily to customer growth
and average rate increases of 6% implemented primarily during the fourth quarter
of 1997. These increases are the result of new channel additions, increased
programming costs and the pass-through of inflation adjustments.

     Pay-per-view revenues for the six months ended June 30, 1998 were $18.4
million, down 31% from the same period in 1997 primarily as a result of the
Tyson/Holyfield boxing event in 1997. Advertising revenues increased 24% to
$58.4 million due to growth in local and national advertising sales during 1998.

     Data revenues for the first six months of 1998 were $6.8 million primarily
as a result of Cox's residential data service, Cox@Home, which as of June 30,
1998, had launched in seven markets with 1,759,182 "data ready" homes passed and
had 34,263 customers. Telephony revenues for the first six months of 1998
increased to $11.6 million from $5.8 million primarily due to growth in the
commercial telephony business. Telephony revenues also included revenues from
Cox's residential telephone offering, which had launched in four markets as of
June 30, 1998.

     Programming costs were $190.7 million for the six months ended June 30,
1998, an increase of 5% over the same period in 1997 due to customer growth,
programming rate increases and new channel additions. Plant operations expenses
decreased 17% to $63.5 million and included the effect of a revised cost
component factor used to capitalize indirect costs relating to network
construction activity. Marketing costs increased by 32% to $47.1 million for the
six months ended June 30, 1998 due in part to costs associated with the rollout
of high-speed data and telephony services. General and administrative expenses
for the first six months of 1998 increased 20% to $182.3 million due primarily
to direct costs associated with high-speed data and telephony services.

     Operating income before depreciation and amortization ("EBITDA") is a
commonly used financial analysis tool for measuring and comparing cable
television companies in several areas, such as liquidity, operating performance
and leverage. EBITDA increased 5% to $301.1 million for the six months ended
June 30, 1998.

     The EBITDA margin (EBITDA as a percentage of revenues) for the six months
ended June 30, 1998 was 37.0%, a slight increase from 36.6% for the comparable
period of 1997.

     Depreciation was $167.4 million for the first six months of 1998, a 6%
increase compared to the same period in 1997 due to the continued upgrade and
rebuild of the broadband network. Operating income for the six months ended June
30, 1998 was $97.3 million, an increase of 5% compared to the same period in
1997.

     Interest expense increased $7.1 million to $104.1 million for the six
months ended June 1998 primarily due to the increase in total debt outstanding.
Equity in net losses of affiliated companies was $270.7 million primarily due to
losses of $155.9 million, $58.9 million and $31.4 million associated with Sprint
PCS, Cox PCS and Teleport, respectively.

                                       14
<PAGE>
 
     In the first six months of 1998, Cox exercised its option to put 20% of its
interest in Cox PCS to Sprint PCS, which resulted in a pre-tax gain of $62.2
million. Also in the first six months of 1998, Cox contributed its partnership
interests, net assets and operations in PrimeStar Partners, L.P. to PrimeStar,
Inc. in exchange for $74.0 million and 18,939,217 shares of common stock of
PrimeStar, Inc. The transaction resulted in recording a 9.43% equity interest in
PrimeStar, Inc. and a pre-tax gain of $37.3 million.

     Net loss for the six months ended June 30, 1998 was $114.2 million as
compared to net income of $23.3 million for the comparable period of 1997.


LIQUIDITY AND CAPITAL RESOURCES

Uses of Cash

     As part of Cox's ongoing strategic plan, Cox has invested, and will
continue to invest, significant amounts of capital to enhance the reliability
and capacity of its broadband cable network in preparation for the offering of
new services and to make investments in affiliated companies primarily focused
on telephony, programming and communications-related activities.

     Capital expenditures are primarily directed at upgrading and rebuilding
broadband cable networks in preparation for the delivery of additional services.
Capital expenditures for 1998 are expected to range between $725 million and
$775 million. Capital expenditures during the six months ended June 30, 1998
were $357.0 million.

     Funding requirements in 1998 for investments in affiliated companies are
expected to be approximately $70 million, primarily for Sprint PCS. Investments
in affiliated companies during the six months ended June 30, 1998 of $35.0
million consists primarily of additional equity funding to Sprint PCS.

     During the six months ended June 30, 1998, net repayments of $800 million
were made for the revolving credit borrowings. In addition, payments for
purchase of cable television systems of $258.1 million were made for purchases
which were closed during the second quarter of 1998.

Sources of Cash

     Cox generated $264.3 million from operating activities during the six
months ended June 30, 1998. Proceeds from borrowings of $522.0 million under the
commercial paper program and $199.3 million of medium term notes under the 1996
Shelf Registration program were used to refinance revolving credit borrowings
mentioned above.

     In July 1998, Cox filed a Form S-3 Registration Statement for the 1998
Shelf Registration program under which Cox may from time to time offer and issue
debentures, notes, bonds or other evidence of indebtedness for a maximum
aggregate amount of $1 billion. During July 1998, Cox sold $400 million of notes
and debentures and $250 million of Reset Put Securities under the 1998 Shelf
Registration.

     Cox Enterprises, Inc. ("CEI") continues to perform day-to-day cash
management services for Cox with settlements of balances between Cox and CEI
occurring periodically at market interest rates. At June 30, 1998, an
intercompany payable of $49.7 million was due to CEI from Cox.

OTHER MATTERS

     Cox is continuing to address the Year 2000 issues to resolve the potential
impact of the Year 2000 on the processing of data-sensitive information by Cox's
computerized information systems. Testing on certain systems and applications
has occurred and will continue on the remainder of the systems and applications
throughout the course of the Year 2000 program.  Total incremental expenses to
bring current systems into compliance are not expected to have a material impact

                                       15
<PAGE>
 
on Cox's financial position, results of operations or cash flows in future
periods. However, if Cox, its customers or vendors are unable to resolve such
processing issues in a timely manner, it could result in a material financial
risk. Accordingly, Cox plans to devote the necessary resources to resolve all
significant year 2000 issues in a timely manner.


ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

     Cox is exposed to interest rate risk due to its various debt instruments.
In accordance with the requirements of SFAS No. 107, "Disclosures About Fair
Value of Financial Instruments," Cox estimated the fair value of its debt
instruments based on discounted cash flow analyses using Cox's incremental
borrowing rate for similar types of borrowing arrangements and dealer
quotations. The revolving credit agreements, commercial paper and floating rate
reset notes, at June 30, 1998 and 1997, bear interest at current market rates
and, thus, approximate fair value. The effect of a hypothetical one percentage
point increase in interest rates would decrease the estimated fair value of
remaining debt with a carrying amount of $1,766.5 million to $1,658.9 million.


                          PART II - OTHER INFORMATION
                                        
                                        
ITEM 1.  LEGAL PROCEEDINGS

     On October 9, 1997, three individual subscribers filed a putative class
action suit in Superior Court of the State of California, County of San Diego
against Cox and its cable system subsidiaries in California (the "Cox California
Systems") arising out of the manner in which the Cox California Systems sell
premium channel cable services. The suit alleges that the Cox California Systems
unlawfully require limited basic cable customers to purchase the expanded basic
services tier in order to purchase premium channels, i.e., channels sold on an a
la carte basis such as Home Box Office and Showtime. The suit asserts causes of
action under California antitrust and consumer protection laws. The suit seeks
injunctive relief as well as an order awarding the class members compensatory
damages, plus statutory damages, punitive damages, interest and attorney's fees.
On February 13, 1998, the Court granted Cox's motion to stay the suit and
referred it on grounds of Primary Jurisdiction to the Federal Communications
Commission for consideration of issues best addressed by the FCC's expertise
should the plaintiffs elect to file a complaint with the FCC. On April 14, 1998,
plaintiffs filed a petition for a peremptory writ of mandate with the California
Court of Appeals. The petition was denied on May 6, 1998. On May 18, 1998, the
plaintiffs filed a petition for review in the Supreme Court of California which
was denied on July 8, 1998.  The outcome of this matter cannot be predicted at
this time.

     Cox and its subsidiaries in Arizona, Oklahoma, Louisiana and Florida are
defendants in seven putative subscriber class action suits in the respective
state courts initiated between October 17, 1997 and January 26, 1998. The suits
all challenge the propriety of late fees charged by the subsidiaries to
customers who fail to pay for services in a timely manner. The suits seek
injunctive relief and various formulations of damages under various claimed
causes of action under various bodies of state law. The actions are being
defended vigorously. The outcome of these matters cannot be predicted at this
time.

     On May 12, 1998, the United States Department of Justice filed a three-
count antitrust complaint styled United States v. PrimeStar, Inc., et al., in
the United States District Court for the District of Columbia, naming Cox as one
of twelve defendants. The complaint seeks to enjoin the consummation of a June
11, 1997 Asset Acquisition Agreement by which PrimeStar, Inc. would acquire
direct broadcast satellite ("DBS") assets owned by defendants MCI Communications
Corp., The News Corporation Limited, and K. Rupert Murdoch. The complaint
alleges that PrimeStar Inc. is controlled by its cable shareholders (Tele-
Communications, Inc.; Time Warner Entertainment Co., L.P.; MediaOne Group;
Comcast Corp.; and Cox) and that the acquisition of the DBS assets would violate
Section 7 of the Clayton Act by reducing competition in a "multichannel video

                                       16
<PAGE>
 
programming service market" in which DBS operators compete with locally-
franchised cable operators. The complaint also alleges that all of the
defendants have violated Section 1 of the Sherman Act by agreeing to purchase
and sell the DBS satellite assets, and that defendants PrimeStar and the cable
company shareholders (including Cox) have violated Section 2 of the Sherman Act
by seeking to acquire the DBS assets. The complaint seeks a preliminary and
permanent injunction against the consummation of the Asset Acquisition
Agreement, or alternatively that the PrimeStar cable owners be required to
divest their ownership interests in PrimeStar, Inc.  A February 1999 trial date
has been set.  The outcome of this matter cannot be determined at this time.


ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

      (a)  Exhibits

           27  --  Financial Data Schedule

      (b)  Reports on Form 8-K filed during the quarter ended June 30, 1998:

           A Form 8-K dated May 5, 1998 (filed May 28, 1998) reported the
           proposed acquisition of Prime South Diversified, Inc. in Item 5 Other
           Events, and filed the Agreement and Plan of Merger associated
           therewith as Exhibit 2.1 of Item 7(c). The 8-K was amended on July 6,
           1998 by the filing of pro forma financial statements reflecting the
           acquisition as Item 7(b).

                                       17
<PAGE>
 
                                   SIGNATURES
                                        


     Pursuant to the requirements of the Securities Exchange Act of 1934,
the registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.



Cox Communications, Inc.




  /s/ Jimmy W. Hayes                                   Date:  August 5, 1998
  ------------------
  Jimmy W. Hayes
  Senior Vice President, Finance and
  Chief Financial Officer
  (Principal Financial Officer)

                                       18