<PAGE>

                                                                    EXHIBIT 31.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER PURSUANT TO RULE 13a-14(a) OF THE
SECURITIES EXCHANGE ACT OF 1934

I, James O. Robbins, Chief Executive Officer of Cox Communications, Inc.,
certify that:

1. I have reviewed this quarterly report on Form 10-Q of Cox Communications,
Inc.;

2. Based on my knowledge, this report does not contain any untrue statement of a
material fact or omit to state a material fact necessary to make the statements
made, in light of the circumstances under which such statements were made, not
misleading with respect to the period covered by this report;

3. Based on my knowledge, the financial statements, and other financial
information included in this report, fairly present in all material respects the
financial condition, results of operations and cash flows of the registrant as
of, and for, the periods presented in this report;

4. The registrant's other certifying officer and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Exchange Act Rules 13a-15(e) and 15d-15(e)) [omitted in accordance with Section
III.E. of SEC Release No. 34-47986] for the registrant and have:

         (a) designed such disclosure controls and procedures, or caused such
         disclosure controls and procedures to be designed under our
         supervision, to ensure that material information relating to the
         registrant, including its consolidated subsidiaries, is made known to
         us by others within those entities, particularly during the period in
         which this report is being prepared;

         (b) [omitted in accordance with Section III.E. of SEC Release No.
         34-47986];

         (c) evaluated the effectiveness of the registrant's disclosure controls
         and procedures and presented in this report our conclusions about the
         effectiveness of the disclosure controls and procedures as of the end
         of the period covered by this report based on such evaluation; and

         (d) disclosed in this report any change in the registrant's internal
         control over financial reporting that occurred during the registrant's
         most recent fiscal quarter (the registrant's fourth fiscal quarter in
         the case of an annual report) that has materially affected, or is
         reasonably likely to materially affect, the registrant's internal
         control over financial reporting; and

5. The registrant's other certifying officer and I have disclosed, based on our
most recent evaluation of internal control over financial reporting, to the
registrant's auditors and the audit committee of the registrant's board of
directors (or persons performing the equivalent functions):

         (a) all significant deficiencies and material weaknesses in the design
         or operation of internal control over financial reporting which are
         reasonably likely to adversely affect the registrant's ability to
         record, process, summarize and report financial information; and

         (b) any fraud, whether or not material, that involves management or
         other employees who have a significant role in the registrant's
         internal control over financial reporting.

Date: May 5, 2004

/s/ James O. Robbins
------------------------------------------
James O. Robbins
President and Chief Executive Officer