Exhibit 13.1

Certification Pursuant to

        Rule 13a-14(b) (17 CFR240.13a-14(b)) or Rule 15d-14(b) (17 CFR240.15d-14(b))

and Section 1350 of Chapter 63 of Title 18 of the United States Code

(18 U.S.C. Section 1350)

        In connection with the Annual Report on Form 20-F of Alcon, Inc., a corporation organized under the laws of Switzerland (the “Company”), for the period ended December 31, 2003 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), each of the undersigned officers of the Company certify pursuant to Rule 13a-14(b) (17 CFR240.13a-14(b)) or Rule 15d-14(b) (17 CFR240.15d-14(b)) and Section 1350 of Chapter 63 of Title 18 of the United States Code (18 U.S.C. Section 1350), as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, as to such officer’s best knowledge, that:

1.) the Report fully complies, in all material respects, with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

2.) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company as of, and for, the periods presented in the Report.

        The foregoing certification is provided solely for purposes of complying with the provisions of Section 906 of the Sarbanes-Oxley Act of 2002 and is not intended to be used or relied upon for any other purpose.

Dated: March 12, 2004                                             /s/ T. R. G. Sear
                                                                         Timothy R.G. Sear 

Chairman, President & Chief Executive Officer

Dated: March 12, 2004                                                      /s/ Jacqualyn A. Fouse
                                                                                                Jacqualyn A. Fouse

                                                                                                 Senior Vice President, 
                                                                                               Finance and Chief Financial Officer

A signed original of this written statement required by Section 906 has been provided to Alcon, Inc. and will be retained by Alcon, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.