Form 6-K

SECURITIES AND EXCHANGE COMMISSION

Report of Foreign Private Issuer
Pursuant to Rules 13a-16 or 15d-16 of
the Securities Exchange Act of 1934

Dated: March 26, 2004

Swisscom AG

Alte Tiefenaustrasse 6
3050 Bern, Switzerland
(Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports under cover Form 20-F or Form 40-F.

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(1):______

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(7):______

Indicate by check mark whether the registrant by furnishing the information contained in this Form is also thereby furnishing the information to the Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

If “Yes” is marked, indicate below the file number assigned to the registrant in connection with Rule 12g3-2(b): 82-____________

Table of Contents

SCM Swisscom AG: Form 6-K

Change of Auditor

Based on a tender conducted earlier this year, the Board of Directors of Swisscom AG (“Swisscom”) is proposing to the Annual General Meeting to be held on April 27, 2004 that KPMG Klynveld Peat Marwick Goerdeler SA (“KPMG”) be appointed as new statutory and Group auditors. In connection with this proposal, the Board of Directors decided to appoint PricewaterhouseCoopers AG (“PwC”) as Swisscom’s new internal auditors, effective with the appointment of KPMG as new statutory and Group auditors. PwC has been Swisscom’s statutory and Group auditors for up to fiscal year 2003 and its activities in 2004 have been limited to the audit of Swisscom’s consolidated financial statements for the year ended December 31, 2003. Up to the end of 2003, KPMG had been Swisscom’s internal auditors.

PwC’s audit reports on Swisscom’s consolidated financial statements for each of the years ended December 31, 2003 and 2002 did not contain an adverse opinion or disclaimer of opinion, nor were they qualified or modified as to uncertainty, audit scope or accounting principles.

During the past two years ended December 31, 2003 and 2002, there have been no disagreements with PwC on any matter of accounting principle or practice, financial statement disclosure or auditing scope or procedure.

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.