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 31, 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

Securities and Exchange Commission
450 Fifth Street, N.W.
Washington D.C. 20549
USA

Ladies and Gentlemen,

please find herewith the following key features of Swisscoms’ sixth shareholders’ meeting and of Swisscoms’ dividend.

*according to the Board of Directors of March 11, 2004

Attached is also the invitation to the Shareholders’ Meeting.

Very truly yours,

Swisscom AG
Group Legal Services

/s/ Stephan Wiederkehr
Stephan Wiederkehr
Head of Corporate & Financial Law

Invitation to the General Meeting of Shareholders

Dear Shareholder

We are pleased to
invite you to the
6th General Meeting
of Shareholders of
Swisscom AG on
Tuesday April 27,
2004, at 2.30 pm,
which will take
place for the first
time in the
SwissLifeArena in
Lucerne,
Eisfeldstrasse 2.

Doors will open at 1.30 pm

Agenda and proposals

Organizational issues

The Annual Report, comprising the annual accounts, the financial statements and the consolidated financial statements for the year ended December 31, 2003, as well as the reports of the statutory auditors and Group auditors, are available for inspection at company headquarters (Swisscom AG, Alte Tiefenaustrasse 6, 3048 Worblaufen). The Annual Report can also be viewed on the Swisscom AG website at www.swisscom.com/ir, or ordered from Swisscom AG, Share Register, PO Box 1226, 4609 Olten, using the enclosed application form (please check the appropriate box).

Please apply for your admission card and voting documents for the General Meeting using the enclosed application form as soon as possible. Admission cards and voting documents will be dispatched between April 1 and April 21, 2004. Because of the time constraint we can not post these items after the April 22, 2004. In the event that you did not receive your admission card and voting documents, please go to the reception desk (GV-desk) prior to the start of the General Meeting, where you will be given your admission card and voting documents in person upon presentation of an identity card.

All shareholders of Swisscom AG registered with voting rights in the share register at 4 pm on April 23, 2004 are entitled to vote at the General Meeting. For those shares which you might have sold after having received your admission card, you’re not eligible to vote anymore. If your admission card is no longer valid due to the fact that you have sold or purchased shares, please show the admission card at the reception desk (GV-desk) prior to the start of the General Meeting so that we can issue new documents for you. The share register will remain closed from 4 pm on April 23 until April 30, 2004.

You may be represented by another shareholder who is entitled to vote or by your legal representative.

You may also choose to be represented at the General Meeting by

If appointing a proxy, please only use the proxy form on the application or admission card.

Custody proxies appointed in accordance with Art. 689d of the Swiss Code of Obligations are kindly asked to notify the Swisscom Share Register as soon as possible (Swisscom AG, Share Register, PO Box 1226, 4609 Olten) of the total number and par value of the shares they represent. This may be done at the latest at the reception desk (GV-desk) on the day of the General Meeting. Institutions subject to the Swiss Banking Law and professional asset managers are permitted to act as custody proxies.

If you leave the General Meeting before it has ended, please present your unused voting documents at the exit so that the change in attendance can be recorded.

The General Meeting will be held in German. Simultaneous interpreting will be provided in French and English.

The minutes of the General Meeting will be available for inspection at company headquarters from May 18 to July 13, 2004 and online at www.swisscom.com/ir.

The General Meeting will be broadcast live on April 27, 2004 at www.swisscom.com/ir.

Due to the lack of parking space at the SwissLifeArena, please use public transportation. If you do come by car, please use the car park next to Lucerne Railway Station. From there, take bus number 6, 7, 8 or 21 to the SwissLifeArena. The admission card entitles you to travel free on these busses.

All participants are cordially invited for refreshments after the Meeting.

Should you have any questions concerning the General Meeting, please contact our Share Register Call Center directly on freephone 0800 800 512 (only available from inside Switzerland), or send an e-mail to investor.relations@swisscom.com.

Further information is also available on www.swisscom.com/ir.

Yours sincerely
On behalf of the Board of Directors of Swisscom AG

Chairman: Dr Markus Rauh

Enclosures:

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.