CERTIFICATION PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY
                 ACT OF 2002 (SUBSECTIONS (A) AND (B) OF SECTION
                1350, CHAPTER 63 OF TITLE 18, UNITED STATES CODE)

In connection  with the attached  Report of The Swiss Helvetia  Fund,  Inc. (the
"Trust") on Form N-CSR to be filed with the Securities  and Exchange  Commission
(the "Report"), each of the undersigned officers of the Fund does hereby certify
that, to the best of such officer's knowledge:

1.   The Report fully  complies with the  requirements  of 13(a) or 15(d) of the
     Securities and Exchange Act of 1934, as applicable; and

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

Dated: March 6, 2006
       ________________

/s/ Rodolphe E. Hottinger
-------------------------
Rodolphe E. Hottinger
Chief Executive Officer

Dated: March 7, 2006
       ________________

/s/ Rudolf Millisits
----------------------
Rudolf Millisits
Chief Financial Officer


THIS  CERTIFICATE IS FURNISHED  PURSUANT TO THE  REQUIREMENTS  OF FORM N-CSR AND
SHALL NOT BE  DEEMED  "FILED"  FOR  PURPOSES  OF  SECTION  18 OF THE  SECURITIES
EXCHANGE ACT OF 1934, OR OTHERWISE SUBJECT TO THE LIABILITY OF THAT SECTION, AND
SHALL NOT BE DEEMED TO BE  INCORPORATED  BY REFERENCE  INTO ANY FILING UNDER THE
SECURITIES ACT OF 1933 OR THE SECURITIES EXCHANGE ACT OF 1934.