UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM N-Q

             QUARTERLY SCHEDULE OF PORTFOLIO HOLDINGS OF REGISTERED
                          MANAGEMENT INVESTMENT COMPANY

                  Investment Company Act file number 811-05128

                          THE SWISS HELVETIA FUND, INC.
                     1270 Avenue of the Americas, Suite 400
                            New York, New York 10020
                                 1-888-SWISS-00

                        Rodolphe E. Hottinger, President
                                Hottinger et Cie
                               3 Place des Bergues
                                    C.P. 395
                                 CH-1201 Geneva
                                   Switzerland


                      Date of fiscal year end: December 31

           Date of reporting period: July 1, 2004 - September 30, 2004






Item 1.  Schedule of Investments


                                                                                                              
                      THE SWISS HELVETIA FUND, INC.
---------------------------------------------------------------------------------------------------------------------------

SCHEDULE OF INVESTMENTS (Unaudited)                                                                       SEPTEMBER 30, 2004

                                                                                                                   Percent
  No. of                                                                                                              Net
  Shares               Security                                                             Value                   Assets
---------------------------------------------------------------------------------------------------------------------------

COMMON STOCKS - 95.89%

BANKS - 10.25%

               243,000 CREDIT SUISSE GROUP(1)
                       REGISTERED SHARES                                                 $ 7,754,905                 2.07%
                       A global operating financial group.
                       (Cost $6,482,308)

               435,000 UBS AG(2)
                       REGISTERED SHARES                                                  30,621,046                 8.18%
                       Largest Swiss bank. It offers
                       consumer, business and construction
                       loans, mortgages, mutual funds, export
                       and structured finance and securities
                       brokerage services, advises on mergers
                       and acquisitions, invests pension funds
                       and sponsors credit cards.
                       (Cost $7,578,949)
                                                                                     ----------------     -----------------
                                                                                          38,375,951                10.25%

BIOTECHNOLOGY - 5.52%

               192,755 ACTELION LTD.(1,2)
                       REGISTERED SHARES                                                  19,758,661                 5.28%
                       Pharmaceutical company that develops and
                       markets synthetic small-molecule drugs against
                       diseases related to the endothelium. The company's
                       drugs, Veletri and Tracleer, are used in the treatment
                       of heart and pulmonary conditions.
                       (Cost $15,945,087)

                35,487 CYTOS BIOTECHNOLOGY AG1
                       REGISTERED SHARES                                                     909,413                 0.24%
                       Develops and produces biopharmaceuticals.  Produces
                       vaccines that immunize the patient against disease-related
                       proteins.  This instructs the immune system to produce
                       antibodies to reverse or prevent disease progression.
                       (Cost $1,433,020)
                                                                                     ----------------     -----------------
                                                                                          20,668,074                 5.52%

CHEMICALS - 8.59%

                18,598 SIKA AG2
                       BEARER SHARES                                                      10,723,601                 2.86%
                       Leading producer of construction chemicals.
                       (Cost $5,039,641)

               224,931 SYNGENTA AG(1,2)
                       REGISTERED SHARES                                                  21,435,724                 5.73%
                       Produces herbicides, insecticides and fungicides,
                       and seeds for field crops, vegetables, and flowers.
                       (Cost $14,558,082)
                                                                                     ----------------     -----------------
                                                                                          32,159,325                 8.59%

CONSTRUCTION - 8.81%

                20,758 GEBERIT AG(2)
                       REGISTERED SHARES                                                  16,124,978                 4.30%
                       Manufactures and supplies water supply
                       pipes and fittings, installation systems,
                       drainage and flushing  systems such as visible  cisterns,
                       and  other  sanitary   systems  for  the  commercial  and
                       residential construction markets.
                       (Cost $7,721,250)

               320,143 HOLCIM LTD.(2)
                       REGISTERED SHARES                                                  16,882,691                 4.51%
                       Produces and markets various building materials,
                       in addition to providing consulting and engineering
                       services in all areas of the cement manufacturing
                       process.
                       (Cost $16,228,963)
                                                                                     ----------------     -----------------
                                                                                          33,007,669                 8.81%

FOOD & BEVERAGES - 13.61%

                   300 LINDT & SPRUNGLI AG
                       REGISTERED SHARES                                                   3,579,723                 0.95%
                       Major manufacturer of premium
                       Swiss chocolates.
                       (Cost $1,196,399)

               207,000 NESTLE AG(2)
                       REGISTERED SHARES                                                  47,410,907                12.66%
                       Largest food and beverage processing
                       company in the world.
                       (Cost $12,427,541)
                                                                                     ----------------     -----------------
                                                                                          50,990,630                13.61%

HEALTH CARE - 30.20%

             1,315,000 NOVARTIS AG(2)
                       REGISTERED SHARES                                                  61,290,142                16.37%
                       One of the leading manufacturers
                       of pharmaceutical and
                       nutrition products.
                       (Cost $16,301,451)

               261,766 PHONAK HOLDING AG
                       REGISTERED SHARES                                                   8,395,714                 2.24%
                       Designs and produces wireless analog and
                       digital hearing aids, transmitters, remote
                       controls, microphones and receivers for use in
                       wireless communications within broadcasting
                       and sports.
                       (Cost $2,469,614)

               420,000 ROCHE HOLDING AG(2)
                       DIVIDEND RIGHTS CERTIFICATES                                       43,389,125                11.59%
                       Worldwide pharmaceutical company.
                       (Cost $8,467,363)
                                                                                     ----------------     -----------------
                                                                                         113,074,981                30.20%

INDUSTRIAL GOODS & SERVICES - 7.67%

             2,014,725 ABB LTD.(1, 2)
                       REGISTERED SHARES                                                  12,294,550                 3.28%
                       The holding company for ABB Group
                       which is one of the largest electrical
                       engineering firms in the world.
                       (Cost $8,602,479)

                 2,055 BELIMO HOLDING AG
                       REGISTERED SHARES                                                   1,035,153                 0.28%
                       World market leader in damper and
                       volume control actuators for ventilation
                       and air-conditioning equipment.
                       (Cost $450,523)

                 4,500 KABA HOLDINGS AG(1)
                       BEARER SHARES                                                       1,061,304                 0.28%
                       Provides mechanical and electronic
                       security systems.
                       (Cost $809,667)

                59,885 KUEHNE & NAGEL INTERNATIONAL AG
                       REGISTERED SHARES                                                   9,807,386                 2.62%
                       Operates sea freight, land and rail
                       transportation businesses and
                       warehousing and distribution facilities.
                       (Cost $3,674,112)

                 6,598 SGS SOCIETE GENERALE DE
                       SURVEILLANCE HOLDING SA
                       REGISTERED SHARES                                                   3,619,468                 0.97%
                       Provides a variety of industrial
                       inspection, analysis, testing and
                       verification services worldwide.
                       (Cost $1,709,324)

                 5,076 SIG HOLDING AG
                       REGISTERED SHARES                                                     910,566                 0.24%
                       Manufactures packaging machinery
                       through subsidaries.   Produces
                       beverage bottling machines, beverage
                       cartons, and filling machines.
                       (Cost $1,012,065)
                                                                                     ----------------     -----------------
                                                                                          28,728,427                 7.67%

INSURANCE - 3.75%

                43,803 SWISS LIFE HOLDING(1)
                       REGISTERED SHARES                                                   5,182,905                 1.38%
                       Provides life insurance, institutional
                       investment management, and private
                       banking services.
                       (Cost $5,802,507)

                68,088 SWISS REINSURANCE COMPANY
                       REGISTERED SHARES                                                   3,917,773                 1.05%
                       Second largest reinsurance company
                       in the world.
                       (Cost $4,038,842)

                34,549 ZURICH FINANCIAL SERVICES AG
                       REGISTERED SHARES                                                   4,924,899                 1.32%
                       Offers property, accident, health, automobile,
                       liability, financial risk and life insurance and
                       retirement products.
                       (Cost $5,493,466)

                                                                                     ----------------     -----------------
                                                                                          14,025,577                 3.75%

RETAILERS - 1.01%

                24,767 GALENICA HOLDING AG
                       REGISTERED SHARES                                                   3,768,503                 1.01%
                       Manufactures and distributes prescription
                       and over-the-counter drugs, toiletries and
                       hygiene products.
                       (Cost $3,158,881)
                                                                                     ----------------     -----------------
                                                                                           3,768,503                 1.01%

TECHNOLOGY - 5.04%

                22,454 HUBER & SUHNER AG
                       REGISTERED SHARES                                                   1,564,425                 0.42%
                       Manufactures a wide range of products, extending
                       from cables for energy and electrical submission
                       to special products such as rubber.
                       (Cost $1,291,221)

               208,530 LOGITECH INTERNATIONAL SA(1)
                       REGISTERED SHARES                                                  10,103,359                 2.70%
                       Manufactures personal computer input
                       devices, as well as producing trackballs,
                       desktop publishing programs and related
                       software. 
                       (Cost $7,189,152)

                81,577 MICRONAS SEMICONDUCTOR HOLDING AG(1)
                       REGISTERED SHARES                                                   3,462,466                 0.92%
                       Develops and manufactures a wide range of  semiconductors
                       and modules used by the  automotive  and  consumer  goods
                       industries.
                       (Cost $3,114,002)

               492,883 TEMENOS GROUP AG(1)
                       REGISTERED SHARES                                                   3,749,811                 1.00%
                       Provides  integrated  software  for the  banking  sector.
                       Develops,  distributes,   implements,  and  supports  its
                       process-oriented  real-time  enterprise software designed
                       for the  management  of  administrative  tasks in Europe,
                       North America, Asia, and the Middle East.
                       (Cost $3,854,386)
                                                                                     ----------------     -----------------
                                                                                          18,880,061                 5.04%

UTILITY SUPPLIERS - 1.44%

                 5,364 ELEKTRIZITAETS-GESELLSCHAFT LAUFENBURG AG
                       REGISTERED SHARES                                                   3,629,839                 0.97%
                       Generates  and sells  electricity.  Operates  nuclear and
                       hydroelectric   generating  plants.  Sells  excess  power
                       throughout Europe.
                       (Cost $3,628,197)

                 3,500 BKW FMB ENERGIE AG
                       REGISTERED SHARES                                                   1,751,822                 0.47%
                       Generates and distributes electricty.  Produces
                       electricity using nuclear, hydroelectric, solar,
                       biomass and wind energy.
                       (Cost $1,673,583)
                                                                                     ----------------     -----------------
                                                                                           5,381,661                 1.44%


                       TOTAL COMMON STOCKS
                       (Cost $171,352,075)                                             $ 359,060,859                95.89%
                       OTHER ASSETS IN EXCESS OF LIABILITIES                              15,391,295                 4.11%
                                                                                     ----------------     -----------------
                       NET ASSETS                                                      $ 374,452,154               100.00%
                                                                                     ================     =================

---------------------------------------------------------------------------------------------------------------------------
1 NON-INCOME PRODUCING SECURITY.
2 ONE OF THE TEN LARGEST PORTFOLIO HOLDINGS.
* COST FOR FEDERAL INCOME TAX PURPOSES IS SUBSTANTIALLY THE SAME AS FOR FINANCIAL STATEMENT PURPOSES AND NET UNREALIZED APPRECIATION
(DEPRECIATION) CONSISTS OF:
GROSS UNREALIZED APPRECIATION                   $189,747,703
GROSS UNREALIZED DEPRECIATION                   ($2,038,919)
                                                ------------
NET UNREALIZED APPRECIATION (DEPRECIATION)      $187,708,784



Item 2.  Controls and Procedures.
(a)  The   registrant's   President  and  Treasurer   have  concluded  that  the
registrant's  disclosure  controls and  procedures  (as defined in rule 30a-3(c)
under the Investment  Company Act of 1940 (the "Act")) are  effective,  based on
their  evaluation of these disclosure  controls and procedures  required by Rule
30a-3(b) as of a date within 90 days of the filing date of this report.

(b) There were no changes in the  registrant's  internal  control over financial
reporting (as defined in rule 30a-3(d)  under the Act) that occurred  during the
registrant's  last  fiscal  quarter  that  have  materially  affected,   or  are
reasonably likely to materially affect,  the registrant's  internal control over
financial reporting.

Item 3.  Certifications  as required by Rule 30a-2(a) under the Act are attached
hereto.

                                   SIGNATURES

Pursuant to the  requirements  of the  Securities  Exchange  Act of 1934 and the
Investment Company Act of 1940, the registrant has duly caused this report to be
signed on its behalf by the undersigned, thereunto duly authorized.


THE SWISS HELVETIA FUND, INC.

By:      /s/ Rodolphe E. Hottinger
         ________________________________
         Rodolphe E. Hottinger, President

Date:    November 8, 2004
         ________________________________

Pursuant to the  requirements  of the  Securities  Exchange  Act of 1934 and the
Investment  Company  Act of  1940,  this  report  has been  signed  below by the
following  persons on behalf of the  registrant and in the capacities and on the
dates indicated.

By:      /s/ Rodolphe E. Hottinger
         ________________________________
         Rodolphe E. Hottinger, President

Date:    November 8, 2004
         ________________________________


By:      /s/ Rudolf S. Millisits
         ________________________________
         Rudolf S. Millisits, Treasurer

Date:    November 5, 2004
         ________________________________