SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

                             ----------------------

                                    FORM 6-K

                        REPORT OF FOREIGN PRIVATE ISSUER

                    Pursuant to Rule 13a-16 or 15d-16 of the
                         Securities Exchange Act of 1934

                          For the month of April, 2004

                        Commission File Number: 000-16977

                               Stolt-Nielsen S.A.
               ---------------------------------------------------
                 (Translation of registrant's name into English)

                            c/o Stolt-Nielsen Limited
                                  Aldwych House
                                  71-91 Aldwych
                                 London WC2B 4HN
                                     ENGLAND
                                     -------
                    (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.

                       Form 20-F   X             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 by furnishing the information contained in
this Form, the registrant is also thereby furnishing the information to the
Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

                        Yes                       No   X
                             ---                      ---

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

<PAGE>
     In accordance with General Instruction B, item (i), attached herewith as
Exhibit 99.1 is a press release, dated April 27, 2004, announcing the financial
results for the registrant's first quarter ended February 29, 2004.

     Certain statements made in the press release furnished pursuant to this
Form 6-K may include "forward-looking statements" within the meaning of Section
27A of the Securities Act of 1933 and Section 21E of the Securities Exchange Act
of 1934. These statements may be identified by the use of words like
"anticipate," "believe," "estimate," "expect," "intend," "may," "plan,"
"project," "will," "should," "seek," and similar expressions. The
forward-looking statements reflect our current views and assumptions and are
subject to risks and uncertainties. The following factors, and others which are
discussed in our public filings and submissions with the U.S. Securities and
Exchange Commission, are among those that may cause actual and future results
and trends to differ materially from our forward-looking statements: the terms,
conditions and amount of our indebtedness; our ability to restructure our
existing indebtedness; our ability to recover costs on significant projects; the
general economic conditions and competition in the markets and businesses in
which we operate; the outcome of legal proceedings; the impact of negative
publicity; environmental challenges and natural conditions facing our
aquaculture business; the impact of laws and regulations; uncertainties inherent
in operating internationally; our relationship with significant customers; and
operating hazards, including marine disasters, spills or environmental damage.
Many of these factors are beyond our ability to control or predict. Given these
factors, you should not place undue reliance on the forward-looking statements.

<PAGE>
                                    SIGNATURE


     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.


                                           STOLT-NIELSEN S.A.


Date:  April 27, 2004                   By:  /s/ Alan B. Winsor
                                           -------------------------------------
                                           Name:  Alan B. Winsor
                                           Title: Attorney-in-Fact