FORM 6-K

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                       REPORT OF A FOREIGN PRIVATE ISSUER
                     PURSUANT TO RULE 13a- 16 OR 15d- 16 OF
                           THE SECURITIES ACT OF 1934

For the month of                      May                                   2004
                  --------------------------------------------------------

                          Canadian Superior Energy Inc.
--------------------------------------------------------------------------------
                (Translation of registrant's name into English)

       Suite 3300, 400 Third Avenue SW, Calgary, Alberta, Canada T2P 4H2
--------------------------------------------------------------------------------
                  (Translation 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                    Form 40-F    X
                           -------                      -------

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.

                       Yes                           No    X
                           -------                      -------

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





                                  Exhibit Index

The following is a list of Exhibits included as part of this Report on Form 6-K.



        Description of Exhibit                                             Page
--------------------------------------------------------------------------------
                                                                     
99.1   First Quarter Interim Financial Statements                            3
       Interim Management's Discussion and Analysis






                                   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.

                                      Canadian Superior Energy Inc.


                                      By: "Greg Noval"
                                      ------------------------------------------
Date: May 11, 2004                    Name:  Greg Noval
                                      Title: Chief Executive Officer