FORM 6-K


                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D. C. 20549



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

                        For the month of September, 2003

                           A/S STEAMSHIP COMPANY TORM
                 (Translation of registrant's name into English)

                                   Marina Park
                                Sundkrogsgade 10
                              DK-2100 Copenhagen 0
                                     Denmark
                    (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 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
                                       ---  ---



INFORMATION CONTAINED IN THIS FORM 6-K REPORT

         Set forth herein as Exhibit 1 is a copy of Share Statement No. 8/2003
issued by A/S STEAMSHIP COMPANY TORM (the "Company") to The Copenhagen Stock
Exchange on September 24, 2003 and as Exhibit 2 is a copy of Share Statement No.
9/2003 issued by the Company to The Copenhagen Stock Exchange on September 24,
2003.



Exhibit 1
---------






K0benhavns Fondsb0rs                               [TORM LOGO]
Nikolaj Plads 6
1067 K0benhavn K







24 September 2003      Share statement no.  8/2003
                       Contact Person: Klaus Nyborg, CFO, (Phone +45 3917 9200)

This is to notify you of changes in the shareholdings of the company's insiders
pursuant according to the Danish Securities Trading Act.



--------------------------------------------------------------------------------------------------------------------
   Securities code       Trade date     Holding          Market            Total Holding          Total market
                                        number           value                number                 value
--------------------------------------------------------------------------------------------------------------------
                                                                                      
          DK0010281468     03.09.2003      -3,850           542,850.00             1,165,389         164,506,304.00
--------------------------------------------------------------------------------------------------------------------




Yours faithfully
A/S Dampskibsselskabet TORM

Klaus Nyborg



Exhibit 2
---------





                                                    [TORM LOGO]
SHARE STATEMENT No.  9 -2003                        ---------------------------
                                                    A/S Dampskibsselskabet TORM
                                                    Marine Park
                                                    Sundkrogsgade 10
                                                    DK-2100 Copenhagen O
                                                    Denmark



24 September, 2003



This is to notify you of changes in the shareholdings of the company's insiders
pursuant according to the Danish Securities Trading Act.



--------------------------------------------------------------------------------------------------------------------
Securities code          Trade date     Holding          Market            Total Holding          Total market
                                        number           value                number                 value
--------------------------------------------------------------------------------------------------------------------
                                                                                      
          DK0010281468     15.09.2003        -690            89,700.00             1,164,399         152,338,320.00
--------------------------------------------------------------------------------------------------------------------





A/S Dampskibsselskabet TORM
Contact person:   Klaus Nyborg, CFO (tel.: +45 39 17 92 00)



                                   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.

                           A/S STEAMSHIP COMPANY TORM
                                  (registrant)



Dated: September 24, 2003            By: /s/ Klaus Nyborg
                                     -------------------------------------------
                                     Klaus Nyborg
                                     Chief Financial Officer






03810.0001 #430643