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 July 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 1) as Exhibit 1 is a copy of Share Statement No.
7/2003 issued by A/S STEAMSHIP COMPANY TORM (the "Company") to The Copenhagen
Stock Exchange on June 20, 2003 and 2) as Exhibit 2 is a copy of Statement No.
7-2003 issued by the Company to the Copenhagen Stock Exchange on June 25, 2003.



                                                           [LOGO]
                                                            TORM
Exhibit 1                                         ----------------------
---------

                                                  A/S Dampskibsselskabet TORM
                                                  Marina Park
                                                  Sundkrogsgade 10
                                                  DK-2100 Copenhagen 0
Kobenhavns Fondsbors                              Denmark
Nikolaj Plads 6
1067 Kobenhavn K                                  Tel:        +45 39 17 92 00
                                                  Fax:        +45 39 17 93 93
                                                  Telex:      22315 TORM DK

                                                  E-mail:     mail@torm.dk
                                                  Website:    www.torm.dk
                                                  Comtext:    A43DK152

                                                  VAT/CVR. No. 2246 0218




20 June 2003      Share statement no. 7/2003
                  Contact Person:  Klaus Nyborg, CFO, (Phone +45 3917 9200)

Please below find the total shareholdings of all insiders and related parties,
including the shareholding of the entire Board of Directors (including related
parties) and the entire Executive Board of Directors (including related parties)
pursuant to the Danish Securities Trading Act.


--------------------------------------------------------------------------------
Securities code                    Holding                      Market value
DK0010281468                       (number)                         (DKK)

                               As at 18 June 2003            As at 18 June 2003
--------------------------------------------------------------------------------
Board of Directors                   4,973                        432,800.19
(incl. related parties)
--------------------------------------------------------------------------------
Executive Board of Directors         5,800                        504,774.00
(incl. related parties)
--------------------------------------------------------------------------------

All (incl. related parties)      1,169,233                    101,758,347.99

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



Yours faithfully
A/S Dampskibsselskabet TORM

Klaus Nyborg



Exhibit 2
---------


                                                  ----------------------
Kobenhavns Fondsbors
(The Copenhagen Stock Exchange)                   A/S Dampskibsselskabet TORM
Nikolaj Plads 6                                   Marina Park
1067 Copenhagen K                                 Sundkrogsgade 10
                                                  DK-2100 Copenhagen 0
                                                  Denmark

                                                  Tel:        +45 39 17 92 00
                                                  Fax:        +45 39 17 93 93
                                                  Telex:      22315 TORM DK

                                                  E-mail:     mail@torm.dk
                                                  Website:    www.torm.dk
                                                  Comtext:    A43DK152

                                                  VAT/CVR. No. 2246 0218




25th June 2003    Statement No. 7 - 2003
                  Contact Person:  Mr. Klaus Kjaerulff, CEO


TORM places order for 2 newbuildings

     o    A/S Dampskibsselskabet TORM has signed a contract with Dalian New
          Shipbuilding Ltd. in the People's Republic of China for construction
          of two high specification 105,000 dwt (Aframax) product tankers. The
          Company has an option for two further vessels.

          The vessels are due to be delivered in 2nd and 3rd quarter 2006 and
          represent the latest additions to a substantial newbuilding programme
          initiated in 1999 now totalling 12 vessels, of which six vessels have
          been delivered to date.

     o    These transactions are a further demonstration of TORM's commitment to
          implementing a strategy based on owning and operating, in conjunction
          with its pool partners, a modern, technologically advanced fleet aimed
          at providing the customers with the capacity, flexibility and quality
          required.



Yours faithfully,
A/S Dampskibsselskabet TORM



Klaus Kjaerulff
CEO



                                   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: July 8, 2003                               By: /s/ Klaus Nyborg
                                                      -----------------
                                                      Klaus Nyborg
                                                      Chief Financial Officer


03810.0001 #415906