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 March 2004

                           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 Announcement No. 03 - 2004
issued by A/S STEAMSHIP COMPANY TORM (the "Company") to The Copenhagen Stock
Exchange (the "Exchange") on March 11, 2004, 2) as Exhibit 2 is a copy of Share
Statement No. 02 - 2004 issued by the Company to the Exchange on March 25, 2004,
3) as Exhibit 3 is a copy of Share Statement No. 03 - 2004 issued by the Company
to the Exchange on March 22, 2004 and 4) as Exhibit 4 is a copy of Announcement
No. 4 - 2004 issued by the Company to the Exchange on March 29, 2004.





Exhibit 1

ANNOUNCEMENT NO. 3 - 2004



11 March 2004


TORM 2003 result as expected - increases expectations for the 2004 result on own
activities before tax and potential gain on NORDEN shares to DKK 750-800 mill.

o    Net profit for the year was DKK 1,051 mill. (2002: DKK 550 mill.). The
     Board of directors considers the result to be highly satisfactory.

o    2003 Net profit includes an unrealized gain of DKK 681 mill. in respect of
     the Company's holding in Dampskibsselskabet `NORDEN' A/S.

o    The result is in line with the revised profits guidance for 2003 announced
     on 6 January 2004.

o    Cash flow from operating activities was DKK 494 mill. whilst cash outflow
     from investing activities was DKK 1,007 mill.

o    Shareholders' equity was DKK 2,464 mill. at 31 December 2003 (2002: DKK
     1,623 mill.).

o    Return on Equity of 51.4% (2002: 36.9%) and Return on Invested Capital of
     13.1% (2002: 4.4%).

o    The Company changed accounting policies in 2003 in order to use the USD as
     the primary measurement currency. This change has led to a reduction in
     Shareholders' equity of DKK 619 mill. and an increase in 2003 Net profit of
     DKK 55 mill.

o    The market value of the fleet exceeded book value by DKK 837 mill. as of 31
     December 2003.

o    New rules were adopted during 2003 by the IMO and the EU for the phasing
     out of older single-hulled tankers.

o    TORM took delivery of four newbuildings during the year, two MR vessels and
     two LR2 vessels.

o    TORM took delivery of a second hand Panamax bulk carrier during the year
     and exercised an option to purchase a time chartered Panamax vessel and in
     2004 has decided to exercise purchase options on two further Panamax bulk
     carriers, both of which will be delivered during 2004. During the first
     quarter 2003, the Company sold a 1992-built MR product tanker.

o    At year-end, the three tanker pools consisted of 61 vessels, whereas the
     Bulk division comprised 19 vessels.

o    For 2004 TORM expects profit before tax of DKK 750-800 mill., excluding any
     gain or loss on the shares of Dampskibsselskabet "NORDEN" A/S. The
     unrealized gain on the NORDEN shares as from 1 January 2004 until 9 March
     2004 was DKK 988 mill.

o    The Board of Directors recommends a dividend of DKK 12 per share (2002: DKK
     2 per share).

Conference call to discuss the results is scheduled for today 11 March 2004 at
17.00 CET (Copenhagen time). The conference call will also be accessible via the
Internet (www.torm.dk). To participate in the call, please call 10 minutes
before the start on tel.: +45 32 71 46 11 (from Europe) or +1 334 420 4950 (from
the US).


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



SAFE HARBOUR STATEMENT - FORWARD LOOKING STATEMENTS

Matters discussed in this release may constitute forward-looking statements.
Forward-looking statements reflect our current views with respect to future
events and financial performance and may include statements concerning plans,
objectives, goals, strategies, future events or performance, and underlying
assumptions and other statements, which are other than statements of historical
facts.

The forward-looking statements in this release are based upon various
assumptions, many of which are based, in turn, upon further assumptions,
including without limitation, management's examination of historical operating
trends, data contained in our records and other data available from third
parties. Although TORM believes that these assumptions were reasonable when
made, because these assumptions are inherently subject to significant
uncertainties and contingencies which are difficult or impossible to predict and
are beyond our control, TORM cannot assure you that it will achieve or
accomplish these expectations, beliefs or projections.

Important factors that, in our view, could cause actual results to differ
materially from those discussed in the forward-looking statements include the
strength of world economies and currencies, changes in charter hire rates and
vessel values, changes in demand for "tonne miles" of crude oil carried by oil
tankers, the effect of changes in OPEC's petroleum production levels and
worldwide oil consumption and storage, changes in demand that may affect
attitudes of time charterers to scheduled and unscheduled drydocking, changes in
TORM's operating expenses, including bunker prices, dry-docking and insurance
costs, changes in governmental rules and regulations including requirements for
double hull tankers or actions taken by regulatory authorities, potential
liability from pending or future litigation, domestic and international
political conditions, potential disruption of shipping routes due to accidents
and political events or acts by terrorists.

Risks and uncertainties are further described in reports filed by TORM with the
US Securities and Exchange Commission, including the TORM Annual Report on Form
20-F and its reports on Form 6-K.






GROUP FINANCIAL HIGHLIGHTS




DKK mill.                                          2003     2002     2001     2000     1999
---------                                          ----     ----     ----     ----     ----
                                                                        

INCOME STATEMENTS
Net revenue                                          1,928    1,539    2,001    1,597      924
Port expenses, Bunkers, Charter hire and
Technical running costs                             (1,281)  (1,237)  (1,248)  (1,012)    (735)
Gross profit (Net earnings from shipping
activities)                                            647      302      753      585      189
Profit from sale of vessels and interests                0       17       92       11        0
Administrative expenses                               (126)    (101)    (113)     (67)     (47)
Other operating income                                  51       55       59       45       26
Profit before depreciation                             572      273      791      574      168
Depreciation                                          (177)    (159)    (178)    (249)    (203)
Profit before financial items                          395      114      613      325      (35)
Financial items                                        657        6     (97)     (169)    (125)
Profit/(loss) before tax                             1,052      120      516      156     (160)
Tax on profit on ordinary activities                    (1)     360     (166)     (53)      56
Profit from continuing operations                    1,051      480      350      103     (104)
Profit before tax from discontinued operations           0       70       17        5       (1)
Tax on discontinued operations                           0        0        0        0        0
                                                 ----------------------------------------------
Net profit for the year                              1,051      550      367      108     (105)
                                                 ----------------------------------------------

BALANCE SHEET
Fixed assets                                         4,169    3,188    2,704    2,787    3,212
Total assets                                         4,894    4,013    4,049    4,040    4,346
Shareholders' equity                                 2,464    1,623    1,355    1,051      932
Total liabilities                                    2,430    2,390    2,335    2,783    3,240
Invested capital                                     3,186    2,844    2,297    2,459    3,073
Net interest bearing debt                            1,698    1,511      980    1,436    2,160
Cash and bonds                                         479      522      827      726      604

CASH FLOW
From operating activities                              494      261      682      287       69
From investing activities                           (1,008)  (1,118)     (54)      591    (522)
    thereof investment in tangible fixed assets     (1,122)    (954)    (554)    (351)    (527)
From financing activities                              471      552     (519)    (756)     319
Cash etc. in companies acquired/divested                 0        0       (8)       0        0
Net cash flow                                          (43)    (305)     101      122     (134)

KEY FIGURES *
Gross margin                                          33.6%    19.6%    37.6%    36.6%    20.5%
Profit before depreciation/Net revenue                29.7%    17.7%    39.5%    35.9%    18.2%
Profit before financial items/Net revenue             20.5%     7.4%    30.6%    20.4%    (3.8%)
Share price, end of period, DKK                      180.5     56.4     46.0     59.0     24.0
Millions of shares, end of period                     18.2     18.2     18.2     18.2     18.2
Earnings per share, DKK                               60.7     31.8     21.0      5.9     (5.8)
Diluted earnings per share, DKK                       59.9     31.8     21.0      5.9     (5.8)
RoE                                                   51.4%    36.9%    30.5%    10.9%      NA
RoIC**                                                13.1%     4.4%    25.8%    11.7%      NA
Equity ratio                                          50.3%    40.4%    33.5%    26.0%    21.4%
Proposed dividend per share, DKK                      12.0      2.0      4.0      2.0      2.0
Exchange rate USD/DKK, end of period                  5.96     7.08     8.41     8.02     7.40
Exchange rate USD/DKK, average                        6.59     7.89     8.32     8.08     6.98




*) Key figures are calculated in accordance with recommendations from the Danish
Society of Financial Analysts.
**) Profit before financial items divided by average Invested capital, defined
as average of beginning and ending balances of (Shareholders' equity plus Net
interest bearing debt less Non-operating assets).



Exhibit 2


SHARE STATEMENT No. 2  -2004



25 March 2004



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




Securities     Trade        Holding   Market       Total Holding  Total
code           date         number    value        number        market value
----           ----         ------    -----        ------        ------------

DK0010281468   17.03.2004   -2.576    978,880.00   1,159,723     440,439,552.00


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






Exhibit 3



SHARE STATEMENT No. 3  -2004





22 March 2004



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



Securities     Trade        Holding   Market        Total Holding   Total
code          date          number    value         number         market value
----          ----          ------    -----         ------         ------------

DK0010281468  12.03.2004    +5,100    1,857,573.00  1,211,774    444,914,688.00
DK0010281468  18.03.2004   +46,951   17,806,166.75  1,211,774    444,914,688.00




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






Exhibit 4


ANNOUNCEMENT NO. 4 - 2004



29 March 2004

BONUS SHARES

o    The Board of Directors of A/S Dampskibsselskabet TORM has decided to submit
     a proposal at the Annual General Meeting on 20 April 2004 for the increase
     of the Company's share capital from nominally DKK 182,000,000 by nominally
     DKK 182,000,000 to nominally DKK 364,000,000 by issue of 18,200,000 bonus
     shares of DKK 10. The bonus shares will be allotted at the ratio of one to
     one.

o    The proposal is motivated by a wish for maintaining and improving the
     liquidity in the Company's shares.

o    The new shares will have the same rights as the existing shares, just as
     the new shares shall carry right to full dividend for the financial year
     2004.

o    The bonus share issue including the publication of a prospectus and
     admission of the new shares for listing on the Copenhagen Stock Exchange is
     intended to be carried out as quickly as possible and before the end of the
     second quarter of this year.

o    Trading in the bonus share rights will not be possible.

A/S Dampskibsselskabet TORM

Contact persons:      Klaus Kjaerulff, CEO (tel.: +45 39 17 92 00)
                      Klaus Nyborg, CFO (tel.: +45 39 17 92 00)

SAFE HARBOUR STATEMENT - FORWARD LOOKING STATEMENTS

Matters discussed in this release may constitute forward-looking statements.
Forward-looking statements reflect our current views with respect to future
events and financial performance and may include statements concerning plans,
objectives, goals, strategies, future events or performance, and underlying
assumptions and other statements, which are other than statements of historical
facts.

The forward-looking statements in this release are based upon various
assumptions, many of which are based, in turn, upon further assumptions,
including without limitation, management's examination of historical operating
trends, data contained in our records and other data available from third
parties. Although TORM believes that these assumptions were reasonable when
made, because these assumptions are inherently subject to significant
uncertainties and contingencies which are difficult or impossible to predict and
are beyond our control, TORM cannot assure you that it will achieve or
accomplish these expectations, beliefs or projections.

Important factors that, in our view, could cause actual results to differ
materially from those discussed in the forward-looking statements include the
strength of world economies and currencies, changes in charter hire rates and
vessel values, changes in demand for "tonne miles" of crude oil carried by oil
tankers, the effect of changes in OPEC's petroleum production levels and
worldwide oil consumption and storage, changes in demand that may affect
attitudes of time charterers to scheduled and unscheduled drydocking, changes in
TORM's operating expenses, including bunker prices, dry-docking and insurance
costs, changes in governmental rules and regulations including requirements for
double hull tankers or actions taken by regulatory authorities, potential
liability from pending or future litigation, domestic and international
political conditions, potential disruption of shipping routes due to accidents
and political events or acts by terrorists.

Risks and uncertainties are further described in reports filed by TORM with the
US Securities and Exchange Commission, including the TORM Annual Report on Form
20-F and its reports on Form 6-K.








                                   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: March 30, 2004           By: /s/ Klaus Nyborg
                                    --------------------------
                                        Klaus Nyborg
                                        Chief Financial Officer



03810.0001 #474454