SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549

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


                                    FORM 8-K

                                 CURRENT REPORT

                     PURSUANT TO SECTION 13 OR 15(D) OF THE

                         SECURITIES EXCHANGE ACT OF 1934

         Date of Report (Date of earliest event reported): May 15, 2003



                            Moore Corporation Limited
             ------------------------------------------------------
             (Exact name of registrant as specified in its charter)


            Canada                       1-8014                   98-0154502
-------------------------------     ----------------         -------------------
(State or other jurisdiction of     (Commission File            (IRS Employer
        incorporation)                   Number)             Identification No.)


             6100 Vipond Drive
        Mississauga, Ontario, Canada                                  L5T 2X1
  ----------------------------------------                          ----------
  (Address of principal executive offices)                          (Zip Code)


                                 (905) 362-3100
              ----------------------------------------------------
              (Registrant's telephone number, including area code)


                                       N/A
          -------------------------------------------------------------
          (Former name or former address, if changed since last report)


ITEM 2. ACQUISITION OR DISPOSITION OF ASSETS

     On May 15, 2003, the merger (the "Merger") of M-W Acquisition, Inc.
("Merger Sub"), a wholly owned subsidiary of Moore Corporation Limited
("Parent"), with and into Wallace Computer Services, Inc. (the "Company"), and
the subsequent merger of the surviving corporation with and into a subsidiary of
Moore Holdings U.S.A. Inc., a wholly owned subsidiary of Parent, as contemplated
by the Agreement and Plan of Merger, dated as of January 16, 2003 (and as
amended and restated as of April 14, 2003) (the "Merger Agreement"), among
Parent, Moore Holdings U.S.A. Inc., Merger Sub and the Company, were
consummated. In the Merger, each share of common stock, par value $1.00 per
share, of the Company will be converted into either, at the stockholder's
election and subject to proration, (A) a number of common shares of Parent
("Parent Common Stock") equal to (i) 1.05 plus (ii) the quotient of (x) 14.40
divided by (y) the average of the daily high and low sales price per share of
Parent Common Stock on the last trading day immediately preceding the closing
date or (B) an amount in cash, without interest, equal to (i) $14.40 plus (ii)
the product of (x) 1.05 multiplied by (y) the average of the daily high and low
sales price per share of Parent Common Stock on the last trading day immediately
preceding the closing date. The Merger Agreement and the transactions
contemplated thereby were adopted and approved at a meeting of the stockholders
of the Company on May 15, 2003.

     Parent obtained $1.25 billion in financing for the Merger. Of that amount,
$850 million consists of bank financing and is comprised of a $500 million term
loan and a $350 million revolving credit facility. In addition, in an
unregistered offering to qualified institutional buyers, a finance subsidiary of
Parent sold $403 million of 7 7/8% senior notes due 2011 (generating $400
million in gross proceeds).

     The foregoing description of the Merger Agreement is qualified in its
entirety by reference to the full text of such agreement, a copy of which is
filed as Exhibit 2.1 hereto and which is incorporated by reference herein.

     The text of the press release announcing the consummation of the
transactions contemplated by the Merger Agreement is set forth under Item 9
below.


ITEM 7(a). FINANCIAL STATEMENTS OF BUSINESSES ACQUIRED.

     Financial statements of the Company will be set forth as part of a Form
8-K/A that Parent expects to file by July 15, 2003.

ITEM 7(b). PRO FORMA FINANCIAL INFORMATION.

     Pro forma financial information for Parent reflecting the Merger described
in Item 2 will be set forth as part of a Form 8-K/A that Parent expects to file
by July 15, 2003.

ITEM 7(c). EXHIBITS.

Exhibit            Description
---------          --------------
2.1                Agreement and Plan of Merger, dated as of January 16, 2003
                   (and as amended and restated as of April 14, 2003), among
                   Moore Corporation Limited, Moore Holdings U.S.A. Inc., M-W
                   Acquisition, Inc. and Wallace Computer Services, Inc.

ITEM 9. REGULATION FD DISCLOSURE.

On May 15, 2003, Parent issued the following press release:


       MOORE CORPORATION LIMITED ANNOUNCES CLOSING OF MERGER WITH WALLACE
                            COMPUTER SERVICES, INC.

MISSISSAUGA, ONTARIO AND STAMFORD, CT (MAY 15, 2003)- Moore Corporation Limited
("Moore") (TSX, NYSE: MCL) today announced the completion of its acquisition of
Wallace Computer Services, Inc. (NYSE: WCS) ("Wallace") following today's
approval of the transaction by Wallace stockholders. Moore and Wallace each
received an opinion from its counsel that the transaction qualifies as a
"reorganization" for United States federal income tax purposes, with the
consequence that Wallace stockholders who receive only shares of Moore in the
transaction generally should not recognize gain or loss for such purposes as a
result of the transaction. Wallace stockholders should consult their tax
advisors as to the tax consequences to them of the transaction.


The preliminary results of the Wallace stockholder elections as to the form of
consideration they wish to receive in the merger, and the related preliminary
proration results, were announced on May 13, 2003. Final election and proration
results are expected to be announced on or about May 19, 2003.

As previously announced on May 14, 2003, Moore's trading symbol for shares
listed on the New York Stock Exchange and the Toronto Stock Exchange will be
changed, effective May 27, 2003, from "MCL" to "MWI". The introduction of the
new ticker symbol coincides with the change in Moore's name from Moore
Corporation Limited to Moore Wallace Incorporated ("Moore Wallace"), previously
approved by Moore shareholders. Moore Wallace shares will begin trading under
the new symbol as of market opening on May 27th. Trading will continue under the
symbol "MCL" through May 23rd.

Morgan Stanley provided mergers and acquisitions advice to Moore, and Sullivan &
Cromwell LLP acted as legal advisor. Dresdner Kleinwort Wasserstein provided
mergers and acquisitions advice to Wallace, and Sidley Austin Brown & Wood acted
as legal advisor.

Moore Corporation Limited is recognized internationally as a leading single
source provider of integrated print management and outsourced communications.
Founded in 1882, Moore Corporation Limited has its registered office in Ontario,
Canada, with principal offices in Toronto, ON, Bannockburn, IL, Stamford, CT and
New York City and manufacturing, distribution and sales facilities located
throughout North America and internationally. For more information, please visit
www.moore.com.

                                    #########

Except for historical information, all other information in this news release
consists of forward-looking statements within the meaning of the Private
Securities Litigation Reform Act of 1995. All forward-looking statements speak
only as of the date hereof and are based on current expectations and involve a
number of assumptions, risks and uncertainties that could cause the actual
results to differ materially from such forward-looking statements. The most
significant of these uncertainties are described in Moore's and Wallace's
respective Form 10-K, Form 8-K and Form 10-Q reports and exhibits to those
reports, and include (but are not limited to) the costs, difficulties, and
uncertainties related to the integration of acquired businesses, the pending
acquisition of Wallace by Moore. Moore and Wallace undertake no obligation to
update or revise any forward-looking statements.

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Inquiries from analysts, investors and media should be directed to Robert G.
Burton Jr., Senior Vice President, Investor Relations for the company at (203)
406-3712.



                                    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 hereunto duly authorized.

                                         MOORE CORPORATION LIMITED

Date: May 15, 2003                       By: /s/  Theodore J. Theophilos
                                             ------------------------------
                                             Name:  Theodore J. Theophilos
                                             Title: Executive Vice President,
                                                    Business and Legal Affairs,
                                                    and Secretary



                                  EXHIBIT INDEX

Exhibit
Number            Description
------            -----------
2.1               Agreement and Plan of Merger, dated as of January 16, 2003
                  (and as amended and restated as of April 14, 2003), among
                  Moore Corporation Limited, Moore Holdings U.S.A. Inc., M-W
                  Acquisition, Inc. and Wallace Computer Services, Inc.