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                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
 
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                               AMENDMENT NO. 1 TO
 
                                 SCHEDULE 14D-9
 
               SOLICITATION/RECOMMENDATION STATEMENT PURSUANT TO
            SECTION 14(D)(4) OF THE SECURITIES EXCHANGE ACT OF 1934
 
                           ALARMGUARD HOLDINGS, INC.
 
                           (Name of Subject Company)
 
                           ALARMGUARD HOLDINGS, INC.
 
                      (Name of Person(s) Filing Statement)
 
                    COMMON STOCK, PAR VALUE $.0001 PER SHARE
 
           (Including the Associated Preferred Stock Purchase Rights)
 
                         (Title of Class of Securities)
 
                                   011649100
 
                     (CUSIP Number of Class of Securities)
 
                             RUSSELL R. MACDONNELL
                CHAIRMAN, CHIEF EXECUTIVE OFFICER AND PRESIDENT
                           ALARMGUARD HOLDINGS, INC.
                               125 FRONTAGE ROAD
                                ORANGE, CT 06477
                                 (203) 795-9000
      (Name, Address and Telephone Number of Person Authorized to Receive
     Notice and Communications on Behalf of the Person(s) Filing Statement)
 
                                   Copies To:
                              DAVID A. HAHN, ESQ.
                                LATHAM & WATKINS
                            701 B STREET, SUITE 2100
                              SAN DIEGO, CA 92101
 
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    This Amendment No. 1 to Schedule 14D-9 amends and supplements the Schedule
14D-9 filed with the Securities and Exchange Commission on January 15, 1999 (the
"Schedule 14D-9") by Alarmguard Holdings, Inc. (the "Company"), relating to a
tender offer commenced by T16 Acquisition Corp., a Delaware corporation
("Purchaser") and an indirect wholly-owned subsidiary of Tyco International
Ltd., a Bermuda company ("Tyco"), on January 15, 1999 to purchase all of the
outstanding shares of the Company's common stock, par value $.0001 per share,
and the preferred stock purchase rights associated therewith (collectively, a
"Common Share"). Unless otherwise indicated, all capitalized terms used but not
defined herein shall have the meanings assigned to them in the Schedule 14D-9.
 
ITEM 3. IDENTITY AND BACKGROUND.
 
    The response to Item 3 is hereby amended by adding the following paragraph
at the end of Item 3(b)(1):
 
    Tyco and Russell R. MacDonnell, Chairman, Chief Executive Officer and
President of the Company, have agreed in principle that Mr. MacDonnell will be
employed by an affiliate of Tyco following the Merger with primary
responsibility for acquiring companies in the alarm industry and integrating
such companies with Tyco's security service operations. The specific terms of
Mr. MacDonnell's employment relationship with Tyco have yet to be agreed upon.
 
ITEM 4. THE SOLICITATION OR RECOMMENDATION.
 
    The response to Item 4 is hereby amended by revising in its entirety the
18th paragraph of Item 4(a) to read as follows:
 
    On December 23, 1998, the Board held a special meeting at which outside
counsel for the Company again reviewed the fiduciary obligations of the Board
under Delaware law in connection with the proposed transaction and presented a
summary of the latest draft Merger Agreement and draft Stock Purchase Agreement.
At this meeting, DLJ and the Company's management reported to the Board that
certain holders of Preferred Stock had agreed to approve the transaction with
Tyco at a purchase price of $1,400 per share of Preferred Stock, which would
correspond to a price of $9.34 per Common Share, conditioned upon payment of
unpaid and accrued dividends on the Preferred Stock through the date of the
Purchase. The Board then discussed that Tyco's position was that its offer price
did not include the payment of unpaid and accrued dividends on the Preferred
Stock during the period from October 1, 1998 through and until the Purchase. The
Board instructed DLJ and management to attempt to convince Tyco to pay such
dividends and to begin discussions with certain holders of Preferred Stock
regarding their approval of the transaction in the event Tyco remained unwilling
to do so. The Board also heard a report from DLJ and management that Tyco again
had declined to increase the aggregate consideration in the proposed
transaction. In addition, DLJ made a presentation to the Board outlining the
results of the financial analyses it had conducted to assess the fairness of the
proposed transaction. DLJ indicated that it believed that it would be in a
position to opine at the next Board meeting that the aggregate consideration to
be received by the holders of the Company's stock pursuant to the proposed
transaction is fair to such holders from a financial point of view, assuming no
significant change in the proposed terms. (See paragraph (ii) of Item 4(b) for a
further discussion of the opinion of DLJ.) Although no formal action was taken,
members of the Board indicated that they would support a transaction with Tyco
with the currently proposed terms.
 
    The response to Item 4 is hereby amended by adding the following at the end
of the 23rd paragraph of Item 4(a):
 
    The opinion of DLJ only relates to the fairness of the aggregate
consideration to be paid to both the holders of Common Shares and Preferred
Stock. The opinion does not address the fairness of the consideration to be
received by the holders of Common Shares in the Offer, and does not constitute
(i) a recommendation to any stockholder as to whether such stockholder should
tender into the Offer or vote on the Merger or (ii) a judgment as to the
appropriate allocation of consideration between the holders of
 
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Common Shares and Preferred Stock. (See paragraph (ii) of Item 4(b) for a
further discussion of the opinion of DLJ.)
 
    The response to Item 4 is hereby amended by revising in its entirety
paragraph (ii) of Item 4(b) to read as follows:
 
    (ii) The opinion of DLJ, the Company's financial advisor, that the aggregate
         consideration to be paid to the Company's stockholders pursuant to the
         Agreements is fair, from a financial point of view, to such
         stockholders. The Board recognized that the opinion of DLJ only relates
         to the fairness of the aggregate consideration to be paid to both the
         holders of Common Shares and Preferred Stock; that the opinion does not
         address the fairness of the consideration to be received by the holders
         of Common Shares in the Offer; and that the opinion does not constitute
         (i) a recommendation to any stockholder as to whether such stockholder
         should tender into the Offer or vote on the Merger or (ii) a judgment
         as to the appropriate allocation of consideration between the holders
         of Common Shares and Preferred Stock. A copy of the opinion rendered by
         DLJ to the Board, setting forth the procedures followed, the matters
         considered, the scope of the review undertaken and the assumptions made
         by DLJ in arriving at its opinion, is attached hereto as Annex I and is
         incorporated herein by reference. Stockholders are urged to read such
         opinion in its entirety.
 
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                                   SIGNATURE
 
    After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.
 
                               
                                ALARMGUARD HOLDINGS, INC.
 
Date: February 2, 1999          By:          /s/ RUSSELL R. MACDONNELL
                                     -----------------------------------------
                                               Russell R. MacDonnell
                                       Chairman, Chief Executive Officer and
                                                     President


 
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