<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                    FORM 10-Q



 [X]    QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES 
        EXCHANGE ACT OF 1934

        For the quarterly period ended  MAY 24, 1998

                                       or

 [ ]    TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
        EXCHANGE ACT OF 1934 

        For the transition period from ____________ to ___________


                         COMMISSION FILE NUMBER 0-10558


                               ALPHA MICROSYSTEMS
             (Exact name of registrant as specified in its charter)



         CALIFORNIA                                   95-3108178
(State or other jurisdiction of                    (I.R.S. Employer
      Identification No.)                    incorporation or organization)




                  2722 S. FAIRVIEW STREET, SANTA ANA, CA 92704
               (Address of principal executive offices) (Zip code)

       Registrant's telephone number, including area code: (714) 957-8500




Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.

                                    Yes   X       No
                                        -----

As of June 30, 1998, there were 10,914,112 shares of the registrant's Common
Stock outstanding.



<PAGE>   2


                               ALPHA MICROSYSTEMS

                                TABLE OF CONTENTS



<TABLE>
<CAPTION>

                                                                              PAGE NUMBER
                                                                              -----------
     <S>                                                                     <C>
        PART I-- FINANCIAL INFORMATION

            Item 1.   Financial Statements

                      Condensed Consolidated Balance Sheets
                      (Unaudited) at May 24, 1998 and
                      February 22, 1998                                             3

                      Condensed Consolidated Statements of
                      Operations (Unaudited) for the Three
                      Months Ended May 24, 1998 and
                      May 25, 1997                                                  4

                      Condensed Consolidated Statements of Cash Flows
                      (Unaudited) for the Three Months Ended May 24, 1998
                      and May 25, 1997                                              5

                      Notes to Condensed Consolidated
                      Financial Statements                                          6

            Item 2.   Management's Discussion and Analysis of
                      Financial Condition and Results of Operations                 9


        PART II-- OTHER INFORMATION

            Item 6.   Exhibits and Reports on Form 8-K                             12



        SIGNATURES                                                                 13

        EXHIBIT INDEX                                                              14

</TABLE>



                                      -2-

<PAGE>   3

PART I.  FINANCIAL INFORMATION
ITEM 1. FINANCIAL STATEMENTS

                               ALPHA MICROSYSTEMS
                      CONDENSED CONSOLIDATED BALANCE SHEETS
                                   (Unaudited)
                        (In thousands, except share data)

<TABLE>
<CAPTION>

                                                        May 24,      February 22,
                                                         1998            1998
                                                        -------      -----------
     <S>                                               <C>           <C>
       ASSETS
       Current assets:
        Cash and cash equivalents                       $  2,741        $  5,003
        Accounts receivable, net of allowance  for
          doubtful accounts of $250 and $294 at
          May 24, 1998 and February 22, 1998, 
          respectively                                     3,727           3,781
        Inventories                                          626             580
        Notes receivable                                     161             161
        Prepaid expenses and other current assets            455             229
                                                        --------        --------
              Total current assets                         7,710           9,754

       Property and equipment, net of accumulated
          depreciation of $9,811 and $9,479 at
          May 24, 1998 and February 22, 1998,
          respectively                                     3,362           3,186
       IT Service contracts, net                           1,538           1,192
       Software costs, net                                 1,145           1,067
       Notes receivable                                      417             417
       Other assets, net                                     218             172
                                                        --------        --------
                                                        $ 14,390        $ 15,788
                                                        ========        ========

       LIABILITIES AND SHAREHOLDERS' EQUITY 
       Current liabilities:
        Bank borrowings                                 $  1,000        $  1,000
        Accounts payable                                   1,518           1,699
        Deferred revenue                                   1,845           1,888
        Accrued compensation                                 183             386
        Other current liabilities                            390             356
        Current portion of long-term debt                     89              92
                                                        --------        --------
              Total current liabilities                    5,025           5,421

       Long-term debt                                         60              60
       Commitments and contingencies

       Shareholders' equity:
        Preferred stock, no par value; 5,000,000
            shares authorized; none issued                    --              --
        Common stock, no par value; 20,000,000 
            shares authorized; 10,914,112
            shares issued and outstanding at 
            May 24, 1998 and February 22, 1998, 
            respectively                                  31,011          31,011
        Accumulated deficit                              (21,750)        (20,761)
        Foreign currency translation adjustment               44              57
                                                        --------        --------
              Total shareholders' equity                   9,305          10,307
                                                        --------        --------
                                                        $ 14,390        $ 15,788
                                                        ========        ========

</TABLE>


See accompanying notes.


                                      -3-


<PAGE>   4


                                  ALPHA MICROSYSTEMS
                    CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS
                                      (Unaudited)
                         (In thousands, except per share data)


<TABLE>
<CAPTION>
                                                         Three Months Ended
                                                       ----------------------
                                                       May 24,        May 25,
                                                        1998           1997
                                                       -------        -------
<S>                                                   <C>            <C>
Net sales:
  IT Services                                          $ 4,064        $ 3,049
  Product                                                1,382          1,500
                                                       -------        -------
    Total net sales                                      5,446          4,549

Cost of sales:
  IT Services                                            3,655          2,219
  Product                                                  854          1,047
                                                       -------        -------
    Total cost of sales                                  4,509          3,266
                                                       -------        -------

Gross margin                                               937          1,283

Operating expenses:
  Selling, general and administrative                    1,601          2,150
  Engineering, research and development                    306            364
                                                       -------        -------
    Total operating expenses                             1,907          2,514
                                                       -------        -------

Loss from operations                                      (970)        (1,231)

Other (income) expense:
  Interest income                                          (26)           (98)
  Interest expense                                          26              1
  Other expense, net                                        16              1
  Foreign exchange gain                                     (9)            (7)
                                                       -------        -------
    Total other (income) expense                             7           (103)

Loss before taxes                                         (977)        (1,128)
Income tax expense                                          12              9
                                                       -------        -------

Net loss                                               $  (989)       $(1,137)
                                                       =======        =======

Basic and diluted net loss per share                   $ (0.09)       $ (0.11)
                                                       =======        =======
Number of shares used in the computation
  of basic and diluted per share amounts                10,914         10,822
                                                       =======        =======
</TABLE>


See accompanying notes




                                      -4-


<PAGE>   5

                               ALPHA MICROSYSTEMS
                 CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
                                   (Unaudited)
                                 (In thousands)
<TABLE>
<CAPTION>

                                                                      Three Months Ended
                                                                    ------------------------
                                                                    May 24,          May 25,
                                                                     1998             1997
                                                                    -------          -------
<S>                                                                <C>              <C>
Cash flows from operating activities:
    Net loss                                                        $  (989)         $(1,137)
    Adjustments to reconcile net loss to cash
        used in operating activities:
            Depreciation and amortization                               504              398
            Provision for losses on accounts receivable                  --               10
            Provision for slow-moving inventory                          (1)               9
    Other changes in operating assets and liabilities:
            Accounts receivable                                          52              327
            Inventories                                                 (46)             (99)
            Notes receivable                                             --                2
            Prepaid expenses and current assets                        (226)             (64)
            Accrued compensation                                       (203)            (150)
            Accounts payable and accrued liabilities                   (147)             149
            Deferred revenue                                           (188)             (74)
            Other, net                                                   (4)               1
                                                                   --------          -------
                Net cash used in operating activities                (1,248)            (628)

Cash flows from investing activities:
    Purchase of short-term investments                                   --           (3,949)
    Proceeds from sale of short-term investments                         --            3,970
    Acquisition of IT service assets                                   (434)              --
    Purchases of equipment                                             (430)            (127)
    Capitalization of software costs                                   (143)            (251)
                                                                   --------          -------
                Net cash used in investing activities                (1,007)            (357)

Cash flows from financing activities:
    Issuance of common stock                                             --                1
    Principal repayments on debt                                         (3)              (4)
                                                                   --------          -------
                Net cash used in financing activities                    (3)              (3)

Effect of exchange rate changes on cash                                  (4)              (1)
                                                                   --------          -------

Decrease in cash and cash equivalents                                (2,262)            (989)
Cash and cash equivalents at beginning of period                      5,003            1,768
                                                                   --------          -------

Cash and cash equivalents at end of period                          $ 2,741          $   779
                                                                   ========          =======

See accompanying notes.

</TABLE>



                                       -5-

<PAGE>   6


                               ALPHA MICROSYSTEMS
              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS


This Quarterly Report on Form 10-Q contains certain forward-looking statements
(as such term is defined in the private Securities Litigation Reform Act of
1995) and information relating to Alpha Microsystems (the "Company" or "Alpha
Micro") that are based on the beliefs of the management of the Company as well
as assumptions made by and information currently available to the management of
Alpha Micro. Forward-looking statements within the meaning of Section 27A of the
Securities Act of 1933 and Section 21E of the Securities Exchange Act of 1934
(The "Exchange Act") and the Company intends that such forward-looking
statements be subject to the safe harbors created thereby. These forward looking
statements, include (i) the outcome of litigation will not have a material
adverse effect, (ii) the Company's ability to successfully complete and
integrate acquisitions within the services industry, (iii) the ability of the
Company to successfully reduce operating costs related to acquired operations.

Assumptions relating to the foregoing involve judgments with respect to, among
other things, future economic, competitive and market conditions, all of which
are difficult or impossible to predict accurately and many of which are beyond
the control of the Company. In addition, the business and operations of the
Company are subject to substantial risks that increase the uncertainty inherent
in the forward-looking information included herein, the inclusion of such
information should not be regarded as a representation by the Company, or any
other person that the objectives or plans of the Company will be achieved.

1. INTERIM ACCOUNTING POLICY

In the opinion of management of Alpha Microsystems (the "Company" or "Alpha
Micro"), the accompanying unaudited condensed consolidated financial statements
contain all adjustments necessary (consisting only of normal recurring
adjustments) to fairly present the consolidated financial position of the
Company at May 24, 1998, and the consolidated results of its operations and cash
flows for the quarters ended May 24, 1998 and May 25, 1997. These condensed
consolidated financial statements do not include all disclosures normally
presented annually under generally accepted accounting principles and,
therefore, they should be read in conjunction with the Company's annual report
on Form 10-K for the year ended February 22, 1998.

Certain amounts have been reclassified in prior periods to conform to the
current period presentation.

The results of operations for the quarter ended May 24, 1998 are not necessarily
indicative of the results to be expected for the full fiscal year.

REVENUE RECOGNITION

The Company recognizes revenue on its product sales on shipment, and recognizes
revenue on its IT service sales and post contract customer support on a
straight-line basis over the contract period. When significant obligations
remain after a software product has been delivered, revenue is not recognized
until obligations have been completed or are no longer significant. The costs of
any insignificant obligations are accrued when the related revenue is
recognized. Revenue is recognized only when collection of the resulting
receivable is probable.



                                      -6-



<PAGE>   7

PER SHARE INFORMATION

Basic and diluted earnings per share is based on the weighted average common
shares outstanding during the periods presented and excludes any dilutive
effects of options and warrants. For the periods presented, the effect of
options and warrants has been excluded from diluted earnings per share as their
effect is anti-dilutive.

RECENT ACCOUNTING PRONOUNCEMENTS

As of February 23, 1998, the Company adopted Statement of Financial Accounting
Standards No. 130, Reporting Comprehensive Income ("SFAS 130"). SFAS 130
establishes new rules for the reporting and display of comprehensive income and
its components; however, the adoption of this Statement had no impact on the
Company's net income or shareholders' equity. SFAS 130 requires foreign currency
translation adjustments, which prior to adoption were reported separately in
shareholders' equity, to be included in other comprehensive income. During the
first quarter of 1999 and 1998, total comprehensive loss amounted to $1,002,000
and $1,139,000, respectively.

The Company adopted SOP 97-2, which supersedes SOP 91-1 and provides guidance on
applying generally accepted accounting principles in recognizing revenue on
software transactions. SOP 97-2 contains more restrictive revenue recognition
provisions for software arrangements containing multiple elements (i.e.
upgrades, enhancements, implementation and other services) similar to the
arrangements entered into by the Company. The adoption of this statement had no
impact on the Company's consolidated financial position, results of operations
or cash flows.

2. INVENTORIES

Inventories are valued at the lower of cost or market. Cost is determined on the
first-in, first-out method. Inventories, net of reserves for excess and obsolete
inventories of $96,000 and $98,000 at May 24, 1998, and February 22, 1998,
respectively, comprise the following:

              (In thousands)
<TABLE>
<CAPTION>
                                                     
                                       MAY 24,       FEBRUARY
                                        1998         22, 1998
                                       -------       --------
             <S>                       <C>           <C>
              Raw materials              $597           $568
              Work in process              14              4
              Finished goods               15              8
                                         ----           ----
                                         $626           $580
                                         ====           ====
</TABLE>


3. DEBT

On June 9, 1998, the Company obtained a new, three-year, $3 million credit
facility from Imperial Bank. Advances under the facility are subject to
availability based on eligible accounts receivable and certain financial
covenants, including tangible net worth, debt to tangible net worth and quick
ratio minimum requirements. Under the facility, a $2 million accounts receivable
line of revolving credit has been designated for working capital and $1 million
has 


                                      -7-



<PAGE>   8

been designated to finance potential acquisitions under the Company's current
business plan. Amounts drawn under the accounts receivable line bear interest at
the bank's prime rate plus 2 percent. Borrowings for acquisitions approved by
the bank mature one year from the date of funding and bear interest at the
bank's prime rate plus 2.5 percent.

4. CONTINGENCIES

The Company's current involvement with litigation is as follows:

Carlos Garralda and Andre Warnier, employees of the Company's former subsidiary,
Alpha Microsystems Belgium, S.A. ("AMB"), filed an action in November 1995
against AMB and the Company in Orange County Superior Court alleging that AMB is
in breach of its obligations under Belgium employment law to pay salaries for a
notice period of up to two years following termination of employment. The
Plaintiffs allege, among other things, that the Company has alter ego liability
for these obligations. The plaintiffs are claiming compensatory damages in
excess of $780,000 and unspecified punitive damages. A settlement of the case
between AMB and Andre Warnier in the Belgium action was effected on October 18,
1996. Five hundred thousand dollars ($500,000) of the compensatory damages in
the Orange County lawsuit are related to the claims by Mr. Warnier. In December
1997, the Company and Warnier executed a settlement agreement, which involved no
payment by the Company, and Warnier dismissed his Orange County case with
prejudice. Separately, Garralda dismissed his Orange County case without
prejudice upon the Company's execution of a Tolling Agreement allowing Garralda
to re-file the suit upon the occurrence of specified conditions. Although no
assurances as to the outcome of the litigation can be given, management believes
that this litigation will not have a material adverse effect on the Company's
consolidated financial position, results of operations or cash flows.

In December 1995, Phoenix Marketing, Inc. d.b.a. Electronic Business Systems,
Inc., in response to the Company's collection efforts for a past due account,
filed an amended cross-complaint alleging damages of $3,200,000 for defective
merchandise, loss of business reputation and loss of future business. The Iowa
court has referred this case to arbitration, which arbitration is now scheduled
to begin in November 1998. Although no assurances as to the outcome of the
litigation can be given, management believes that the plaintiff's claims are
without merit.

The Company is currently involved in certain other claims and litigation. The
Company does not consider any of these other claims or litigation to be
material. Management has made provisions in the Company's financial statements
for the settlement of lawsuits for which unfavorable outcomes are both probable
and estimable. In the opinion of management, results of known existing claims
and litigation will not have a material adverse effect on the Company's
consolidated financial position, results of operations or cash flows.


                                      -8-



<PAGE>   9



ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
        OF OPERATIONS

SUMMARY

The following table was derived from the Condensed Consolidated Statements of
Operations as a percentage of net sales for the quarters ended May 24, 1998 and
May 25, 1997:

<TABLE>
<CAPTION>

                                                        RELATIONSHIP TO NET SALES
                                                        -------------------------
                                                            THREE MONTHS ENDED
                                                        -------------------------
                                                        MAY 24,           MAY 25,
                                                         1998              1997
                                                        -------           -------
<S>                                                    <C>               <C>
Net sales:
  IT Service                                              74.6%              67.0%
  Product                                                 25.4               33.0
                                                         -----              -----
     Total net sales                                     100.0              100.0
Cost of sales                                             82.8               71.8
                                                         -----              -----
Gross margin                                              17.2               28.2

Selling, general and administrative expense               29.4               47.3
Engineering, research and development expense              5.6                8.0
Interest (income) expense, net                             -                 (2.2)
Other (income) expense, net                                0.1               (0.1)
                                                         -----              -----
Loss before taxes                                        (17.9)             (24.8)
Net loss                                                 (18.2)%            (25.0)%
                                                         =====              =====
</TABLE>


GENERAL

During the first quarter of fiscal 1999, the Company continued to implement its
IT services business acquisition and growth strategy and its internet strategy
of pursuing strategic alliances for its AlphaCONNECT internet technology. As a
result of International Data Corporation's affirmation of the AlphaCONNECT
technology as published in an independent recent research bulletin, the Company
expects to increase its investment going forward. In the first quarter of fiscal
1999, the Company acquired the ongoing IT services contracts and certain related
assets of M & J Technologies for an estimated purchase price of $950,000. The
purchase price, which is contingent on future annualized revenues, is to be paid
over 18 months, with 50 percent of the purchase price paid on the closing date
of the acquisition. During the fourth quarter of fiscal 1998, the Company
acquired the telephony service division ("ATI") of Applied Cellular Technologies
Corporation and to date the Company has not realized the anticipated
contribution to the results of operations.

The Company had negative earnings before interest, taxes, depreciation and
amortization ("EBITDA") of $466,000, during the first quarter ended May 24,
1998, compared to a negative EBITDA of $833,000, during the same period of the
prior fiscal year. The current quarter loss includes $179,000 relating to the
operations of ATI not included in the prior quarter.



                                      -9-


<PAGE>   10


RESULTS OF OPERATIONS

Three Months Ended May 24, 1998 and May 25, 1997

Net sales increased $897,000, or 19.7 percent, to $5,446,000 for the quarter
ended May 24, 1998 from $4,549,000 for the quarter ended May 25, 1997. The 1998
quarter includes $756,000 attributable to ATI, not included in the prior year.

Total IT service revenue increased $1,015,000, or 33.3 percent, to $4,064,000
for the quarter just ended from $3,049,000 for the same period in the prior
year. IT service contract revenues derived from the Company's proprietary AMOS
product line decreased from approximately 70 percent in the first quarter of
1998 to less than 40 percent in the first quarter of 1999. This shift of the
Company's IT service focus from proprietary to third-party product IT services
demonstrates the success of its IT services business strategy and also mitigates
the significance of the decline in proprietary product and service revenues as
it becomes a smaller percentage of total revenues.

Total product revenues declined $118,000, or 7.9 percent, to approximately
$1,382,000 from approximately $1,500,000 for the comparable period. While
domestic product sales remained flat, European product sales declined $115,000.
No assurances can be made as to future product sales levels whether domestic or
international.

Total gross margin for the Company for the first quarter of fiscal 1999
decreased to 17.2 percent compared to 28.2 percent during the same period last
year. IT services gross margin declined to 10.1 percent during the quarter ended
May 24, 1998, from 27.2 percent during the same period in the prior year. This
decline reflects a negative 13 percent gross margin impact during the first
quarter of fiscal 1999 primarily from the ATI operations acquired after the
first quarter of 1998, and subsequent cost reductions including payroll costs
have been made by the Company in response to such results. Additionally, the
gross margin was negatively impacted 4 percent in 1999 due to increased
depreciation related to IT service business acquisitions and increased payroll
costs related to new IT service personnel hired for recently awarded IT service
contracts, for which no service revenue was recognized during the first quarter
of 1999. Further, due to the shift from proprietary to third-party IT services,
the Company does not expect gross margins to remain at historical levels.

Product gross margin for the quarter ended May 24, 1998, increased to 38.2
percent compared to 30.2 percent during the same period in the prior year. This
improvement is primarily due to operating cost reductions.

Selling, general and administrative expenses decreased $549,000 to $1,601,000
for the quarter ended May 24, 1998, compared to $2,150,000 for the quarter ended
May 25, 1997. The decline in quarter to quarter costs is primarily due to
reduced spending related to the AlphaCONNECT internet technology.

Research and development expenses (which include engineering support and
services) incurred for the three months ended May 24, 1998, decreased by $58,000
to $306,000 from $364,000 during the same period in the prior fiscal year.
Research and development expenses as a percentage of product sales decreased to
22.1 percent for the three months just ended from 24.2 percent during the
comparable period in the prior fiscal year.



                                      -10-


<PAGE>   11


LIQUIDITY AND CAPITAL RESOURCES

During the three months ended May 24, 1998, the Company's working capital
decreased $1,648,000 to $2,685,000 from $4,333,000 at February 22, 1998. This
decline includes anticipated working capital requirements as follows: $434,000
in direct acquisition costs; $210,000 of working capital utilized in the further
implementation of the Company's new integrated information system; and
approximately $250,000 due to equipment purchases to support new service
capabilities such as AS-400, Sun Microsystems and other products.

The Company believes that its current cash position, augmented by future
operating activities, and working capital available through its Imperial Bank
revolving credit facility, will provide sufficient resources to finance its
working capital requirements through fiscal year 1999. Advances under the bank
facility are subject to availability based on eligible accounts receivable and
certain financial covenants, including tangible net worth, debt to tangible net
worth and quick ratio minimum requirements. The Company has also received a
Letter of Commitment from ING Equity Partners II, L.P. to provide up to $20
million as an equity investment. The letter is subject to customary provisions
including, among other things, no material adverse changes and is contingent
upon the consummation of a qualifying acquisition. The Company is also pursuing
additional financing from other sources to support its acquisition strategy,
although there can be no assurances that any financing will be available on
acceptable terms. The Company's future capital requirements depend on a variety
of factors, including, but not limited to, the rate of decline in the
traditional proprietary business; the success, timing, and amount of investment
required to penetrate the Internet/intranet markets; service revenue growth or
decline; and potential acquisitions.







                                      -11-

<PAGE>   12

PART II.  OTHER INFORMATION

ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K.

(a)     See Exhibit Index.

(b)     A Current Report on Form 8-K was filed by the Company on June 2, 1998
        regarding a Letter of Intent from ING Equity Partners to make an equity
        investment.





                                      -12-

<PAGE>   13

                                   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.




                                                   ALPHA MICROSYSTEMS
                                                   (Registrant)


Date: July 2, 1998                                 By: /s/ Douglas J. Tullio
                                                   -------------------------
                                                   President and
                                                   Chief Executive Officer

Date: July 2, 1998                                 By: /s/ Jeffrey J. Dunnigan
                                                   ---------------------------
                                                   Vice President and
                                                   Chief Financial Officer






                                      -13-

<PAGE>   14

                                  EXHIBIT INDEX


Number                Description of Documents
------                ------------------------

2.9            First Amendment to Agreement of Purchase and Sale by and between
               the Registrant and M & J Technologies, Inc., effective May 1,
               1998

4.7            Warrant to Purchase Common Stock issued to Imperial Bank dated
               June 9, 1998

10.64          Security and Loan Agreement by and between Registrant and
               Imperial Bank dated June 9, 1998

10.65          Addendum to Security and Loan Agreement by and between Registrant
               and Imperial Bank dated June 9, 1998

10.66          General Security Agreement by and between Registrant and Imperial
               Bank dated June 9, 1998

10.67          Credit Terms and Conditions ("Credit Agreement") by and between
               Registrant and Imperial Bank dated June 9, 1998

27.            Financial Data Schedule







                                      -14-