<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549

                                    FORM 10-Q

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

                    FOR THE QUARTER ENDED SEPTEMBER 30, 1998

                         COMMISSION FILE NUMBER 0-21202

                          FIRSTWAVE TECHNOLOGIES, INC.


          7372                    GEORGIA                     58-1588291
(Primary Std. Ind.          (State of incorporation)          (IRS Employer
 Classification Code #)                                        Identification #)


                        2859 Paces Ferry Road, Suite 1000
                             Atlanta, Georgia 30339
                    (Address of principal executive offices)


                                 (770-431-1200)
                        (Telephone number of registrant)


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


Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the latest practicable date.

      Outstanding as of November 6, 1998:
      ----------------------------------

      Common Stock, no par value                       5,151,322 Shares




<PAGE>   2


                          FIRSTWAVE TECHNOLOGIES, INC.

                                    FORM 10-Q

                    For the quarter ended September 30, 1998




                                      Index
                                 --------------


<TABLE>
<CAPTION>
                                                                        Page No.
                                                                        -------
<S>       <C>                                                           <C>
Part I.   Financial Information

Item 1.   Consolidated Financial Statements

    Balance Sheet - December 31, 1997 and September 30, 1998                3

    Statement of Operations - For the Three and Nine Months ended
        September 30, 1997 and September 30, 1998                           4

    Statement of Changes in Shareholders' Equity -
        For the Nine Months Ended September 30, 1998                        5

    Statement of Cash Flows - For the Nine Months Ended
       September 30, 1997 and September 30, 1998                            6

    Notes to Financial Statements                                           7



Item 2.   Management's Discussion and Analysis of                           8
          Financial Condition and Results of Operations


Part II.  Other Information                                                12
</TABLE>








                                      - 2 -
<PAGE>   3
PART I.  FINANCIAL INFORMATION
Item 1.  Financial Statements



                          FIRSTWAVE TECHNOLOGIES, INC.
                                  CONSOLIDATED

                                  Balance Sheet


<TABLE>
<CAPTION>
                                                           DEC 31,         SEPT 30,
                                                            1997             1998
                                                          ---------       -----------
                                                                          (unaudited)
                                                                (in thousands)
<S>                                                       <C>             <C>    
                              ASSETS

Current assets:
  Cash and marketable securities                            $ 4,969        $ 2,868
  Accounts receivable, less allowance for
    doubtful accounts of $703 and $495, respectively          3,047          2,989
  Other assets                                                  636            736
                                                            -------        -------
                Total current assets                          8,652          6,593
  Property and equipment, net                                 1,938          1,787
  Deferred income tax benefit                                 2,362          2,362
  Software development costs, net                             1,089            712
  Intangible assets                                             245            670
                                                            -------        -------
                                                            $14,286        $12,124
                                                            =======        =======



                LIABILITIES AND SHAREHOLDERS' EQUITY

Current liabilities:
  Accounts payable                                          $   868        $ 1,377
  Accrued restructuring costs                                   325             92
  Deferred revenue                                            1,545          1,184
  Accrued employee compensation
    and benefits                                                614            311
  Other accrued liabilities                                     282            385
                                                            -------        -------
                Total current liabilities                     3,634          3,349

Common stock subject to repurchase                              300              0

Shareholders' equity                                         10,352          8,775
                                                            -------        -------
                                                            $14,286        $12,124
                                                            =======        =======
</TABLE>



The accompanying notes are an integral part of these financial statements.


                                      - 3 -

<PAGE>   4
                          FIRSTWAVE TECHNOLOGIES, INC.
                                  CONSOLIDATED

                             Statement of Operations
                                   (unaudited)


<TABLE>
<CAPTION>
                                   For the Three Months Ended   For the Nine Months Ended
                                   --------------------------   -------------------------
                                      Sept 30,      Sept 30,       Sept 30,      Sept 30,
                                        1997          1998           1997          1998
                                     ---------     --------       --------       --------
                                           (In thousands, except per share amounts)
<S>                                  <C>           <C>            <C>            <C>     
Net Revenues
  Software                             $  921      $    679       $  2,831       $  2,866
  Services                              1,204         1,575          3,805          3,840
  Maintenance                           1,254         1,373          3,898          3,977
  Other                                   131           135            464            427
                                       ------      --------       --------       --------
                                        3,510         3,762         10,998         11,110
                                       ------      --------       --------       --------
Cost and Expenses
  Cost of revenues
    Software                              156           184            354            524
    Services                              828         1,041          2,756          2,761
    Maintenance                           364           430          1,296          1,257
    Other                                 131           131            460            411
  Sales and marketing                   1,368         1,419          3,812          4,440
  Product development                     587           519          1,511          1,608
  General and administrative               67           893          1,895          2,299
                                       ------      --------       --------       --------
                                        3,501         4,617         12,084         13,300
                                       ------      --------       --------       --------

    Operating income/(loss)                 9          (855)        (1,086)        (2,190)

Interest expense                            0             0            (40)             0
Interest income                            46            39            138            154
                                       ------      --------       --------       --------
Income/(loss) before income taxes          55          (816)          (988)        (2,036)
 Income tax                                 0           (10)             0            (80)
                                       ------      --------       --------       --------
Net income/(loss)                      $   55      $(   826)      $(   988)      $( 2,116)
                                       ======      ========       ========       ========
Basic and diluted
 net income/(loss) per share           $ 0.01      $(  0.16)      $(  0.20)      $(  0.41)
                                       ======      ========       ========       ========

Weighted average number of common
  and common share equivalents          5,345         5,145          4,956          5,120
                                       ======      ========       ========       ========
</TABLE>






The accompanying notes are an integral part of these financial statements.



                                       -4-



<PAGE>   5

                          FIRSTWAVE TECHNOLOGIES, INC.
                                  CONSOLIDATED

                  Statement of Changes in Shareholders' Equity
                                   (unaudited)

                  For the Nine Months Ended September 30, 1998


<TABLE>
<CAPTION>
                                    Common Stock                 Unrealized                    Accumulated
                              -----------------------   Add'l     loss on                        other
                                                      paid-in    marketable   Comprehensive   comprehensive  Accumulated
                               Shares       Amount    capital    securities   income/(loss)      income        deficit      Total
                              ----------  ----------  -------    ----------   --------------  -------------  -----------   --------
                                          (In thousands, except share data)

<S>                           <C>         <C>         <C>        <C>          <C>              <C>          <C>             <C>    
Balance at December 31, 1997  5,033,027         $9    $19,329        $(14)            $0              $0        $(8,972)    $10,352

Employee stock purchase           4,556          0         15           0              0               0              0          15

Stock isssued related to
   Netgain acquisition           77,703          0        347           0              0               0              0         347

Exercise of common stock         34,511          0        112           0              0               0              0         112
  options

Issuance of stock options             0          0          7           0              0               0              0           7

Comprehensive Loss
   Net loss                           0          0          0           0         (2,116)              0         (2,116)     (2,116)

   Foreign currency
    translation adjustment            0          0          0           0             58              58              0          58
                                                                                 -------
     Comprehensive Loss                                                          $(2,058)
                              ---------         --    -------        ----        =======             ---       --------      ------

Balance at September 30, 1998 5,149,797         $9    $19,810        $(14)                           $58       $(11,088)     $8,775
                              =========         ==    =======        ====                            ===       ========      ======
</TABLE>



The accompanying notes are an integral part of these financial statements.


                                      -5-

<PAGE>   6
                          FIRSTWAVE TECHNOLOGIES, INC.
                                  CONSOLIDATED

                             Statement of Cash Flows
                                   (unaudited)



<TABLE>
<CAPTION>
                                                                 For the Nine Months Ended
                                                               ------------------------------
                                                               Sept 30, 1997     Sept 30, 1998
                                                               -------------     ------------
                                                                        (In thousands)

<S>                                                            <C>               <C>     
Cash flows provided by/(used in) operating activities             $   658         $(1,554)

Cash flows from investing activities
  Acquisition of Co-cam UK                                              0            (246)
  Purchases of property and equipment                                (133)           (493)
                                                                  -------         -------
       Net cash used in investing activities                         (133)           (739)
                                                                  -------         -------

Cash flows from financing activities
  Repayments of borrowings under line of credit                    (1,975)              0
  Repayments of borrowings under notes payable                       (208)              0
  Proceeds from employee stock purchase plan                           18              15
  Exercise of common stock options                                     40             119
                                                                  -------         -------
       Net cash (used in)/provided by financing activities         (2,125)            134
                                                                  -------         -------

                                                                  -------         -------
Effect of exchange rate changes                                         0              58
                                                                  -------         -------

Decrease in cash                                                   (1,600)         (2,101)
Cash and marketable securities, beginning of period                 6,947           4,969
                                                                  -------         -------
Cash and marketable securities, end of period                     $ 5,347         $ 2,868
                                                                  =======         =======

Supplemental disclosure of cash flow information
                                                                  -------         -------
  Cash paid during the period for interest                        $    84         $     0
                                                                  =======         =======
  Cash paid during the period for income taxes                    $     0         $    80
                                                                  =======         =======
</TABLE>



The accompanying notes are an integral part of these financial statements.












                                       -6-
<PAGE>   7

                          FIRSTWAVE TECHNOLOGIES, INC.
                          NOTES TO FINANCIAL STATEMENTS
                               SEPTEMBER 30, 1998


A.       BASIS OF PRESENTATION


         The accompanying unaudited financial statements have been prepared in
         accordance with the instructions to Form 10-Q and do not include all of
         the information and footnotes required by generally accepted accounting
         principles for complete financial statements. In the opinion of
         management, all adjustments (consisting only of normal occurring
         accruals) considered necessary for a fair presentation have been
         included.


B.       ACCOUNTING POLICIES

         BASIC AND DILUTED NET INCOME/(LOSS) PER COMMON SHARE
         Basic net income/(loss) per common share is presented in accordance
         with Financial Accounting Standards 128,"Earnings per Share", which
         provides for new accounting principles used in the calculation of
         earnings per share and was effective for financial statements for both
         interim and annual periods ended after December 15, 1997. The Company
         has restated the basic and diluted net income/(loss) per common share
         for all periods presented to give effect to FAS 128. Basic net
         income/(loss) per common share is based on the weighted average number
         of shares of common stock outstanding during the period. Stock options
         were the only securities issued which would have been included in the
         diluted earnings per share calculation had they not been antidilutive.

C.       ACQUISITION

         On April 30, 1998 the Company acquired its largest international
         distributor, Co-cam UK. Based in London, Co-cam UK now operates as
         Firstwave UK. The transaction was an asset purchase from PMS Creative
         Ltd., a wholly owned subsidiary of Policy Management Systems
         Corporation. The purchase price of approximately $426,000 is payable in
         cash in four quarterly installments beginning July 31, 1998, after a
         payment of approximately $85,000 on the date of closing. The excess of
         cost over the estimated fair value of the net assets acquired was
         $455,000 (including direct costs of the acquisition of approximately
         $180,000) and has been accounted for as goodwill which is being
         amortized over five years.




                                       -7-

<PAGE>   8

ITEM 2.

                          FIRSTWAVE TECHNOLOGIES, INC.
                     MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS

RESULTS OF OPERATIONS - THE THREE MONTHS ENDED SEPTEMBER 30, 1998 COMPARED TO
THE THREE MONTHS ENDED SEPTEMBER 30, 1997, AND THE NINE MONTHS ENDED SEPTEMBER
30, 1998 COMPARED TO THE NINE MONTHS ENDED SEPTEMBER 30, 1997.


Third quarter 1998 yielded total revenues of $3,762,000 and a net loss of
$826,000, in line with market expectations. These results include the first full
quarter of contribution from Firstwave UK, which was acquired April 30, 1998.
During the quarter and year to date, all revenues were attributed to the
Company's Takecontrol line of Unix and client/server products and services.
After one and one-half years of design and development, Netgain Sales, an
enterprise-class sales information system built exclusively with Internet
technologies, was released on September 30, 1998.

Total revenues increased 7.2% from $3,510,000 in the third quarter of 1997 to
$3,762,000 in the third quarter of 1998 primarily due to increased services and
maintenance revenues. During the third quarter of 1998 total revenue from
Firstwave UK was $1,537,000 representing 40.9% of total revenue. Year to date,
total revenues increased slightly from $10,998,000 in 1997 to $11,110,000 in
1998. While software revenues decreased 26.3% from $921,000 in the third quarter
of 1997 to $679,000 in the same period of 1998 due to lower domestic license
revenue, year to date, software revenues remained consistent at $2,866,000 in
1998 compared to $2,831,000 in 1997. The Company's quarter-to-quarter revenues
are significantly dependent upon the timing of the closing of license
agreements.

Revenues from international license sales increased 94.3% from $264,000 in the
third quarter of 1997 to $513,000 in the corresponding quarter of 1998. Year to
date, revenues from international licenses increased 47.2% from $1,544,000 in
1997 to $2,273,000 in 1998. As a percentage of total revenues, international
license revenues increased from 7.5% in the third quarter of 1997 to 13.6% in
third quarter of 1998, and year to date increased as a percentage of total
revenues from 14.0% in 1997 to 20.5% in 1998.

Services revenues increased 30.8% from $1,204,000 in the third quarter of 1997
to $1,575,000 in the third quarter of 1998 primarily as a result of the addition
of services revenues from Firstwave UK. Year to date, services revenues
increased slightly from $3,805,000 in 1997 to $3,840,000 in 1998.




                                       -8-

<PAGE>   9
Maintenance revenues increased 9.5% from $1,254,000 in the third quarter of 1997
to $1,373,000 in third quarter of 1998. Year to date, maintenance revenues
increased 2.0% from $3,898,000 in 1997 compared to $3,977,000 in 1998. The
current release, Takecontrol '98 has been well received and development of
Takecontrol '99 is nearing completion.

Other revenues remained consistent at $135,000 in the third quarter of 1998
compared to $131,000 in the third quarter of 1997. Year to date, other revenues
decreased 8.0% from $464,000 in 1997 to $427,000 in 1998. These changes are due
to changes in reimbursable travel charges.

Cost of software revenues increased 18.0% from $156,000 in the third quarter of
1997 to $184,000 in the third quarter of 1998. Year to date, cost of software
revenues increased 48.0% from $354,000 in 1997 to $524,000 in 1998. These
increases are a result of an increase in third party software costs associated
with the Netgain product and an increase in amortization of capitalized
software. For the first nine months of the year, amortization of capitalized
software increased from $293,000 in 1997 to $377,000 in 1998. This increase
resulted from the Company's release of Take Control '97, a major upgrade, in
late February 1997 which allowed only seven months of amortization year to date
at September 1997 compared to nine months of amortization year to date at
September 1998. Cost of software revenues include costs of third party software,
amortization of capitalized software costs and costs of packaging and
documentation materials and related media costs.

Cost of revenues for services increased 25.7% from $828,000 in the third quarter
of 1997 to $1,041,000 in the third quarter of 1998 due to increases in the
number of service personnel and related costs associated with the addition of
Firstwave UK. These increases are consistent with the increase in services
revenues provided by Firstwave UK. Year to date, cost of revenues for services
remained consistent at $2,761,000 in 1998 compared to $2,756,000 in 1997. Cost
of revenues for maintenance increased 18.1% from $364,000 in the third quarter
of 1997 to $430,000 in the third quarter of 1998 due to the addition of
Firstwave UK. Year to date, cost of revenues for maintenance decreased 3.0% from
$1,296,000 in 1997 to $1,257,000 in 1998.

Cost of other revenues remained constant at $131,000 in the third quarter of
1998; and, year to date, decreased 10.7% from $460,000 in 1997 to $411,000 in
1998. These variances are due to fluctuations in reimbursable travel charges
consistent with the changes in other revenue.




                                       -9-


<PAGE>   10


Sales and marketing expense increased 3.7% from $1,368,000 in the third quarter
of 1997 to $1,419,000 in the third quarter of 1998. Year to date, sales and
marketing expense increased 16.5% from $3,812,000 in 1997 to $4,440,000 in 1998.
The increases are related to increased marketing materials and advertising
expenses associated with the new corporate identity and name change from Brock
International, Inc. to Firstwave Technologies, Inc. as well as marketing
expenses related to the launch of Netgain.

The Company's product innovation and development expenditures decreased 11.6%
from $587,000 in the third quarter of 1997 to $519,000 in the third quarter of
1998. The decrease is due to decreased contract services related to a
development project during the third quarter 1997 that did not recur in 1998,
offset by increases related to Netgain product development. Year to date,
product innovation and development expenditures increased 6.4% from $1,511,000
in 1997 to $1,608,000 in 1998 due to increased resources dedicated to Netgain
product development. Development resources totaled 14 employees at September 30,
1997 compared to 23 employees at September 30, 1998.

General and administrative expenses increased 1232.8% from $67,000 in the third
quarter of 1997 to $893,000 in the third quarter of 1998. Year to date, general
and administrative expenses increased 21.3% from $1,895,000 in 1997 to
$2,299,000 in 1998. The increases are primarily due to a favorable settlement of
a legal dispute that resulted in a one-time credit to general and administration
expense of $603,000 during the third quarter of 1997 offset by the addition of
Firstwave UK administrative costs during 1998.

The above factors combined to result in net income of $55,000 in the third
quarter of 1997 compared to a net loss of $826,000 in the third quarter of 1998,
and net income per share of $.01 for the third quarter of 1997 compared to a net
loss per share of $.16 for the third quarter of 1998. Year to date, net loss
increased 114.2% from $988,000 in 1997 compared to $2,116,000 in 1998. Year to
date, net loss per share increased 105.0% from $0.20 per share in 1997 to $0.41
per share in 1998.














                                      -10-

<PAGE>   11


BALANCE SHEET

Cash and cash equivalents decreased 42.3% from $4,969,000 at December 31, 1997,
to $2,868,000 at September 30, 1998, due to investments in product development
of future technologies, acquisition costs and funding of operations of Firstwave
UK. Other assets increased 15.7% due to the acquisition of Co-cam UK. Intangible
assets increased 173.5% from $245,000 at December 31, 1997 to $670,000 at
September 30, 1998, due to goodwill resulting from the acquisition of Co-cam UK
offset by the related amortization. Accounts payable increased 58.6% from
$868,000 at December 31, 1997 to $1,377,000 at September 30, 1998 due to the
acquisition of Co-cam UK. Accrued restructuring costs declined 71.7% from
$325,000 at December 31, 1997 to $92,000 at September 30, 1998. The remaining
accrual represents costs associated with non-cancelable leases which will
amortize over the remaining life of the leases. Other accrued liabilities
increased 36.5% from $282,000 at December 31, 1997 to $385,000 at September 30,
1998 due to the acquisition of Co-cam UK.




LIQUIDITY AND CAPITAL RESOURCES

At September 30, 1998, the Company had cash and marketable securities of
$2,868,000 and believes that its present liquidity position and available line
of credit are sufficient to finance the Company's operations during 1998 and
1999. Firstwave UK generated positive cash flow from operations during the third
quarter. As of September 30, 1998, there were no borrowings against the
$3,000,000 line of credit, which carries an expiration date of March 31, 1999.

The Company's product line is Year 2000 compatible. A review of Year 2000
compatibility for the Company's internal systems has been completed and revealed
some internal systems are not yet Year 2000 compliant. However, the cost to
comply has been determined to be immaterial.











                                      -11-

<PAGE>   12


PART II.  OTHER INFORMATION


Item 1.    Legal Proceedings

         Not Applicable

Item 2.    Changes in Securities

         Not Applicable


Item 3.    Defaults Upon Senior Securities

         Not applicable


Item 4.    Submission of Matters to a Vote of Security Holders

         Not applicable


Item 5.    Other Information

         The proxy or proxies designated by the Company will have discretionary
         authority to vote on any matter properly presented by a shareholder for
         consideration at the 1999 Annual Meeting of Shareholders but not
         submitted for inclusion in the proxy materials for such meeting unless
         notice of the matter is received by the Company at its principal
         executive office not later than February 19, 1999 and certain other
         conditions of the applicable rules of the Securities and Exchange
         Commission are satisfied.


Item 6.    Exhibits and Reports on form 8-K

         27 - Financial Data Schedule (for SEC use only)





                                      -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.


                                    FIRSTWAVE TECHNOLOGIES, INC.



DATE:   November 10, 1998           /s/ Judith A. Vitale
                                    ---------------------------------------
                                    Judith A. Vitale
                                    Director of Finance and Administration
































                                      -13-