<PAGE>   1
FORM 10-QSB - QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
                             EXCHANGE ACT OF 1934

                 For the quarterly period ended June 30, 1998

                    U.S. SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C. 20549




                           Zaxis International Inc.
                 (Name of Issuer as specified in its charter)

       Delaware                    0-15476                 68-0080601
(State of Incorporation)    (Commission File Number)     (IRS Employer 
                                                         Identification No.)



                   1890 Georgetown Road, Hudson, Ohio 44236
                    (Address of principal executive office)



                                 (330)650-0444
                        (Registrant's telephone number)




Check whether the registrant (1) filed all reports required to be filed by
Section 13 or 15(d) of the Exchange Act during the past 12 months and (2) has
been subject to such filings for the past 90 days. Yes[X] No[ ]

As of June 30, 1998, there were 5,783,848 shares of Common Stock outstanding.










Page 1 of 10 Pages.




<PAGE>   2





                           ZAXIS INTERNATIONAL INC.
                                  FORM 10-QSB



                                                                        Page No.
                                                                        --------

PART I. FINANCIAL INFORMATION

Item 1.  Financial Statements:

         Consolidated Balance Sheets                                      3

         Consolidated Statements of Operations:

         Quarters ended June 30, 1998 and 1997                            4

         Six Months ended June 30, 1998 and 1997                          5

         Consolidated Statements of Cash Flows                            6

         Notes to Consolidated Financial Statements                       7


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

PART II. OTHER INFORMATION

Item 4.  Submission of Matters to a Vote of Security Holders              9

Item 5.  Other Information                                                9

Item 6.  Exhibits and Reports on Form 8-K.                                9


SIGNATURES                                                               10







Page 2 of 10 Pages.

<PAGE>   3
<TABLE>
<CAPTION>


                    ZAXIS INTERNATIONAL INC. AND SUBSIDIARY
                          CONSOLIDATED BALANCE SHEETS

                                                      ASSETS
                                                      ------

                                                                                     JUNE 30,         DECEMBER 31,
                                                                                      1998               1997
                                                                                 ----------------   ----------------
                                                                                   (Unaudited)
<S>                                                                                <C>                  <C>        
 CURRENT ASSETS:
      Cash                                                                         $    22,852          $    81,410
      Accounts receivable, net                                                          16,164               39,071
      Inventory                                                                         72,514               76,320
      Prepaid expenses and other                                                        16,908               16,908
                                                                                   -----------          -----------
                   Total current assets                                                128,437              213,709
PROPERTY AND EQUIPMENT:
      Machinery and equipment                                                          359,218              353,461
      Office equipment                                                                 189,905              189,117
      Leasehold improvements                                                            86,992               86,992
                                                                                   -----------          -----------
                                                                                       636,115              629,570
      Less accumulated depreciation                                                    343,046              289,610
                                                                                   -----------          -----------
                                                                                       293,069              339,960
OTHER ASSETS:
      Patent costs                                                                      40,646               41,853
      Organization costs                                                                 1,579                2,764
                                                                                   -----------          -----------
                                                                                        42,225               44,617
                                                                                   -----------          -----------

                   TOTAL ASSETS                                                    $   463,731          $   598,286
                                                                                   ===========          ===========

                                      LIABILITIES AND STOCKHOLDERS' EQUITY
                                      ------------------------------------

CURRENT LIABILITIES:
      Current portion of lease obligations                                         $    10,238          $    10,238
       Notes Payable to directors                                                      225,000              612,020
      Notes payable                                                                    138,000              138,000
      Accounts payable                                                                 433,729              430,513
      Accrued expenses                                                                 350,208              222,327
                                                                                   -----------          -----------
                   Total current liabilities                                         1,157,175            1,413,098

LONG TERM LIABILITIES:
      Capitalized lease obligation                                                      34,243               38,763
      Notes payable                                                                    481,289              251,289
      Notes payable to directors                                                       790,195              257,590
                                                                                   -----------          -----------
                                                                                     1,305,727              547,642
STOCKHOLDERS' EQUITY:
      Common stock                                                                      57,624               57,450
        $.01 par value, 12,000,000 shares authorized,
           5,762,360 and 5,744,991 shares issued and outstanding
      Additional paid-in capital                                                     5,945,600            5,937,628
      Accumulated deficit                                                           (8,002,395)          (7,357,532)
                                                                                   -----------          -----------
                   Total stockholders' equity                                       (1,999,171)          (1,362,454)
                                                                                   -----------          -----------

                   TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY                      $   463,731          $   598,286
                                                                                   ===========          ===========
See notes to consolidated financial statements 
</TABLE>

 Page 3 of 10 Pages.


<PAGE>   4
<TABLE>
<CAPTION>


                    ZAXIS INTERNATIONAL INC. AND SUBSIDIARY
                     CONSOLIDATED STATEMENTS OF OPERATIONS

                                   UNAUDITED



                                                                                        THREE MONTHS ENDED
                                                                                             JUNE 30,
                                                                                  --------------------------------
                                                                                      1998               1997
                                                                                  ------------        ------------

<S>                                                                               <C>                 <C>        
Net sales                                                                         $    45,604         $    75,339

Cost of goods sold                                                                    143,448              76,498

Selling, general and administrative expenses                                          209,954             244,519
                                                                                  -----------         -----------

             Loss from operations                                                    (307,798)           (245,678)

Other income (expense):
  Interest income                                                                         133                  80
  Miscellaneous income                                                                  6,152                --
  Loss on sale of asset                                                                  (173)
  Interest expense                                                                    (43,242)            (20,533)
                                                                                  -----------         -----------

             Total other income (expense)                                             (37,130)            (20,453)
                                                                                  -----------         -----------

             Net loss                                                             $  (344,928)        $  (266,131)
                                                                                  ===========         ===========

Net loss per common share
             Basic                                                                $     (0.06)        $     (0.05)
                                                                                                      ===========
             Diluted                                                              $     (0.06)        $     (0.05)
                                                                                  ===========         ===========

Weighted average number of shares outstanding
             Basic                                                                  5,762,360           5,452,901
                                                                                  ===========         ===========
             Diluted                                                                5,762,360           5,452,901
                                                                                  ===========         ===========

 See notes to consolidated financial statements.

</TABLE>










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<PAGE>   5
<TABLE>
<CAPTION>


                    ZAXIS INTERNATIONAL INC. AND SUBSIDIARY
                     CONSOLIDATED STATEMENTS OF OPERATIONS

                                   UNAUDITED



                                                                                           SIX MONTHS ENDED
                                                                                               JUNE 30,
                                                                                  ----------------------------------
                                                                                      1998                 1997
                                                                                  -----------           ------------

<S>                                                                               <C>                   <C>        
Net sales                                                                         $    95,388           $   142,800

Cost of goods sold                                                                    281,300               165,869

Selling, general and administrative expenses                                          381,732               482,585
                                                                                  -----------           -----------

             Loss from operations                                                    (567,644)             (505,654)

Other income (expense):
  Interest income                                                                         366                 1,287
  Miscellaneous income                                                                  6,152                  --
  Loss on sale of asset                                                                  (173)
  Interest expense                                                                    (75,418)              (44,039)
                                                                                  -----------           -----------

             Total other income (expense)                                             (69,073)              (42,752)
                                                                                  -----------           -----------

             Net loss                                                             $  (636,717)          $  (548,406)
                                                                                  ===========           ===========

Net loss per common share
              Basic                                                               $     (0.11)          $     (0.10)
                                                                                  ===========           ===========
              Diluted                                                             $     (0.11)          $     (0.10)
                                                                                  ===========           ===========

Weighted average number of shares outstanding
             Basic                                                                  5,762,360             5,468,778
                                                                                  ===========           ===========
             Diluted                                                                5,762,360             5,468,778
                                                                                  ===========           ===========

 See notes to consolidated financial statements 

</TABLE>






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<PAGE>   6
<TABLE>
<CAPTION>


                    ZAXIS INTERNATIONAL INC. AND SUBSIDIARY
                     CONSOLIDATED STATEMENTS OF CASH FLOWS

                                   UNAUDITED


                                                                                         SIX MONTHS ENDED
                                                                                             JUNE 30,
                                                                                   ------------------------------
                                                                                      1998               1997
                                                                                   -----------        -----------
<S>                                                                                 <C>                <C>       
OPERATING ACTIVITIES:
Net loss                                                                            $(636,717)         $(548,405)
Adjustments to reconcile net loss to cash
  used in operating activities:
    Depreciation and amortization                                                      57,690             56,643
    Compensation due to stock option grants                                              --                5,616
    Changes in operating assets and liabilities:
      Accounts receivable                                                              22,907             (3,025)
      Inventory and prepaid expenses                                                    3,806            (21,702)
      Accounts payable and accrued expenses                                           131,097            (74,209)
                                                                                    ---------          ---------

           Cash used in operating activities                                         (421,217)          (585,082)

 INVESTING ACTIVITIES:
  Purchase of property and equipment                                                   (6,545)           (74,455)
  Deposits                                                                             17,684
  Patent cost expenditures                                                             (1,861)            (5,363)
                                                                                    ---------          ---------

           Cash used in investing activities                                           (8,406)           (62,134)

FINANCING ACTIVITIES:
  Proceeds from sales of common stock                                                 245,948
  Payments on notes payable
  Proceeds from notes payable                                                         375,585            372,360
  Payments on capital lease obligations                                                (4,520)            51,679
                                                                                    ---------          ---------

           Cash provided by financing activities                                      371,065            669,987
                                                                                    ---------          ---------

Increase in cash                                                                      (58,558)            22,772
Cash at beginning of period                                                            81,410              1,090
                                                                                    ---------          ---------

Cash at end of period                                                               $  22,852          $  23,862
                                                                                    =========          =========



 See notes to consolidated financial statements.


</TABLE>

Page 6 of 10 Pages.





<PAGE>   7









                    ZAXIS INTERNATIONAL INC. AND SUBSIDIARY

                  NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

1. BASIS OF PRESENTATION

The financial statements present the consolidated financial position and
results of operations of Zaxis International Inc. (International) and Zaxis
Inc. (Zaxis or the Company), its wholly-owned subsidiary.

Zaxis Incorporated was founded in 1989 as a privately held Ohio corporation.
On August 25, 1995, Zaxis merged with a subsidiary of The InFerGene Company
(InFerGene). InFerGene was an inactive publicly traded Delaware corporation
founded in 1985. Neither InFerGene nor its subsidiary had any assets or
liabilities. The merger, for accounting purposes, was a reverse acquisition in
which Zaxis acquired InFerGene. The acquisition was accounted for as a
purchase with no value assigned to InFerGene. InFerGene then changed its name
to Zaxis International Inc. The financial statements include the operations of
Zaxis for all periods presented and the operations of International since the
date of acquisition. All intercompany transactions and balances have been
eliminated.

As an interim report, the financial statements and notes thereto do not
include all of the disclosures necessary for a full presentation of financial
condition and operating results, and should be read in conjunction with the
financial statements for the year ended December 31, 1997.

2.    LIQUIDITY

Zaxis incurred losses of $636,717 during the six months ended June 30, 1998
and $548,406 in 1997. The operations of the Company have been financed mainly
by loans from companies and individuals associated with members of the Board
of Directors.

The Company continues to rely upon these sources to sustain on-going
operations, research, production development and sales development.
Discussions have been conducted with potential new investors for long-term
debt or equity funding, but to date no transactions have been completed. The
Company will necessarily be reliant upon such sources of funding until the
marketing of the companies principal products can be brought to a level
sufficient to support the operating requirements of the Company. These
conditions cause doubt about the Company's ability to continue as a going
concern. No adjustments to the amounts or classification of assets and
liabilities which could result from the outcome of this uncertainty are
reflected in the financial statements.


3. NET LOSS PER COMMON SHARE

The effects of outstanding options and warrants has not been included in the
calculation of net loss per share.












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<PAGE>   8



                         PART 1. FINANCIAL INFORMATION

Item 2. Management's Discussion and Analysis.

Management's Discussion and Analysis of Financial Condition and Results of
Operations

Results of Operations

Two aspects of the business account for the change in results of operation
between 1998 and 1997. Sales were down $47,412 and interest expense up
$31,379. Sales for the six months ended June 30, 1998, totaled $95,388
compared with $142,800 for 1997's first six months. The decline was largely
due to decrease in pre-cast gel sales as a result of removing the previous
principle product line from market until redesigned and reintroduced at trial
test sights late 4th quarter 1997. Also, sales of molecular grade water and
gel mix were postponed from first half of 1998. Sales in the second quarter
were $45,604, compared to $49,784 in the first quarter.

Cost of goods sold for the six months ended June 30, 1998, was $281,300,
exceeding sales by $185,912. Cost of goods sold for the same period in 1997
was $165,869, exceeding sales by $23,069. Production capacity, built in 1996
in anticipation of rapid sales growth, is greater than sales volumes achieved,
causing inefficient application of labor and overhead. In March of 1997, the
Company took delivery on a custom designed automated product packaging system
for protein gels.

Selling, general and administrative expenses were $381,732 for the six months
ended June 30, 1998, down from $482,585 for the same period in 1997. Reduction
in general and administrative staff accounted for $41,327, or 41% of decrease.
Selling expenses, including sales salaries, advertising and travel expenses
were reduced by $16,580, or 16% of decrease.

Financial Condition and Liquidity

Borrowings added $375,585 to cash in the six months ended June 30, 1998. These
funds were used for operations, which used $421,217 in cash. Since the end of
1997, the excess of current liabilities over current assets has decreased by
$170,651 in the period, to $1,028,738 from $1,199,389.

The Company needs to secure immediate financing to allow it to explore several
opportunities from new products that are now available for market introduction
and to afford it time to build sales volumes of these new products to
profitable levels. In the period required for product introduction and sales
growth, the company will need to satisfy obligations to current creditors.
Pursuant to this need, the Company continues to seek interim funding

                          PART II. OTHER INFORMATION

Item 1.  Legal Proceedings

      None of substantial nature.

Item 2(c).  Changes in Securities

      None

Item 3.  Defaults upon Senior Securities

      The Company is more than thirty days past due on principal payments on
      three individual C Series Notes totalling $105,000 in principal. The 
      Company is more than thirty days past due on interest payments on above 
      referenced C series notes in the amount of $13,621 and is more than thiry 
      days past due on interest payments on the Z series notes in the amount of
      $28,591.




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<PAGE>   9



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

On July 22, 1998, the Company held its Annual Meeting of Shareholders at Zaxis
International's offices in Hudson, Ohio. A slate of five Directors presented
by Management in a duly issued Proxy Statement and Form of Proxy were elected
to one-year terms by a favorable vote of more than 98% each. The votes for the
five directors elected were: Conaly Bedell, receiving 3,496,069 votes For,
65,085 Against; Craig Jones, receiving 3,496,069 For, 65,085 Against; Alan
Scott receiving 3,496,057 For, 65,097 Against; Calvin D. Wible, receiving
3,496,045 For, 65,109 Against; and Leonard A. Duval receiving 3,496,037 For,
65,117 Against. The only other matter to come before the Shareholders for a
vote at the Annual Meeting was the re-appointment of Ernst & Young as
Independent Accountants. The vote was 3,460,322 For, 100,819 Against. Ernst
and Young has been the auditor firm for Zaxis International for all but two
years since inception.

Item 5.  Other Information

Item 6.  Exhibits and Reports on Form 8-K

     A.   Exhibits:
            None

     B. Reports on Form 8-K during the Quarter Ended June 30, 1998:
            None




















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<PAGE>   10






                                  SIGNATURES

In accordance with the requirements of the Exchange Act, the registrant caused
this report to be signed on its behalf by the undersigned, thereunto duly
authorized.

                                           Zaxis International Inc.
                                           ------------------------
                                                (Registrant)


August 12, 1998                             BY:  /s/ Conaly Bedell
                                               ------------------------
                                               Conaly Bedell, President
                                               Chief Executive Officer


August 12, 1998                             BY:  /s/ Sharon Killinger
                                               ----------------------
                                               Sharon Killinger, Controller
                                               Accounting Officer

























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