<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 March 31, 1998

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




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

<TABLE>
<S>                          <C>                           <C>
        Delaware                     0-15476                           68-0080601
(State of Incorporation)     (Commission File Number)      (IRS Employer Identification No.)
</TABLE>



                    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 May 5, 1998, there were 5,766,242 shares of Common Stock outstanding.






Page 1 of 9 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 March 31, 1998 and 1997               4


                       Consolidated Statements of Cash Flows                5


              Notes to Consolidated Financial Statements                    6


Item 2. Management's Discussion and Analysis                                7-8




SIGNATURES                                                                  9




Page 2 of 9 Pages.


<PAGE>   3

                     ZAXIS INTERNATIONAL INC. AND SUBSIDIARY
                           CONSOLIDATED BALANCE SHEETS
                                    UNAUDITED

<TABLE>
<CAPTION>
                                     ASSETS
                                     ------

                                                                           MARCH 31           DECEMBER 31
                                                                             1998                1997
                                                                         ------------        ------------

<S>                                                                      <C>                 <C>        
CURRENT ASSETS:
      Cash                                                               $    27,938         $    81,410
      Accounts receivable, net                                                 9,993              39,071
      Inventory                                                               73,907              76,320
      Prepaid expenses and other                                              16,908              16,908
                                                                         -----------         -----------
                   Total current assets                                      128,747             213,709
PROPERTY AND EQUIPMENT:
      Machinery and equipment                                                358,543             353,461
      Office equipment                                                       190,420             189,117
      Leasehold improvements                                                  86,992              86,992
                                                                         -----------         -----------
                                                                             635,956             629,570
      Less accumulated depreciation                                          317,067             289,610
                                                                         -----------         -----------
                                                                             318,889             339,960
OTHER ASSETS:
      Patent costs                                                            41,443              41,853
      Organization costs                                                       2,171               2,764
                                                                         -----------         -----------
                                                                              43,614              44,617
                                                                         -----------         -----------

                   TOTAL ASSETS                                          $   491,250         $   598,285
                                                                         ===========         ===========

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

CURRENT LIABILITIES:
      Current portion of lease obligations                               $    10,238         $    10,238
       Bank loan payable                                                 $         -         $         -
       Notes Payable to directors                                        $   611,030         $   612,020
      Notes payable                                                          138,000             138,000
      Accounts payable                                                       413,410             430,513
      Accrued expenses                                                       269,991             222,327
                                                                         -----------         -----------
                   Total current liabilities                               1,442,669           1,413,098

  LONG TERM LIABILITIES:
        Capitalized lease obligations                                         36,546              38,763
        Notes Payable                                                        326,289             251,289
         Notes Payable to directors                                          324,895             257,590
                                                                         -----------         -----------
                   Total long term liabilites                                687,729             547,642

STOCKHOLDERS' EQUITY:
      Common stock                                                            57,450              57,450
        $.01 par value, 12,000,000 shares authorized,
            5,744,991 and 5,744,991 shares issued and outstanding
      Additional paid-in capital                                           5,945,774           5,937,628
      Deferred compensation                                                        -                   -
      Accumulated deficit                                                 (7,642,372)         (7,357,532)
                                                                         -----------         -----------
                   Total stockholders' equity                             (1,639,148)         (1,362,454)
                                                                                             -----------
                   TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY            $   491,250         $   598,285
                                                                         ===========         ===========
</TABLE>


 See notes to consolidated financial statements.


 PAGE 3 OF 9


<PAGE>   4

                     ZAXIS INTERNATIONAL INC. AND SUBSIDIARY
                      CONSOLIDATED STATEMENTS OF OPERATIONS

<TABLE>
<CAPTION>
                                    UNAUDITED
                                                           THREE MONTHS ENDED
                                                                MARCH 31
                                                     -------------------------------
                                                        1998                 1997
                                                     -----------         -----------

<S>                                                  <C>                 <C>        
Net sales                                            $    49,784         $    67,461

Cost of goods sold                                       137,852              89,370

Selling, general and administrative expenses             171,778             238,066
                                                     -----------         -----------

             Loss from operations                       (259,845)           (259,975)

Other income (expense):
  Interest income                                            233               1,207
  Miscellaneous income                                         -                   -
  Interest expense                                       (32,176)            (23,506)
                                                     -----------         -----------

             Total other income (expense)                (31,943)            (22,299)
                                                                         -----------

             Net loss                                $  (291,787)        $  (282,274)
                                                     ===========         ===========

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


Weighted average number of shares outstanding
             Basic                                     5,744,991           5,449,519
                                                     ===========         ===========
             Diluted                                   5,744,991           5,449,519
                                                     ===========         ===========
</TABLE>




PAGE 4  OF 9

<PAGE>   5


                     ZAXIS INTERNATIONAL INC. AND SUBSIDIARY
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                    UNAUDITED



<TABLE>
<CAPTION>
                                                                             THREE MONTHS ENDED
                                                                                 MARCH 31,
                                                                      ------------------------------
                                                                         1998               1997
                                                                      ------------      ------------
<S>                                                                    <C>               <C>       
OPERATING ACTIVITIES:
Net loss                                                               $(291,787)        $(282,274)
Adjustments to reconcile net loss to cash
  used in operating activities:
    Depreciation and amortization                                         29,571            26,640
    Compensation due to stock option grants                                    -             2,808
    Changes in operating assets and liabilities:
      Accounts receivable                                                 29,078            17,211
      Inventory and prepaid expenses                                       2,413            33,827
      Accounts payable and accrued expenses                               45,654           (35,945)
                                                                       ---------         ---------

           Cash used in operating activities                            (185,071)         (237,733)

 INVESTING ACTIVITIES:
  Purchase of property and equipment                                      (6,386)          (79,116)
  Patent cost expenditures                                                (1,113)              (18)
                                                                       ---------         ---------

           Cash used in investing activities                              (7,499)          (79,134)

FINANCING ACTIVITIES:
  Proceeds from sales of common stock and excercise of warrants                -           105,000
  Proceeds from notes payable and bank loan payable                      141,315           164,900
  Payments on capital lease obligations                                   (2,217)           57,280
                                                                       ---------         ---------

           Cash provided by financing activities                         139,098           327,180
                                                                                         ---------

Increase in cash                                                         (53,472)           10,313
Cash at beginning of period                                               81,410             1,090
                                                                       ---------         ---------

Cash at end of period                                                  $  27,938         $  11,403
                                                                       =========         =========
</TABLE>




PAGE 5 OF 9


<PAGE>   6




                     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.

On August 25, 1995, Zaxis merged with a subsidiary of The InFerGene Company
(InFerGene). InFerGene was an inactive public company and neither InFerGene nor
its subsidiary had any assets or liabilities. The merger, for accounting
purposes, was a reverse acquisition in which Zaxis acquire 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.

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

The Company has a deficit in stockholders equity of $1,639,148 compared to
$1,362,454 in 1997. There is a working capital deficit of $1,313,922 compared to
$1,199,389 in 1997. The operations of the Company have been financed mainly by
private sales of common stock and by loans of members of the Board of Directors
and private investors.

Management recognizes that additional financial resources must be obtained in
order to execute its plans and to fund operations until they can generate cash,
and is in the process of pursuing several possibilities for interim and
long-term financing. The Company has engaged an investment banking firm to
assist in the private placement of debt securities for interim needs and with
them pursuing long-term financing, possibly through the sale of common stock.
There can be no assurance that the Company will be successful in obtaining the
interim of long-term financing. These conditions raise substantial doubt about
the Company's ability to continue as a going concern. No adjustments to the
amounts of 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 have not been included in the
calculation of net loss per share.








Page 6 of 9 Pages


<PAGE>   7




                          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

Sales for the three months ended March 31, 1998, totaled $49,784 compared with
$67,461 for 1997's first three months.

Cost of goods sold for the three months ended March 31, 1998, was $137,852,
exceeding sales by $88,068. Cost of goods sold for the same period in 1997 was
$89,370, exceeding sales by $21,909. A significant portion of increase was due
to production runs used for in house testing of production method improvements.

Selling, general and administrative expenses were $171,778 for the three months
ended March 31, 1998, down $66,288 for the same period in 1997.

Financial Condition and Liquidity

Borrowings added $141,315 to cash in the first quarter of 1998. These funds were
used mainly in operations, which used $185,071 in cash. Since the end of 1997,
the excess of current liabilities over current assets has increased by $114,533
in the period, to $1,313,922 from $1,199,389.

The Company needs to secure immediate financing to allow it to exploit several
opportunities from new products that are at the end of the development stage,
afford it time to build sales volumes of these new products to profitable
levels, and satisfy obligations to current creditors. In August 1997, the Board
approved an offering of $660,000 in Convertible Two Year Notes which goal was
exceeded, bringing in $821,183 through this date. Currently, the company is
negotiating details of an infusion of funds from a private investor in the mid
six figures. Also the company is involved in other preliminary discussions with
private investors for infusion of one million dollars.

The Board voted on December 19, 1997, to extend the expiration date on Class B
Warrants to 5 p.m. EST on September 30, 1998.


                           PART II. OTHER INFORMATION

Item 1.  Legal Proceedings

      None of substantial nature.

Item 2(c).  Changes in Securities



Item 3.  Defaults upon Senior Securities

         None


Page 7 of 9 Pages.


<PAGE>   8


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

None


Item 5.  Other Information

None


Item 6.  Exhibits and Reports on Form 8-K

      A.   Exhibits:
                None

      B. Reports on Form 8-K during the Quarter Ended March 31, 1998:
                None








Page 8 of 9 Pages.



<PAGE>   9



                                   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)


May 15, 1998                                 BY:  S/S Conaly Bedell
                                                 ------------------------------
                                                 Conaly Bedell, President
                                                 Chief Executive Officer



May 15, 1998                                 BY:  S/S Sharon Killinger
                                                  ------------------------------
                                                  Sharon Killinger, Controller
                                                  Accounting Officer







Page 9 of 9 Pages