<PAGE>   1

                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C.  20549


                                  FORM 10-QSB


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


For the quarterly period ended          MARCH 31, 1998
                                ---------------------------------------


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

                         Commission File Number 0-20791


                         AMARILLO BIOSCIENCES, INC.
--------------------------------------------------------------------------------
      (Exact name of small business issuer as specified in its charter)

         TEXAS                                              75-1974352         
-------------------------------------------------------------------------------
(State or other jurisdiction of                          (IRS Employer
incorporation or organization)                          Identification No.)
                                                       
800 West Ninth, Amarillo, TX                                   79101    
-------------------------------------------------------------------------------
(Address of principal executive offices)                    (Zip Code)
                                                       
     806-376-1741                                        FAX 806-376-9301 
-------------------------------------------------------------------------------
(Issuer's telephone number, including area code)       


         Check whether the issuer (1) filed all reports required to be filed by
Section 13 or 15(d) of the Exchange Act during the past 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 March 31, 1998, there were 5,414,232 shares of the issuer's common stock
outstanding.

                        This report contains 13 pages.





                                       1
<PAGE>   2


                          AMARILLO BIOSCIENCES, INC.


                                    INDEX



<TABLE>
 <S>                <C>                                                                              <C>
 PART I:            FINANCIAL INFORMATION                                                          PAGE NO.
                                                                                                   --------

 Item 1.            Financial Statements

                    Consolidated Balance Sheets - December 31, 1997 and March 31, 1998  . . . .        3

                    Consolidated Statements of Operations - Three Months Ended March 31,               
                    1997 and 1998 and Cumulative from June 25, 1984 (Inception) through                
                    March 31, 1998  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        4
                                                                                                       
                    Condensed Consolidated Statements of Cash Flows - Three Months Ended               
                    March 31, 1997 and 1998 and Cumulative from June 25, 1984 (Inception)              
                    through March 31, 1998  . . . . . . . . . . . . . . . . . . . . . . . . . .        5
                                                                                                       
                    Notes to Consolidated Financial Statements  . . . . . . . . . . . . . . . .        6
                                                                                                       
 Item 2.            Management's Discussion and Analysis of Results of Operations and                  
                    Financial Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . .        7
                                                                                                       
                                                                                                       
 PART II:           OTHER INFORMATION                                                                  
                                                                                                       
                                                                                                       
 Item 6.            Exhibits and Reports on Form 8-K  . . . . . . . . . . . . . . . . . . . . .        9
                                                                                                       
 Signatures         . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       10
</TABLE>





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<PAGE>   3
                 AMARILLO BIOSCIENCES, INC. AND SUBSIDIARIES
                     (COMPANIES IN THE DEVELOPMENT STAGE)

                         CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                                                    December 31,            March 31,     
                                                                                        1997                  1998
                                                                                     ----------             ----------
<S>                                                                                  <C>                    <C>
ASSETS
Current assets:

  Cash and cash equivalents                                                          $  879,170             $  299,259
  Marketable securities                                                               6,007,182              6,089,092
  Other current assets                                                                   70,779                 57,142
                                                                                     ----------             ----------
   Total current assets                                                               6,957,131              6,445,493

Property and equipment, net                                                             125,179                125,263
Patent license, net of accumulated amortization of $73,824 and
  $75,637 at December 31, 1997 and March 31, 1998, respectively                          51,176                 49,363
Organization cost, net of accumulated amortization of $4,962 and
  $6,084 at December 31, 1997 and March 31, 1998, respectively                            1,122                     --
Investment in ISI common stock                                                          114,023                 93,516
                                                                                     ----------             ----------
Total assets                                                                         $7,248,631             $6,713,635
                                                                                     ==========             ==========
LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:

  Accounts payable                                                                   $   74,754             $  166,284
  Accrued interest expense                                                               91,356                120,606
  Other accrued expenses                                                                 47,958                 19,324
                                                                                     ----------             ----------
    Total current liabilities                                                           214,068                306,214
Notes payable to related party                                                        2,600,000              2,600,000
                                                                                     ----------             ----------
Total liabilities                                                                     2,814,068              2,906,214

STOCKHOLDERS' EQUITY:
  Common stock, $.01 par value:
    Authorized shares - 10,000,000
    Issued shares - 5,414,232                                                            54,142                 54,142
  Additional paid-in capital                                                         13,392,138             13,392,138

  Deficit accumulated during the development stage                                   (9,045,415)            (9,652,050)
  Unrealized gain (loss) on marketable securities                                        33,698                 13,191
                                                                                     ----------             ----------
Total stockholders' equity                                                            4,434,563              3,807,421
                                                                                     ----------             ----------
Total liabilities and stockholders' equity                                           $7,248,631             $6,713,635
                                                                                     ==========             ==========
</TABLE>

                           See accompanying notes.





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<PAGE>   4

                 AMARILLO BIOSCIENCES, INC. AND SUBSIDIARIES
                     (COMPANIES IN THE DEVELOPMENT STAGE)

                    CONSOLIDATED STATEMENTS OF OPERATIONS

<TABLE>
<CAPTION>
                                                       Three months ended                                   
                                                            March 31,                  Cumulative from June 
                                                -------------------------------        25, 1984 (Inception) 
                                                     1997              1998           through March 31, 1998
                                                -------------     -------------       ----------------------
<S>                                             <C>               <C>                         <C>
Revenues:
  Contract revenues                             $          --     $          --             $   9,000,000
  Interferon sales                                         --                --                   420,974
  Interest income                                     101,068            89,811                 1,207,629
  Sublicense fees                                          --                --                   113,334
  Royalty income                                           --                --                    31,544
  Gain on sale of ISI stock                                --                --                   188,562
  Other                                                26,000                --                   604,371
                                                -------------     -------------             -------------
                                                      127,068            89,811                11,566,414

Expenses:
  Research and development
    expenses                                          349,680           368,517                10,348,111
  Selling, general, and
    administrative expenses                           291,788           298,679                10,106,159
  Interest expense                                     29,625            29,250                   729,194
                                                -------------     -------------             -------------
                                                      671,093           696,446                21,183,464
                                                -------------     -------------             -------------

Loss before income taxes                             (544,025)         (606,635)               (9,617,050)
Income tax expense                                         --                --                    35,000
                                                -------------     -------------             -------------
Net loss                                        $    (544,025)    $    (606,635)            $  (9,652,050)
                                                =============     =============             =============
Basic and diluted loss per share                $       (0.10)    $       (0.11)
                                                =============     =============   
Weighted average shares outstanding                 5,414,232         5,414,232
                                                =============     =============   
</TABLE>


                           See accompanying notes.





                                      4
<PAGE>   5

                 AMARILLO BIOSCIENCES, INC. AND SUBSIDIARIES
                     (COMPANIES IN THE DEVELOPMENT STAGE)

               CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS

<TABLE>
<CAPTION>
                                                             Three months ended                Cumulative from June
                                                                 March 31,                     25, 1984 (Inception)
                                                        ---------------------------------             through      
                                                            1997                 1998              March 31, 1998  
                                                        -----------           -----------          --------------- 
 <S>                                               <C>                 <C>                              <C>
 Net cash used in operating activities                  $  (685,178)          $  (575,470)          $(8,647,351)
                                                        -----------           -----------           ----------- 

 Net cash provided by (used in) investing
   activities                                                    --                (4,441)           (6,530,409)
                                                        -----------           -----------           ----------- 
 Net cash provided by financing activities                       --                    --            15,477,019
                                                        -----------           -----------           ----------- 
 Net increase (decrease) in cash and cash
   equivalents                                             (685,178)             (579,911)              299,259
                                                        -----------           -----------           ----------- 
 Cash and cash equivalents at beginning
   of period                                              2,799,297               879,170                    --
                                                        -----------           -----------           ----------- 
 Cash and cash equivalents at end of
   period                                               $ 2,114,119           $   299,259           $   299,259
                                                        ===========           ===========           ===========
 Supplemental Disclosure of Cash Flow
   Information
 Cash paid for income taxes                             $        --           $        --           $    37,084
                                                        ===========           ===========           ===========

 Cash paid for interest                                 $        --           $        --           $     6,466
                                                        ===========           ===========           ===========
</TABLE>


                           See accompanying notes.





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<PAGE>   6
                  AMARILLO BIOSCIENCES, INC. AND SUBSIDIARIES
                      (COMPANIES IN THE DEVELOPMENT STAGE)

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

1.       Basis of Presentation.  The accompanying consolidated financial
         statements, which should be read in conjunction with the consolidated
         financial statements and footnotes included in the Company's Form
         10-KSB, are unaudited (except for the December 31, 1997 consolidated
         balance sheet which was derived from the Company's audited financial
         statements), but have been prepared in accordance with generally
         accepted accounting principles for interim financial information.
         Accordingly, they 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 recurring adjustments) considered necessary
         for a fair presentation have been included.

         Operating results for the three months ended March 31, 1998 are not
         necessarily indicative of the results that may be expected for the
         full year ending December 31, 1998.

2.       Loss per share.  Loss per share is computed based on the weighted
         average number of common shares outstanding.

3.       Reclassification.  Certain amounts have been reclassified from
         selling, general and administrative expenses to research and
         development expenses for the three months ended March 31, 1997.  The
         impact of the reclassification was approximately $91,000.

4.       Comprehensive income.  As of January 1, 1998, the Company adopted
         Financial Accounting Standards Board Statement No. 130, Reporting
         Comprehensive Income. Statement 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. Statement 130 requires unrealized
         gains or losses on the Company's available-for-sale securities, which
         prior to adoption were reported separately in shareholders' equity, to
         be included in other comprehensive income. Prior year financial
         statements have been reclassified to conform to the requirements of
         Statement 130.

         During the first quarter of 1998 and 1997, total comprehensive income
         amounted to $627,142 and $552,025.





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<PAGE>   7
ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF RESULTS
         OF OPERATIONS AND FINANCIAL CONDITION

         RESULTS OF OPERATIONS

         Three Months Ended March 31, 1997 Compared to Three Months Ended March
         31, 1998.

         During the three months ended March 31, 1997, the Company had total
         revenues of $127,068 compared to total revenues of $89,811 during the
         three months ended March 31, 1998.  During the first quarter of 1997,
         the Company received a $26,000 partial payment for the preparation of
         a research agreement and business plan for a foreign country.  Other
         1997 revenues consisted of interest income of $101,068.  Revenues for
         the first quarter of 1998 consisted of interest income of $89,811.

         During the 1997 first quarter, research and development expenses were
         $349,680 as compared to $368,517 during the 1998 first quarter.  The
         $18,837 increase in research and development expenses in 1998 was due
         to the completion of certain clinical studies and the commencement of
         new clinical studies.

         During 1997 and 1998, the Company incurred general and administrative
         expenses of $291,788 and $298,679, respectively.  There was no
         significant difference reflected in 1998 compared to 1997.





                                       7
<PAGE>   8
         LIQUIDITY AND CAPITAL RESOURCES

         At March 31, 1998, the Company had cash of $299,259 and marketable
         securities of $6,089,092 with accounts payable of $166,284 and other
         funding commitments for clinical studies of approximately $627,000.

         The Company intends to focus its development activities on the
         treatment of Sjogren's syndrome, fibromyalgia, opportunistic
         infections in patients who are HIV positive, myeloproliferative
         diseases, hepatitis B and hepatitis C.

         The Company anticipates, based on its currently proposed plans and
         assumptions relating to its operations (including assumptions
         regarding the progress of its research and development and the timing
         and costs associated with its development projects), that the
         Company's existing capital resources will be sufficient to satisfy the
         Company's estimated cash requirements for at least the next 21 months.
         Unless the Company generates significant revenues during such period,
         the Company will need additional financing to fully fund such
         development.  Moreover, the Company's estimate of the amount required
         to complete its development projects may prove to be inaccurate.  The
         Company has no current arrangements with respect to, or sources of,
         additional financing and it is not anticipated that any of the
         officers, directors or shareholders of the Company will provide any
         portion of the Company's future financing requirements.  There can be
         no assurance that, when needed, additional financing will be available
         to the Company on commercially reasonable terms, or at all.  In the
         event that the Company's plans change, its assumptions change or prove
         inaccurate, or if the remaining net proceeds of the Company's public
         offering, together with other capital resources, otherwise prove to be
         insufficient to fund operations, the Company could be required to seek
         additional financing sooner than currently anticipated.  Any inability
         to obtain additional financing when needed would have a material
         adverse effect on the Company, including requiring the Company to
         significantly curtail or possibly cease its operations.





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                         PART II - OTHER INFORMATION

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

         Exhibit 27.   Financial Data Schedule



         No reports on Form 8-K were filed during the quarter ended March 31, 
         1998.





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<PAGE>   10

                                   SIGNATURES





         Pursuant to the requirements of Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.



                                  AMARILLO BIOSCIENCES, INC.


Date:  May 11, 1998               By: /s/ JOSEPH M. CUMMINS 
                                      -----------------------------------------
                                      Joseph M. Cummins
                                      President, Chief Executive Officer 
                                      and Chief Financial Officer





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<PAGE>   11

                                 EXHIBIT INDEX

<TABLE>
<CAPTION>
EXHIBIT
NUMBER                    DESCRIPTION
-------                   -----------
<S>                    <C>
  27                    Financial Data Schedule
</TABLE>