<PAGE>   1
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM 10-Q


(Mark One)

[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

                                       OR

[ ]  Transition Report Pursuant to Section 13 or 15(d) of the 
     Securities Exchange Act of 1934

                  For the Transition Period From           to
                                                 ---------    ---------

                         Commission File Number 0-22147

                               ILEX ONCOLOGY, INC.
             (Exact name of registrant as specified in its charter)

       Delaware                                           74-2699185
    (State or other                                    (I.R.S. Employer 
    jurisdiction of                                   Identification No.)
    incorporation or
    organization)


                          11550 I.H. 10 West, Suite 300
                            San Antonio, Texas 78230
                    (Address of principal executive offices)
                                   (Zip Code)

                                 (210) 949-8200
              (Registrant's telephone number, including area code)

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

         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.

         On May 5, 1998, there were outstanding 12,307,567 shares of Common
Stock, $.01 par value, of the registrant.


<PAGE>   2

                               ILEX ONCOLOGY, INC.

                                    FORM 10-Q

                                      INDEX
<TABLE>
<CAPTION>
PART I.  FINANCIAL INFORMATION                                                    PAGE
                                                                                  ----
<S>                                                                               <C>
Item 1:  Financial Statements

         Consolidated Condensed Balance Sheets - December 31, 1997 and 
         March 31, 1998                                                           3-4

         Consolidated Condensed Statements of Operations - For the three month 
         periods ended March 31, 1997 and March 31, 1998                          5

         Consolidated Condensed Statements of Cash Flows - For the three month 
         periods ended March 31, 1997 and March 31, 1998                          6

         Notes to the Consolidated Condensed Financial Statements                 7-9

Item 2:  Management's Discussion and Analysis of Financial Condition              9-14
                  and Results of Operations

PART II. OTHER INFORMATION

Items 1-6:        Other Information                                               15


SIGNATURES                                                                        16
</TABLE>



                                      -2-

<PAGE>   3

                         PART I - FINANCIAL INFORMATION

Item 1. Financial Statements

                               ILEX ONCOLOGY, INC.
                      CONSOLIDATED CONDENSED BALANCE SHEETS

               (In Thousands, Except Shares and Per Share Amounts)

<TABLE>
<CAPTION>
                                                                        March 31, 
                                                       December 31,        1998
                          ASSETS                           1997        (unaudited)
                                                       ------------    -----------
<S>                                                       <C>           <C>    
 CURRENT ASSETS:
   Cash and cash equivalents                              $ 22,655      $18,241
   Investments in marketable securities                     10,111       11,698
   Accounts receivable, net of allowance
     for doubtful accounts of $123 at
     both December 31, 1997 and March 31, 1998-
       Related parties                                       1,255        1,002
       Others                                                2,508        2,066
   Revenues in excess of billings                              889        1,313
   Prepaid expenses and other                                  720          752
                                                          --------      -------
              Total current assets                          38,138       35,072
                                                          --------      -------
 NONCURRENT ASSETS:
  Investment in joint ventures and European affiliate         (113)         489
  Intangible assets, net of amortization                     4,847        4,577
  Investments in marketable securities                       9,880        7,125
                                                          --------      -------
              Total noncurrent assets                       14,614       12,191
                                                          --------      -------
 PROPERTY AND EQUIPMENT, Net of accumulated
  depreciation and amortization of $562 and
  $717 at December 31, 1997 and March 31, 1998,
  respectively:                                              2,559        2,933
                                                          --------      -------
              Total assets                                $ 55,311      $50,196
                                                          ========      =======
</TABLE>

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



                                      -3-
<PAGE>   4
                               ILEX ONCOLOGY, INC.
                      CONSOLIDATED CONDENSED BALANCE SHEETS

               (In Thousands, Except Shares and Per Share Amounts)

<TABLE>
<CAPTION>
                                                                            March 31,
                                                             December 31,     1998
                 LIABILITIES AND STOCKHOLDERS' EQUITY           1997       (unaudited)
                                                             ------------  -----------
<S>                                                           <C>           <C>     
 CURRENT LIABILITIES:
    Accounts payable-
      Related parties                                         $    163      $     64
      Other                                                        345           554
    Accrued subcontractor costs-
      Related parties                                              982           316
      Other                                                        657           645
    Accrued liabilities                                            727           718
    Deferred revenue                                               928           194
                                                              --------      --------
               Total current liabilities                         3,802         2,491
                                                              --------      --------
 OTHER LONG-TERM LIABILITIES                                       433           425
                                                              --------      --------
 COMMITMENTS AND CONTINGENCIES (Note 3)

 STOCKHOLDERS' EQUITY:
    Common stock, $0.01 par value; 40,000,000 shares
      authorized; 12,279,530 and 12,280,730 shares
      issued and outstanding at December 31, 1997 and
      March 31, 1998, respectively                                 123           123
    Additional paid-in capital                                  61,090        64,239
    Receivables on sale of common stock                            (82)          (82)
    Accumulated deficit                                        (10,055)      (17,000)
                                                              --------      --------
               Total stockholders' equity                       51,076        47,280
                                                              --------      --------
               Total liabilities and stockholders' equity     $ 55,311      $ 50,196
                                                              ========      ========
</TABLE>

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


                                      -4-
<PAGE>   5

                               ILEX ONCOLOGY, INC.
                 CONSOLIDATED CONDENSED STATEMENTS OF OPERATIONS
                                   (Unaudited)

                    (In Thousands, Except Per Share Amounts)

<TABLE>
<CAPTION>
                                                 Three Months
                                                   ended
                                                  March 31,
                                            ----------------------
                                              1997          1998
                                            --------      --------
<S>                                         <C>           <C>     
 REVENUE:
   Product development                      $  1,371      $    811
   Contract research services, net             1,212         2,128
                                            --------      --------
            Total revenue                      2,583         2,939
                                            --------      --------
 OPERATING EXPENSES:
   Research and development costs              1,564         2,034
   Direct costs                                1,096         1,605
   Selling, general, and administrative          699         1,749
   Licensing fees                                 --         3,393
   PRN amortization                               --           269
                                            --------      --------
            Total operating expenses           3,359         9,050
                                            --------      --------
 OPERATING LOSS                                 (776)       (6,111)
                                            --------      --------
 OTHER INCOME (EXPENSE):
   Equity in losses of joint ventures
     and European affiliate                     (104)       (1,401)
   Interest income                               412           567
                                            --------      --------
 NET LOSS                                   $   (468)     $ (6,945)
                                            ========      ========
 BASIC AND DILUTED NET LOSS PER SHARE       $   (.04)     $   (.57)
                                            ========      ========
 WEIGHTED AVERAGE SHARES USED IN
    COMPUTING BASIC AND DILUTED LOSS
    PER SHARE OF COMMON STOCK                 10,884        12,281
                                            ========      ========
</TABLE>

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


                                      -5-
<PAGE>   6

                               ILEX ONCOLOGY, INC.
                 CONSOLIDATED CONDENSED STATEMENTS OF CASH FLOWS
                                   (Unaudited)
                                 (In Thousands)
<TABLE>
<CAPTION>
                                                                     Three months ended
                                                                          March 31,
                                                                    ----------------------
                                                                      1997          1998
                                                                    --------      --------
<S>                                                                 <C>           <C>      
 CASH FLOWS FROM OPERATING ACTIVITIES:
     Net loss                                                       $   (468)     $ (6,945)
     Adjustments to reconcile net loss to net cash used in
       operating activities-
        Depreciation and amortization                                     54           425
        Equity in losses of joint ventures and European
          affiliate in excess of distributions                           104         1,401
      Valuation of warrants issued in payment as licensing fees           --         3,143
        Change in assets and liabilities-
          (Increase) decrease in assets-
            Accounts receivable, net                                     110          (255)
         Revenues in excess of billings                                   --          (424)
            Prepaid expenses and other                                   158           (32)
          Increase (decrease) in liabilities-
            Accounts payable                                            (325)          110
            Accrued liabilities                                          (29)         (687)
            Deferred revenue                                             (95)         (734)
            Other long-term liabilities                                   67            (8)
                                                                    --------      --------
      Net cash used in operating activities                             (424)       (4,006)
                                                                    --------      --------
 CASH FLOWS FROM INVESTING ACTIVITIES:
   Purchases of marketable securities                                 (5,118)       (2,982)
   Maturities of marketable securities                                   215         4,150
   Purchase of property and equipment                                 (1,103)         (529)
   Investments in joint ventures and European affiliate                   --        (1,053)
                                                                    --------      --------
      Net cash used in investing activities                           (6,006)         (414)
                                                                    --------      --------
 CASH FLOWS FROM FINANCING ACTIVITIES:
   Issuance of common stock for cash, net of issuance cost            29,229             6
   Payments of receivables on sale of common stock                         5            --
                                                                    --------      --------
       Net cash provided by financing activities                      29,234             6
                                                                    --------      --------
 NET INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS                 22,804        (4,414)

 CASH AND CASH EQUIVALENTS, beginning of period                        5,037        22,655
                                                                    --------      --------
 CASH AND CASH EQUIVALENTS, end of period                           $ 27,841      $ 18,241
                                                                    ========      ========

 SUPPLEMENTAL DISCLOSURES OF CASH FLOW INFORMATION:
     Cash paid during the period for-
       Interest                                                     $     --            --
       Income taxes                                                       --            --
 SUPPLEMENTAL DISCLOSURES OF NON-CASH INVESTING ACTIVITIES:
     Contribution made to L & I Partners as a reduction in
       accounts receivable                                          $     --      $    950
</TABLE>


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



                                      -6-
<PAGE>   7

                               ILEX ONCOLOGY, INC.
            NOTES TO THE CONSOLIDATED CONDENSED FINANCIAL STATEMENTS
                                   (Unaudited)
                                 March 31, 1998

                (Amounts in Thousands, Except Share Information,
                Per Share Information or As Otherwise Indicated)

1.   PRINCIPLES OF CONSOLIDATION AND BASIS OF PRESENTATION:

The accompanying interim consolidated condensed financial statements presented
herein include the accounts of ILEX Oncology, Inc. and its wholly-owned
subsidiaries("the Company"). All significant intercompany transactions and
accounts have been eliminated in consolidation. These interim consolidated
condensed financial statements have been prepared by the Company, without audit,
pursuant to the rules and regulations of the Securities and Exchange Commission.
Certain information and footnote disclosures normally included in financial
statements prepared in accordance with generally accepted accounting principles
have been condensed or omitted pursuant to such rules and regulations. In
management's opinion, all adjustments, which are necessary for a fair
presentation of financial position and results of operations have been made. It
is recommended that these interim consolidated condensed financial statements be
read in conjunction with the financial statements and notes thereto included in
the Company's Annual Report on Form 10-K for the year ended December 31, 1997.
The results of operations for any interim period are not necessarily indicative
of the results of operations for the entire year. Certain prior period amounts
have been reclassified to conform to the current period presentation.

2.   SIGNIFICANT ACCOUNTING POLICIES:

In February 1997, Statement of Financial Accounting Standards No. 128, "Earnings
Per Share" ("FAS128"), was issued. In accordance with FAS 128, basic net loss
per share was computed by dividing net loss by the weighted average number of
shares of common stock outstanding during the period. Diluted net loss per share
is equal to basic net loss per share as the effect of all common stock
equivalents is antidilutive.

3. INVESTMENTS IN JOINT VENTURES:

In May 1997, the Company entered into an agreement with LeukoSite, Inc.
("LeukoSite"), for an equally owned joint venture, L&I Partners, L.P. ("L&I"),
for research collaboration endeavors. During the three months ended March 31,
1998, the Company provided funding of $1,050 in cash and $950 by contributing
accounts receivable from L&I. The following is summarized information for L&I as
of and for the three months ended March 31, 1998:



                                      -7-
<PAGE>   8

     Summarized Income Statement Information

                Revenue                   $    --
                Operating expenses          2,556
                Operating loss             (2,556)
                Net loss                   (2,551)

     Summarized Balance Sheet Information

                Assets                        651
                Liabilities                 3,249
                Partners' equity           (2,598)

4.   COMMITMENTS & CONTINGENCIES:

In March 1998, the Company entered into an agreement with The Burnham Institute
to license a compound for development by the Company. The agreement called for
an initial payment of $250 and a warrant to purchase 590,113 shares of the
Company's common stock. Using a pricing model, the value of the warrant was
determined to be $3.1 million. The agreement also requires subsequent payments
to The Burnham Institute at the attainment of various milestones. The first of
these milestones is expected to be reached in the fourth quarter of 1998.

5.   SEGMENT INFORMATION:

The Company has two reportable segments: services and products. The services
segment provides contract research services for the development, manufacturing,
and regulatory approval of oncology compounds. The products segment is involved
in the development of proprietary compounds for the treatment of cancer. The
Company's reportable segments are strategic business units which are managed
separately because each business requires different technology and marketing
strategies.

The accounting policies of the segments are the same as those of the Company.
The Company evaluates performance based on the profit or loss from operations
before income taxes.

The Company accounts for intersegment revenues at the cost of providing the
services, including general and administrative expenses.



                                      -8-
<PAGE>   9

                          SELECTED SEGMENT INFORMATION

<TABLE>
<CAPTION>
                                               For the three months ended                  For the three months ended 
                                                    March 31, 1997                                March 31, 1998
                                          ------------------------------------         ------------------------------------
                                          Services       Products        Total         Services       Products        Total
                                          --------       --------        -----         --------       --------        -----
<S>                                       <C>            <C>            <C>            <C>            <C>            <C>    
 Revenues from external customers         $ 1,212        $ 1,371        $ 2,583        $ 2,128        $   811        $ 2,939
 Intersegment revenues                      1,564             --          1,564          2,034             --          2,034
 Direct cost                                1,096             --          1,096          1,605             --          1,605
 Segment Operating loss                      (183)          (392)          (575)          (269)        (5,267)        (5,536)
 Equity in losses in joint ventures
    and European affiliate                     --           (104)          (104)            55         (1,456)        (1,401)
 Segment loss                                (183)          (496)          (679)          (214)        (6,723)        (6,937)
</TABLE>


                      Reconciliation of Segment Information
                        To Consolidated Condensed Totals

<TABLE>
<CAPTION>
                                                       Three months         Three months 
                                                       ended March 31,      ended March 31, 
                                                           1997                  1998
                                                       ---------------      ---------------
<S>                                                       <C>                  <C>     
 OPERATING LOSS:
   Reportable segment operating loss                      $(575)               $(5,536)
   Unallocated general and administrative expense          (201)                  (575)
                                                          -----                -------
 Consolidated operating loss                              $(776)               $(6,111)
                                                          =====                =======

 NET LOSS:
   Reportable segment net loss                            $(679)               $(6,937)
   Unallocated general and administrative expense          (201)                  (575)
   Interest income                                          412                    567
                                                          -----                -------
 Consolidated net loss                                    $(468)               $(6,945)
                                                          =====                =======
</TABLE>



                                      -9-
<PAGE>   10

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

FORWARD-LOOKING STATEMENTS - CAUTIONARY STATEMENTS

         Certain statements contained in this Quarterly Report on Form 10-Q,
including statements regarding the anticipated development and expansion of the
Company's business, expenditures, the intent, belief or current expectations of
the Company, its directors or its officers, primarily with respect to the future
operating performance of the Company and other statements contained herein
regarding matters that are not historical fact, are "forward-looking statements"
(as such term is defined in the Private Securities Litigation Reform Act of
1995). Because such statements include risks and uncertainties, actual results
may differ materially from those expressed or implied by such forward-looking
statements. Factors that could cause actual results to differ materially from
those expressed or implied by such forward-looking statements include, but are
not limited to, those discussed in other filings including those contained in
the Company's Registration Statement on Form S-1 (File No. 333-17769), the
Company's Annual Report on Form 10-K for the year ended December 31, 1997, and
in other reports filed with the Securities and Exchange Commission. The Company
does not intend to update these forward-looking statements.

GENERAL

         The Company is engaged in the businesses of (i) acquiring rights to
(generally in exchange for the payment of licensing fees and future royalty
payments), and developing for commercialization, drugs for the treatment of
patients with cancer and for the prevention of cancer and (ii) providing
clinical research, development and manufacturing services on a contract basis to
pharmaceutical and biotechnology companies engaged in the development of
oncology products.

         During the first quarter of 1998, the Company announced the acquisition
of a license for the compound THP-Dox from The Burnham Institute.

         The Company has no products available for sale and does not expect to
have any products resulting from its drug development efforts, including its
collaborations with others, commercially available for several years, if at all.
The Company has incurred losses and expects to incur additional losses for the
foreseeable future as the Company continues to invest in research and
development. The Company's revenue for the foreseeable future will be limited to
development funding under its collaborative relationships, fee-for-service
revenues pursuant to contracts with its Contract Research Organization ("CRO")
clients, interest income and other miscellaneous income.

         The following is a discussion of the financial condition and results of
operations for the Company for the three-month periods ended March 31, 1998 and
1997. It should be read in conjunction with the Interim Consolidated Condensed
Financial Statements of the Company, the Notes thereto and other financial
information included elsewhere in this report.



                                      -10-
<PAGE>   11

RESULTS OF OPERATIONS

         THREE MONTHS ENDED MARCH 31, 1998 COMPARED TO THREE MONTHS ENDED 
MARCH 31, 1997

Operating Revenues

         Total revenue increased from approximately $2.6 million in the first
quarter of 1997 to $2.9 million in the first quarter of 1998. The increase of
approximately $0.3 million, or 12%, was due to an additional $900,000 of
contract research revenues offset by a reduction of $560,000 in product
development revenues. The reduction in product development revenues to
approximately $800,000 compares to $1.4 million in the first quarter of 1997.
The decrease reflects the elimination of revenue from the development of
crisnatol and mitoguazone, which was partially offset by the addition of
CAMPATH-1H and an increase in the development funding for piritrexim. The $0.9
million, or 75%, increase in contract research services revenues to $2.1
million, compared to approximately $1.2 million in first quarter 1997, reflects
an increase in both the number of contracts underway as well as in the size and
complexity of the contract research projects.

Operating Expenses

         Total Operating Expenses. Total operating expenses increased from
approximately $3.4 million in the first quarter of 1997 to $9.0 million in the
first quarter of 1998. This increase of approximately $5.6 million includes a
one-time, non-cash expense of $3.1 million for the value of a warrant to
purchase shares of common stock of the Company issued to The Burnham Institute
in exchange for the licensing of THP-Dox. The remaining increase of $2.5
million, or 74%, reflects increases in research and development costs, selling,
general, and administrative costs, and direct costs.

         Research and Development Costs. Research and development costs
increased from approximately $1.6 million in the first quarter of 1997 to $2.0
million in the first quarter of 1998. This increase of $0.4 million, or 25%, was
primarily attributable to increased spending for the development of CAMPATH-1H,
piritrexim, and ILX23-7553 (Vitamin D3 analogue).

         Selling, General and Administrative Costs. Selling, general and
administrative costs increased from approximately $700,000 in the first quarter
of 1997 to $1.7 million in the first quarter 1998. This increase of $1.0
million, or 143%, is primarily attributable to increases in rental expense,
business development activities, legal costs and compensation related to
additional administrative staff.

         Direct Costs. Direct costs increased from $1.1 million in the first
quarter of 1997 to $1.6 million in the first quarter of 1998. This increase of
$0.5 million, or 45%, is primarily attributable to increases in expenditures
required to support growth in the number and size of contract research
contracts.

         Licensing Fees. Licensing fees for the first quarter of 1998 of $3.4
million relate to the acquisition of a license for THP-Dox from The Burnham
Institute. Payment of the fee was $250,000 in cash and the issuance to The
Burnham Institute of a warrant to purchase 590,113 shares of the Company's
common stock, which was valued at $3.1 million using a pricing model. No
licensing fees were incurred in the first quarter of 1997.


                                      -11-
<PAGE>   12

         PRN Amortization. Amortization of the cost of the 312,188 shares of
common stock issued to Physician Reliance Network, Inc. in connection with the
July 1997 strategic alliance agreement was $269,000 in the first quarter of
1998. This cost is recorded as an intangible asset and is being amortized over a
five-year period.

Operating Loss

         The loss from operations increased from ($0.8 million) in the first
quarter of 1997 to ($6.1 million) in the first quarter of 1998. This increase of
($5.3 million) includes a one-time, non-cash charge for the value of a warrant
to purchase shares of common stock of the Company issued to The Burnham
Institute for payment, in part, of a licensing fee for the compound THP-Dox, in
the amount of $3.1 million. Additionally, spending on ILEX's portfolio products,
not reimbursed by partners, increased by $1.0 million.

Equity in Loss of Joint Ventures and European Affiliate

         Equity in losses of joint ventures and European affiliate increased
from ($104,000) in the first quarter of 1997 to ($1.4 million) in the first
quarter 1998. The increase of $1.3 million relates to increased development
costs for CAMPATH-1H and piritrexim, which are being developed by the Company's
joint ventures with LeukoSite Inc. and MPI, L.L.C., respectively. Additionally,
significant expense was incurred by L & I Partners, LP., the Company's joint
venture with LeukoSite, Inc., for manufacturing of clinical supplies of
CAMPATH-1H. These losses were partially offset by income from ILEX's European
affiliate, PFK-ILEX, of $55,000.

Net Interest Income

         Net interest income increased from approximately $412,000 in the first
quarter of 1997 to $567,000 in the first quarter of 1998. This increase of
$155,000, or 38%, is attributable to an increase in average balances of cash,
cash equivalents and investments in marketable securities resulting from
proceeds received from ILEX's initial public offering completed in February
1997.

Net Loss

         The net loss increased ($6.4 million) from ($468,000) in the first 
quarter of 1997 to ($6.9 million) in the first quarter of 1998.

Net Loss Per Share

         The net loss per share increased ($.53) from ($.04) in the first
quarter of 1997 to ($.57) in the first quarter of 1998.

SEASONALITY

         ILEX expects that results of operations in the future will fluctuate
significantly from period to period. Such fluctuations may result from numerous
factors, including the amount and timing of revenues earned under existing or
future collaborative relationships or joint ventures, if any, technological
advances and determinations as to the commercial potential of compounds, the
progress of the Company's drug development programs, the receipt of regulatory
approvals, acquisitions, the timing of start-up 



                                      -12-
<PAGE>   13

expenses for new facilities, changes in the Company's mix of services, the cost
of preparing, filing, prosecuting, maintaining, defending and enforcing patent
claims and other intellectual property rights, the status of competing products
and technologies and the timing and availability of financing for the Company,
including existing or future strategic alliances and joint ventures with third
parties. In addition, with respect to the Company's contract research services
revenues, fluctuations may result due to a number of factors, including the
commencement, completion or cancellation of large contracts and progress of
ongoing contracts. ILEX believes that comparisons of its quarterly and annual
historical results may not be meaningful and should not be relied upon as an
indication of future performance.

INCOME TAXES

     The availability of net operating loss carryforwards to reduce U.S. federal
taxable income is subject to various limitations under the Internal Revenue Code
of 1986 (the "Code"), as amended, in the event of an ownership change as defined
in Section 382 of the Code. As of December 31, 1997, the Company had incurred at
least a 31 percent ownership change during the applicable three-year period. The
Company does not believe that this change in ownership significantly impacts the
Company's ability to utilize its net operating loss and tax credit carryforwards
as of December 31, 1997, because the amount of the annual limitation under the
Code of such carryforwards is in excess of the total amount of net operating
loss and tax credit carryforwards. There was no material ownership change during
the three-month period ended March 31, 1998.

LIQUIDITY AND CAPITAL RESOURCES

         ILEX has financed its operations primarily through the sale of its
capital stock, through development and licensing fee revenues provided by its
partners under its collaborative agreements and through fee-for-service or
participatory revenues pursuant to contracts with its CRO clients. The Company
receives payments under collaborative agreements primarily in the form of
development funding, milestone payments if milestones are achieved, and
royalties if products are commercialized.

         To date, the majority of the Company's expenditures have been for
research and development activities. The Company does not expect to receive
royalties or other revenues based upon net sales of drugs that may be developed
for a significant number of years, if at all. ILEX expects research and
development expenses to be significant for the next several years as its
development programs progress. As of March 31, 1998, the Company had cash, cash
equivalents and investments in marketable securities of approximately $37.1
million and working capital of approximately $32.6 million. The Company believes
that such amounts will be used primarily to support continued research and
development of its compounds, expand its CRO services business, for general and
administrative expenses and for other general corporate purposes.

         As of March 31, 1998, the Company had no material commitments for
capital expenditures.

         ILEX's future expenditures and capital requirements will depend on
numerous factors, including without limitation, the progress of its research and
development programs, the progress of its preclinical and clinical testing, the
magnitude and scope of these activities, the time and costs involved in
obtaining regulatory approvals, the cost of filing, prosecuting, defending and
enforcing any patent claims and other intellectual property 



                                      -13-
<PAGE>   14

rights, competing technological and market developments, changes in or
termination of existing collaborative arrangements, the ability of the Company
to establish, maintain and avoid termination of collaborative arrangements and
the purchase of capital equipment and acquisitions of compounds, technologies or
businesses. The Company's cash requirements are expected to increase each year
as the Company expands its activities and operations. There can be no assurance
that the Company will ever be able to generate product revenue or achieve or
sustain profitability.

YEAR 2000 COMPLIANCE

         The efficient operation of the Company's business is dependent on its
computer software programs and operating systems (collectively, "Programs and
Systems"). These Programs and Systems are used in several key areas of the
Company's business, including information management services and financial
reporting, as well as in various administrative functions. The Company has been
evaluating its Programs and Systems to identify potential year 2000 compliance
problems, as well as manual processes, external interfaces with customers, and
services supplied by vendors to coordinate year 2000 compliance and conversion.
The year 2000 problem refers to the limitations of the programming code in
certain existing software programs to recognize date sensitive information for
the year 2000 and beyond. Unless modified prior to the year 2000, such systems
may not properly recognize such information and could generate erroneous data or
cause a system to fail to operate properly.

         Based on current information, the Company expects to attain year 2000
compliance and institute appropriate testing of its modifications and
replacements in a timely fashion and in advance of the year 2000 date change. It
is anticipated that modification or replacement of the Company's Programs and
Systems will be performed in-house by company personnel. The Company believes
that, with modifications to existing software and conversions to new software,
the year 2000 problem will not pose a significant operational problem for the
Company. However, because most computer systems are, by their very nature,
interdependent, it is possible that non-compliant third party computers may not
interface properly with the Company's computer systems. The Company could be
adversely affected by the year 2000 problem if it or unrelated parties fail to
successfully address this issue. Management of the Company currently anticipates
that the expenses and capital expenditures associated with its year 2000
compliance project will not have a material effect on its financial position or
results of operations.



                                      -14-
<PAGE>   15

                           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: Not Applicable

Item 6.  Exhibits and Reports on Form 8-K

         (a)  Exhibit 10.1*:   Drug Development and Commercialization  
                               Agreement by and between The Burnham Institute
                               and Ilex Oncology, Inc. dated March 27, 1998#
              Exhibit 11.1*:   Computation of Net Loss Per Share
              Exhibit 27.1*:   Financial Data Schedule

              *Filed herewith
                  #Confidential treatment has been requested with respect to 
              certain portions of this Exhibit. Omitted portions have been 
              filed separately with the Securities and Exchange Commission

         (b)  Reports on Form 8-K: Not Applicable




                                      -15-
<PAGE>   16

                                   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.


                                             ILEX ONCOLOGY, INC.
                                             (Registrant)



Dated:   May 14, 1998                       By: /s/ Richard L. Love
                                                -------------------------------
                                                Richard L. Love
                                                President and Chief Executive
                                                Officer
                                                (Principal Executive Officer)



Dated:   May 14, 1998                       By: /s/ James R. Koch
                                                -------------------------------
                                                James R. Koch
                                                Vice President and Chief 
                                                Financial Officer
                                                (Principal Financial and
                                                Accounting Officer)



                                      -16-
<PAGE>   17
                               INDEX TO EXHIBITS

EXHIBIT 
NUMBER         DESCRIPTION
------         -----------

 10.1*         Drug Development and Commercialization Agreement by and between
               The Burnham Institute and Ilex Oncology, Inc. dated 
               March 27, 1998#

 11.1*         Computation of Net Loss Per Share

 27.1*:        Financial Data Schedule



 * Filed herewith

 # Confidential treatment has been requested with respect to certain portions 
   of this Exhibit. Omitted portions have been filed separately with the 
   Securities and Exchange Commission