<PAGE>   1
                                                                   EXHIBIT 10.3


                            STOCK PURCHASE AGREEMENT

         THIS STOCK PURCHASE AGREEMENT ("Agreement") is entered into as of the
16th day of July, 1999, by and between ILEX Oncology, Inc., a Delaware
corporation, (the "Company"), and each of the Investors listed on the Schedule
of Investors attached hereto as Schedule A (collectively, the "Investors" and
individually, each an "Investor").


                                    ARTICLE I
                           PURCHASE AND SALE OF SHARES

         1.1 Purchase and Sale. Subject to the terms and conditions hereof, the
Investors agree to purchase from the Company, and the Company agrees to issue
and sell to the Investors, an aggregate number of shares of the Company's common
stock, $.01 par value, equal to the quotient obtained by dividing (x)
$20,000,000 by (y) 85% of the Market Price (the "Shares") for an aggregate
purchase price of twenty million dollars ($20,000,000) (the "Purchase Price").
The number of Shares to be sold by the Company to each Investor and the
aggregate consideration to be received by the Company from each Investor is set
forth opposite Investor's name on the Schedule of Investors attached hereto.
"Market Price" shall mean the average of the closing bid and asked prices of a
share of Common Stock for the 30 consecutive trading days immediately prior to
the Closing Date.

         1.2 The Closing. The closing ("Closing") of the purchase and sale of
the Shares shall take place in such manner as the parties may mutually agree.
The date of the Closing is hereinafter referred to as the "Closing Date." At the
Closing, the Company shall deliver stock certificates representing the Shares in
such denomination and registered in the name of each Investor as set forth on
the Schedule of Investors upon delivery to the Company by each Investor of the
aggregate amount of the purchase price of the Shares to be purchased by such
Investor as set forth on the Schedule of Investors in United States dollars in
immediately available funds by wire transfer to an account designated prior to
the Closing Date in writing by the Company for such purpose.


                                   ARTICLE II
                         REPRESENTATIONS OF THE COMPANY


         The Company represents and warrants to the Investors as follows:

         2.1 Organization, Good Standing and Qualification. The Company: (a) is
a corporation duly organized, validly existing and in good standing under the
laws of the State of Delaware; (b) has all requisite corporate power and
authority to own and operate its properties and assets and to carry on its
business as it is presently being conducted and as proposed to be conducted; and
(c) is qualified and is in good standing as a foreign corporation in all other
jurisdictions in which the failure so to qualify would have a material adverse
effect on its business or properties.

         2.2 Capitalization. Immediately prior to the Closing, the authorized
capital of the Company consists of 60,000,000 shares of Common Stock, of which
12,979,678 shares were issued

<PAGE>   2

and outstanding on July 15, 1999, all of which have been validly issued, and are
fully paid and non-assessable, and 20,000,000 shares of Preferred Stock, none of
which were issued and outstanding on the date hereof.

         2.3 Authorization. All corporate action on the part of the Company and
its officers, directors and shareholders necessary for the authorization,
execution and delivery of this Agreement, the performance of all obligations of
the Company hereunder and the authorization, issuance and delivery of the Shares
has been taken or will be taken on or prior to the Closing, and this Agreement
constitutes a valid and legally binding obligation of the Company.

         2.4 Valid Issuance of Shares. When issued in accordance with the terms
of this Agreement, the Shares shall be duly and validly authorized and issued
(including, without limitation, issued in compliance with applicable federal and
state securities laws), fully paid and non-assessable and not subject to any
preemptive rights, liens, claims or encumbrances, or other restriction on
transfer. Furthermore, the certificates representing the Shares will be in due
and proper form and have been duly and validly executed by the officers of the
Company named thereon.

         2.5 Governmental Consents. All consents, approvals, orders,
authorizations, registrations, qualifications, designations, declarations or
filings of or with any federal, state or local governmental authority on the
part of the Company required in connection with the consummation of the
transactions contemplated herein have been or shall be obtained prior to the
Closing and shall be effective as of the Closing.

         2.6 Litigation. There are no actions, suits, proceedings or
investigations pending or, to the best of the Company's knowledge and belief,
any basis therefor or threat thereof, against or affecting the Company which
question the validity of this Agreement or the right of the Company to enter
into it, or to consummate the transactions contemplated hereby, or which might
result, either individually or in the aggregate, in any material adverse change
in the business, prospects, conditions, affairs or operations of the Company or
in any of the properties or assets, or in any material impairment of the right
or ability of the Company to carry on its business as now conducted or as
proposed to be conducted. The foregoing includes, without limitation, actions
pending or threatened (or any basis therefor known to the Company) involving the
prior employment of any of the Company's employees, use in connection with the
Company's business of any information or techniques allegedly proprietary to any
former employers of the Company's employees, or obligations of the Company's
employees under any agreements with their prior employers. The Company is not a
party or subject to the provisions of any order, writ, injunction, judgment or
decree of any court or governmental agency or instrumentality. There is no
action, suit, proceeding or investigation by the Company currently pending or
which the Company intends to initiate.

         2.7 No Conflict With Other Instruments. The Company is not in violation
or default of any provisions of its Amended and Restated Certificate of
Incorporation or Bylaws, as amended, or of any instrument, judgment, order,
writ, decree or contract to which it is a party or by which it is bound or, to
its knowledge, of any provision of federal or state statute, rule or regulation
applicable to the Company, which violation or default would be materially
adverse to the Company. The execution, delivery and performance of this
Agreement will not result in any violation of, be in conflict with, or
constitute a default under, with or without the passage of time or the giving of


                                      -2-
<PAGE>   3

notice: (a) any provision of the Company's Certificate of Incorporation or
Bylaws; (b) any provision of any judgment, decree or order to which the Company
is a party or by which it is bound; (c) any material contract, obligation or
commitment to which the Company is a party or by which it is bound; or (d) to
the Company's knowledge, any statute, rule or governmental regulation applicable
to the Company.

         2.8 Securities and Financial Statement Matters. Company has duly filed
in a timely manner (without any permitted extension) all reports (the "SEC
Reports") required to be filed by Company with the Securities and Exchange
Commission (the "SEC") under the Securities Exchange Act of 1934, as amended
(the "1934 Act"). The SEC Reports (including, in each case, without limiting the
generality thereof, the audited and unaudited financial statements of Company
included therein) when filed contained all statements required to be stated
therein in accordance with the 1934 Act and did not contain any untrue statement
of material fact or omit to state a material fact necessary to make any of the
statements contained therein not misleading in light of the circumstances under
which they were made and otherwise complied in all material respects with the
applicable requirements of the 1934 Act. The consolidated financial statements
included in the SEC Reports comply as to form with the requirements of
Regulation S-X, as promulgated by the SEC under the Securities Act of 1933, as
amended (the "1933 Act"), and are derived from the applicable books and records
of Company, have been prepared in conformity with generally accepted accounting
principles (as required by Regulation S-X) and present fairly the financial
condition, results of operations, changes in security holders' equity and cash
flows of Company on a consolidated basis, as at the close of business, or for
the period ended, on the date of each of such financial statements.

         2.9 Absence of Certain Changes or Events. Except as disclosed in the
financial statements referred to in Section 2.8, the Company's Annual Report on
Form 10-K for the year ended December 31, 1998 and the Company's Quarterly
Report on Form 10-Q for the quarter ended March 31, 1999, or as otherwise
disclosed in Section 2.9 of the Disclosure Schedule attached hereto, since March
31, 1999, neither Company nor any of its subsidiaries or affiliates has incurred
any liabilities or obligations, direct or contingent, or entered into any
transactions, not in the ordinary course of business, that are material to
Company and its subsidiaries and affiliates, taken as a whole, and there has not
been (i) any material change in the capital stock of the Company or its
subsidiaries that would have a Material Adverse Effect (as defined below) or
(ii) any event, change or occurrence which individually or in the aggregate
might (x) have a material adverse effect on the condition (financial or other),
assets, business, or results of operations of Company, taken as a whole, (y)
materially adversely affect Company's ability to consummate any of the
transactions contemplated hereby or to perform its obligations under this
Agreement or (each of (x) and (y) being referred to herein, individually or in
the aggregate as a "Material Adverse Effect"). No event has occurred since March
31, 1999, with respect to which Company would be required to file a Current
Report on Form 8-K under the 1934 Act.

         2.10 Corporate Documents. The Amended and Restated Certificate of
Incorporation and Bylaws, as amended, of the Company are in the form previously
provided to each Investor.

         2.11 Registration Rights. Except as provided in Section 2.11 of the
Disclosure Schedule, the Company is under no contractual obligation to register
(now or in the future, whether contingent


                                      -3-
<PAGE>   4

or not) under the 1933 Act any of its presently outstanding securities or any of
its securities that may subsequently be issued.

         2.12 Brokers and Finders. The Company has not retained any investment
banker, broker, finder, consultant or intermediary and is not obligated to any
such person for any fee, in connection with the transactions contemplated by
this Agreement.

         2.13 SEC Documents. The Company has provided to each Investor its
Annual Report on Form 10-K for the year ended December 31, 1998, its Quarterly
Report on Form 10-Q for the quarter ended March 31, 1999, and its proxy
statement with respect to the Annual Meeting of Stockholders held on May 26,
1999.

         2.14 Investment Company Act. The Company is not an "investment company"
or a company controlled by an "investment company" as such terms are defined in
the Investment Company Act of 1940, as amended.

         2.15 Compliance with Law. The business of the Company is not being
conducted in violation of any material law, ordinance or regulation of any
governmental entity (including, without limitation, those relating to
environmental protection and occupational safety and health practices). All
material governmental approvals, permits and licenses required to conduct the
current business of the Company have been obtained and are in full force and
effect and are being complied with in all material respects.

         2.16 Form S-3. The Company is a registrant qualified and entitled to
use a registration statement on Form S-3.


                                   ARTICLE III
                        REPRESENTATIONS OF EACH INVESTOR

         Each Investor represents and warrants to the Company as follows:

         3.1 Authorization. The Investor has full power and authority to enter
into this Agreement. This Agreement constitutes a valid and legally binding
obligation of each Investor.

         3.2 Brokers and Finders. No Investor has retained any investment
banker, broker, finder, consultant or intermediary and is not obligated to any
such person for any fee, in connection with the transactions contemplated by
this Agreement.


                                   ARTICLE IV
                                 SECURITIES LAWS


         4.1 Securities Laws Representations and Covenants of the Investors.
Each Investor represents, warrants and covenants to the Company as follows:


                                      -4-
<PAGE>   5

             (a) Purchase Entirely for Own Account. The Shares are being
acquired for investment for each Investor's own account, not as a nominee or
agent, and not with a view to the resale or distribution of any part thereof,
and no Investor has any present intention of selling, granting any participation
in, or otherwise distributing the same. No Investor has any contract,
undertaking, agreement or arrangement with any person to sell, transfer or grant
participation to such person or to any third person, with respect to any of the
Shares. No Investor was organized solely for the purpose of acquiring the
Shares.

             (b) Disclosure of Information. Each Investor believes it has
received all information it considers necessary or appropriate for deciding
whether to purchase the Shares. Each Investor has had an opportunity to ask
questions and receive answers from the Company regarding the terms and
conditions of the offering of the Shares.

             (c) Investment Experience. Each Investor has previously invested in
companies in the development stage, can bear the economic risks of the
investment and has such knowledge and experience in financial or business
matters that it is capable of evaluating the merits and risks of its investment
in the Shares.

             (d) Accredited Investor. Each Investor is an accredited investor as
defined in Rule 501(a) of Regulation D, as amended, of the SEC under the 1933
Act.

             (e) Restricted Securities. Each Investor understands that the
Shares it is purchasing pursuant to this Agreement are characterized as
"restricted securities" under the federal securities laws inasmuch as they are
being acquired from the Company in a transaction not involving a public offering
and that under such laws and applicable regulations the Shares may be resold
without registration under the 1933 Act only in certain limited circumstances.
In this connection, each Investor is familiar with SEC Rule 144, as presently in
effect, and understands the resale limitations imposed thereby and by the 1933
Act.

             (f) Disposition of Shares. No Investor will dispose of any of the
Shares (other than pursuant to SEC Rules 144 or 144A or any similar or analogous
rule or rules) unless and until (i) such Investor shall have notified the
Company of the proposed disposition and the circumstances surrounding the
proposed disposition and, if reasonably requested by the Company, such Investor
shall have furnished the Company with an opinion of counsel reasonably
satisfactory in form and substance to the Company to the effect that such
disposition will not require registration under the 1933 Act; or (ii) there is
in effect a registration statement under the 1933 Act covering the proposed
disposition and the proposed disposition is made in accordance with such
registration statement.

         4.2 Legends. The certificates evidencing the Shares may bear the
restrictive legend set forth below:

         THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED
         UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "ACT"), OR UNDER ANY
         APPLICABLE STATE SECURITIES LAWS. NEITHER THE SECURITIES NOR ANY
         INTEREST THEREIN MAY BE OFFERED FOR SALE, SOLD, TRANSFERRED, PLEDGED OR
         OTHERWISE DISPOSED OF EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION
         STATEMENT UNDER


                                      -5-
<PAGE>   6

         THE ACT AND SUCH STATE SECURITIES LAWS OR AN EXEMPTION FROM
         REGISTRATION UNDER SUCH ACT AND SUCH LAWS WHICH, IN THE OPINION OF
         COUNSEL FOR THE HOLDER, WHICH COUNSEL AND OPINION ARE REASONABLY
         SATISFACTORY TO THE COUNSEL FOR THIS CORPORATION, IS AVAILABLE.


                                    ARTICLE V
             CONDITIONS OF THE INVESTORS' OBLIGATIONS AT THE CLOSING

         The obligations of the Investors under this Agreement to purchase the
Shares from the Company are subject to the fulfillment on or before the Closing
of each of the following conditions, any of which may be waived in writing by
the Investors:

         5.1 Representations and Warranties. The representations and warranties
of the Company contained in Article II of this Agreement shall be true on and as
of the Closing with the same effect as though such representation and warranties
had been made on and as of the Closing.

         5.2 Performance. The Company shall have performed and complied with all
agreements, obligations and conditions contained in this Agreement that are
required to be performed or complied with by it on or before the Closing.

         5.3 Compliance Certificate. The Company shall have delivered to the
Investors a certificate dated as of the Closing, executed by an executive
officer of the Company and in a form reasonably acceptable to the Investor,
certifying that the conditions set forth in Sections 5.1 and 5.2 have been
satisfied and that there has been no material adverse change in the assets,
properties, prospects, condition, affairs, operations or business of the
Company, as now conducted or as proposed to be conducted, since the date of this
Agreement.

         5.4 Proceedings and Documents. All corporate and other proceedings
taken by the Company in connection with the transactions contemplated by this
Agreement and all documents incident thereto shall be reasonably satisfactory in
form and substance to the Investors, and the Investors shall have received all
such documents as it may have reasonably requested.

         5.5 Acquisition of Convergence. The Company shall have completed the
acquisition of Convergence Pharmaceuticals, Inc.

         5.6 Opinion of Counsel. The Investors shall have received an opinion
from the Company's counsel, dated as of the Closing and in a form and substance
reasonably acceptable to the Investors, to the effect that:

             (a) The Company is a corporation duly organized, validly existing
and in good standing under the laws of the State of Delaware, and the Company
has the requisite corporate power and authority to own its properties and to
conduct its business;

             (b) The Company has the corporate power and authority to execute,
deliver and perform its obligations under the terms of the Agreement. This
Agreement has been duly authorized, executed


                                      -6-
<PAGE>   7

and delivered by the Company and constitutes a legal, valid and binding
obligation of the Company enforceable against it in accordance with its terms,
except (i) as the enforceability thereof may be limited by bankruptcy,
insolvency or other laws relating to or affecting creditors' rights generally,
(ii) as rights to indemnity and contribution may be limited under applicable law
or by principles of public policy and (iii) as such enforceability may be
limited or affected by general principles of equity, whether applied by a court
of law or equity;

             (c) The execution, delivery and performance by the Company with the
terms of this Agreement do not violate any provision of the Company's
Certificate of Incorporation or By-laws and, to such counsel's knowledge, do not
conflict with or constitute a default under the provisions of any judgment,
writ, decree or order known to such counsel or any material agreement to which
the Company is a party or by which it is bound and which is filed as an exhibit
to, or incorporated by reference in, the Company's Form 10-K for the fiscal year
ended December 31, 1998, and the Company's Form 10-Q for the quarter ended March
31, 1999;

             (d) All consents, approvals, orders or authorizations of, and all
qualifications, registrations, designations, declarations, or filings with, any
federal, Delaware or Texas governmental authority required to be made prior to
the Closing in connection with the consummation of the transactions contemplated
by this Agreement have been made or obtained, and are effective, and such
counsel is not aware of any proceedings, or threat thereof, which question the
validity thereof;

             (e) Based in part upon the representations of the Investors set
forth in this Agreement, the offer and sale of the Shares pursuant to the terms
of this Agreement are exempt from the registration requirements of Section 5 of
the Securities Act;

             (f) To such counsel's knowledge, there is no action, proceeding or
investigation pending or threatened against the Company, which questions the
validity of this Agreement, or any action be taken by the Company pursuant to or
in connection with the Agreement;

             (g) The Shares have been duly authorized and, when issued in
compliance with this Agreement, will be fully paid and non-assessable and will
be free of any liens or encumbrances created by the Company; and

             (h) There are no preemptive rights with respect to the issuance and
sale of the Shares and there are no restrictions on transfer of the Shares other
than those arising under federal and state securities laws.

         5.7 SBA Sideletter. The Company shall have executed the letter
agreement between the Company, Chase Venture Capital Associates, L.P. and ILEX
Chase Partners (Alto Bio), LLC attached hereto as Exhibit 5.7 regarding small
business matters (the "Small Business Sideletter").


                                      -7-
<PAGE>   8

                                   ARTICLE VI
             CONDITIONS OF THE COMPANY'S OBLIGATIONS AT THE CLOSING

         The obligations of the Company under this Agreement to issue and sell
the Shares to the Investor are subject to the fulfillment on or before the
Closing of each of the following conditions, any of which may be waived in
writing by the Company:

         6.1 Representations and Warranties. The representation and warranties
of each Investor contained in Article III and Article IV of this Agreement shall
be true on and as of the Closing with the same effect as though such
representations and warranties had been made on and as of the Closing.

         6.2 Payment of Purchase Price. The Investors shall at the Closing pay
the Purchase Price upon delivery by the Company of a certificate representing
the Shares.


                                   ARTICLE VII
                      POST-CLOSING COVENANTS OF THE COMPANY

         With a view to making available to the Investors the benefits of SEC
Rule 144 and any other rule or regulation of the SEC that may at any time permit
the Investors to sell securities of the Company to the public without
registration, the Company agrees to use best efforts to file with the SEC in a
timely manner all reports and other documents required of the Company under the
1933 Act and the 1934 Act.


                                  ARTICLE VIII
                               REGISTRATION RIGHTS

         8.1 Registration Rights. As soon after Closing as is reasonably
practicable, the Company will use its best efforts to file a registration
statement on Form S-3 (or any successor to Form S-3) (or other appropriate
registration statement) with the SEC and such applications or other filings as
required under applicable state securities or blue sky laws sufficient to permit
the public offering of the Shares to be made on a continuous basis pursuant to
Rule 415 under the 1933 Act, and shall use its best efforts to cause such
registration statement to be declared effective so that the Shares will be
registered for the offering on such Form. Notwithstanding the foregoing, the
Company shall not be obligated to effect a registration (i) in any particular
jurisdiction in which the Company would be required to execute a general consent
to service of process in effecting such registration, qualification or
compliance unless the Company is already subject to service in such jurisdiction
and except as may be required by the 1933 Act; or (ii) if the Company shall
furnish to the Investors a certificate signed by the President of the Company
stating that in the good faith judgment of the Board of Directors of the Company
the filing of a registration statement would require the disclosure of material
information that the Company has a bona fide business purpose for preserving as
confidential and that is not then otherwise required to be disclosed, then the
Company's obligation to use its best efforts to file a registration statement
shall be deferred for a period not to exceed 180 days from the date of such
notice.


                                      -8-
<PAGE>   9

         8.2 Registration Procedures and Expenses. As provided in Section 8.1
hereof, the Company shall, as expeditiously as is reasonably practicable, do
each of the following:

             (a) prepare and file with the SEC a registration statement with
respect to the Shares and, subject to the limitations under Section 8.1 hereof,
use its best efforts to cause such registration statement to become effective
and remain effective for two years as provided herein;

             (b) cooperate with the Investors and any underwriter who shall sell
the Shares in connection with their review of the Company made in connection
with such registration;

             (c) prepare and file with the SEC such amendments and supplements
to such registration statement and the prospectus used in connection therewith
as may be necessary to keep such registration statement effective until the
earlier to occur of the sale of all of the Shares by the Investors or the second
anniversary of the effectiveness of the registration statement, and to comply
with the provisions of the 1933 Act and the 1934 Act, with respect to the
disposition of all the Shares covered by such registration statement for such
period;

             (d) furnish to the Investors such number of copies of the
prospectus forming a part of such registration statement (including each
preliminary prospectus), in conformity with the requirements of the 1933 Act,
and such other documents as the Investors may reasonably request in order to
facilitate the disposition of the Shares; and

             (e) notify the Investors, at any time when a prospectus relating to
the Shares is required to be delivered under the 1933 Act, of the happening of
any event as a result of which the prospectus forming a part of such
registration statement, as then in effect, includes an untrue statement of a
material fact or omits to state any material fact required to be stated therein
or necessary to make the statements therein not misleading in the light of the
circumstances then existing, prepare and furnish to the Investor a reasonable
number of copies of any supplement to or any amendment of such prospectus that
may be necessary so that, as thereafter delivered to the purchasers of the
Shares, such prospectus shall not include any untrue statement of a material
fact or omit to state a material fact required to be stated therein or necessary
to make the statements therein not misleading in light of the circumstances then
existing.

         8.3 Agreement by each Investor. In the event that each Investor
participates, pursuant to this Article 8, in the offering of the Shares, such
Investor shall:

             (a) furnish the Company all material information reasonably
requested by the Company concerning the Investor and the proposed method of sale
or other disposition of the Shares and such other information and undertakings
as shall be reasonably required in connection with the preparation and filing of
the registration statement covering the Shares in order to ensure full
compliance with the 1933 Act and the rules and regulations of the SEC
thereunder;

             (b) cooperate in good faith with the Company and its underwriters,
if any, in connection with such registration, including placing the Shares in
escrow or custody to facilitate the sale and distribution thereof, provided that
such escrow or custody arrangement shall be no more


                                      -9-
<PAGE>   10

restrictive upon the Investors than upon any other holder of stock of the
Company for the benefit of whom such registration is undertaken; and

             (c) make no further sales or other dispositions, or offers
therefor, of the Shares under such registration statement if, during the
effectiveness of such registration statement, an intervening event should occur
which, in the opinion of counsel to the Company, makes the prospectus included
in such registration statement no longer comply with the 1933 Act, so long as
written notice containing the facts and legal conclusions relied upon by the
Company in this regard has been received by each Investor from the Company,
until such time as each Investor has received from the Company copies of a new,
amended or supplemented prospectus complying with the 1933 Act, which prospectus
shall be delivered to the Investors by the Company as soon as practicable after
such notice.

         8.4 Allocation of Expenses. The Company shall pay the costs and
expenses in connection therewith, other than the attorneys' fees of the
Investors; provided, however, that the Investors shall pay all underwriting
discounts, selling commissions and stock transfer taxes attributable to the
Shares under such registration statement.

         8.5 Indemnification.

             (a) Upon the registration of any of the Shares under the 1933 Act
pursuant to Article 8 hereof, each of the Investors registering such shares,
severally and not jointly, shall indemnify and hold harmless the Company, each
director and officer of the Company, each underwriter and any person who
controls the Company or such underwriter within the meaning of Section 5 of the
1933 Act, and the Company's accountants and legal counsel, against all expenses,
claims, losses, damages and liabilities (or actions or proceedings in respect
thereof) including any of the foregoing incurred in settlement of any commenced
or threatened litigation, arising out of or based upon any untrue statement (or
alleged untrue statement) of any material fact, or omission (or alleged
omission) of any material fact required to be stated therein or necessary to
make the statements therein, in light of the circumstances in which they were
made, not misleading contained in any such registration statement, preliminary
prospectus or final prospectus, offering circular or other document, or any
amendment or supplement thereto, incident to any such registration qualification
or compliance, if such statement or omission was made in reliance upon and in
conformity with information furnished in writing to the Company or its
underwriter by or on behalf of such Investor specifically for use therein.

             (b) The Company will indemnify each Investor, with respect to which
registration, qualification or compliance has been effected pursuant to this
Agreement, and each underwriter, if any, and each person who controls any
underwriter within the meaning of Section 5 of the 1933 Act, against all
expenses, claims, losses, damages and liabilities (or actions or proceedings in
respect thereof), including any of the foregoing incurred in settlement of any
commenced or threatened litigation, arising out of or based upon any untrue
statement (or alleged untrue statement) of a material fact contained in any
registration statement, prospectus, offering circular or other document, or any
amendment or supplement thereof, incident to any such registration,
qualification or compliance, or arising out of or based upon any omission (or
alleged omission) to state therein a material fact required to be stated therein
or necessary to make the statements therein, in the light of


                                      -10-
<PAGE>   11

the circumstances in which they were made, not misleading, provided that the
Company will not be liable to indemnify such Investor(s) or a underwriter in any
such case to the extent that any such claim, loss, damage, liability or expense
arises out of or is based on any untrue statement or omission or alleged untrue
statement or omission, made in reliance upon and in conformity with information
furnished in writing to the Company by or on behalf of a Investor or a
underwriter specifically for use therein.

             (c) Each party entitled to indemnification under this Section 8.5
(the "Indemnified Party") shall give notice to the party required to provide
indemnification (the "Indemnifying Party") promptly after such Indemnified Party
has actual knowledge of any claim as to which indemnity may be sought, and shall
permit the Indemnifying Party to assume the defense of any such claim or any
litigation resulting therefrom, provided that counsel for the Indemnifying
Party, who shall conduct the defense of such claim or litigation shall be
approved by the Indemnified Party (whose approval shall not unreasonably be
withheld). Without limiting the generality of the foregoing, the Indemnified
Party may withhold its consent to any such counsel who also acts as counsel to
the Indemnifying Party (with respect to such claim or otherwise) if the
Indemnified Party reasonably believes that there exists a conflict of interest
between the Indemnified Party and the Indemnifying Party, with respect to such
claim or litigation. In such event, the Indemnifying Party shall bear the
expense of another counsel who shall represent the Indemnified Party and any
other persons or entities who have indemnification rights from the Indemnifying
Party hereunder, with respect to such claim or litigation, and shall be selected
as provided in the first sentence of this Section 8.5(c). The Indemnified Party
may participate in such defense at such party's expense (except to the extent
that the Indemnifying Party is required to pay the expense of such counsel
pursuant to this Section 8.5(c), and provided further that the failure of any
Indemnified Party to give notice as provided herein shall not relieve the
Indemnifying Party of its obligations under this Agreement, unless such failure
causes material harm to the Indemnifying Party's defense such claim or
litigation. No Indemnifying Party, in the defense of any such claim or
litigation, shall, except with the consent of each Indemnified Party, consent to
entry of any judgment or enter into any settlement which does not include as an
unconditional term thereof the giving by the claimant or plaintiff to such
Indemnified Party of a release from all liability with respect to such claim or
litigation.

             (d) If the indemnification provided for in this Section 8.5(d) is
held by a court of competent jurisdiction to be unavailable to an Indemnified
Party with respect to any loss, liability, claim, damage or expense referred to
therein, then the Indemnifying Party, in lieu of indemnifying such Indemnified
Party hereunder, shall contribute to the amount paid or payable by such
Indemnified Party as a result of such loss, liability, claim damage or expense
in such proportion as is appropriate to reflect the relative fault of the
Indemnifying Party on the one hand and of the Indemnified Party on the other in
connection with the statements or omissions which resulted in such loss,
liability, claim, damage or expense as well as any other relevant equitable
considerations. The relative fault of the Indemnifying Party and of the
Indemnified Party shall be determined by reference to, among other things,
whether the untrue or alleged untrue statement of a material fact or the
omission to state a material fact relates to information supplied by or on
behalf of the Indemnifying Party or by the Indemnified Party and the parties'
relative intent, knowledge, access to information and opportunity to correct or
prevent such statement or omission.


                                      -11-
<PAGE>   12

             (e) Notwithstanding the foregoing, to the extent that the
provisions on indemnification and contribution contained in the underwriting
agreement entered into in connection with an underwritten public offering are in
conflict with the foregoing provisions, the provisions in the underwriting
agreement shall control.


                                   ARTICLE IX
                                  MISCELLANEOUS

         9.1 Entire Agreement. This Agreement (together with any attachments or
exhibits including, without limitation, the Registration Rights Agreement)
constitutes the entire agreement between the Company and the Investors relating
to the subject matter hereof, and no party shall be liable or bound to the other
in any manner by any warranties, representations or covenants except as
specifically set forth herein.

         9.2 Successors and Assigns. The terms and conditions of this Agreement
shall inure to the benefit of and be binding upon the respective successors and
assigns of the parties. Except as expressly provided in this Agreement and the
Registration Rights Agreement, nothing in this Agreement, express or implied, is
intended to confer upon any party, other than the parties hereto or their
respective successors and assigns, any rights, remedies, obligations or
liabilities under or by reason of this Agreement.

         9.3 Governing Law. This Agreement shall be governed by and construed in
accordance with the laws of the State of Texas without application of the choice
of laws provisions of such laws.

         9.4 Counterparts. This Agreement may be executed in one or more
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.

         9.5 Headings. The headings used in this Agreement are for convenience
and shall not by themselves be considered in construing or interpreting this
Agreement.

         9.6 Notices. Any notice required or permitted hereunder shall be given
in writing and shall be conclusively deemed effectively given upon either (a)
personal delivery; (b) one day after facsimile transmission to the facsimile
number indicated below and evidenced by a written record of completed
transmission to such number; or (c) five days after deposit in the United States
mail, by registered or certified mail, postage prepaid, addressed to the
following address, or to such other address as the party may designate by ten
(10) days' advance written notice to the other party:

         If to the Investors:

             At the address on the Company's stock ledger, or such other address
as may be provided by such Investor;


                                      -12-
<PAGE>   13

         If to the Company:

                  ILEX Oncology, Inc.
                  11550 I.H. 10 West, Suite 100
                  San Antonio, Texas 78230
                  Attn:  President
                  Facsimile No: (210) 949-8227

         9.7 Survival of Warranties. The warranties, representations and
covenants of the parties contained in or made pursuant to this Agreement shall
survive the execution and deliver of this Agreement and the Closing and shall in
no way be affected by any investigation of the subject matter thereof by or on
behalf of the Investors; provided, however, that such representations and
warranties need only be accurate as of the date of such execution and delivery
and as of the Closing.

         9.8 Finder's Fees. Each party agrees to indemnify and hold harmless the
other party from and against any liability for any commission or compensation in
the nature of investment banking or finder's fees in connection with the
transactions contemplated by this Agreement (and the costs and expenses of
defending against such liability or asserted liability) for which the
indemnifying party or any of its officers, employees or representatives is
responsible.

         9.9 Expenses. On the Closing Date, the Company will pay the reasonable
legal fees and expenses of the Investors up to $20,000, in connection with the
negotiation, execution, delivery and performance of this Agreement.

         9.10 Amendments and Waivers. Except as expressly provided in this
Agreement, any provision of this Agreement may be amended only by the mutual
written agreement of the parties and the observance of any term of this
Agreement may be waived (either generally or in a particular instance and either
retroactively or prospectively) only in a written document executed by the
waiving party.

         9.11 Severability. If one or more provisions of this Agreement are held
to be unenforceable under applicable law, such provision shall be excluded from
this Agreement and the balance of this Agreement shall be interpreted as if such
provision were so excluded and shall be enforceable in accordance with its
terms.

         9.12 Regulatory Matters. Each Investor agrees to cooperate with the
Company in all reasonable respects in complying with the terms and provisions of
the Small Business Sideletter, provided that no Investor shall be required under
this Section 9.12 to take any action that would adversely affect in any material
respect such Investor's rights under this Agreement or as a stockholder of the
Company.


                                      -13-
<PAGE>   14

         IN WITNESS WHEREOF the parties have executed this Agreement effective
as of the day and year first above written.

                                   ILEX ONCOLOGY, INC.



                                   By:
                                      -----------------------------------------
                                            Richard L. Love
                                            President


                                   INVESTORS:

                                   ALTA BIOPHARMA PARTNERS, L.P.
                                   By: Alta BioPharma Management, LLC



                                             By:
                                                -------------------------------
                                                      Managing Partner

                                   ILEX CHASE PARTNERS (ALTA BIO), LLC
                                   By: Alta/Chase BioPharma Management, LLC



                                   By:
                                      -----------------------------------------
                                            Member

                                   ALTA EMBARCADERO
                                     BIOPHARMA PARTNERS, LLC



                                   By:
                                      -----------------------------------------
                                            Member


                                   CHASE VENTURE CAPITAL ASSOCIATES, L.P.

                                   By:
                                      -----------------------------------------



                                             By:
                                                -------------------------------
                                                      Managing Partner



                                   --------------------------------------------
                                   B. J. McCombs


                                      -14-
<PAGE>   15

                                   ADVENT HEALTH CARE AND LIFE
                                    SCIENCES II LIMITED PARTNERSHIP

                                   By: Advent International Limited Partnership,
                                         General Partner
                                   By: Advent International Corporation,
                                         General Partner


                                         By:
                                            ------------------------------------
                                               Vice President/Senior
                                                Vice President


                                   ADVENT HEALTH CARE AND LIFE
                                    SCIENCES II BETEILIGUNG GMBH & CO. KG

                                   By: Advent Health Care and Life Sciences II
                                         Verwaltungs GmbH, General Partner
                                   By: Advent International Limited Partnership,
                                         Managing General Partner
                                   By: Advent International Corporation, General
                                         Partner


                                         By:
                                            ------------------------------------
                                               Vice President/Senior
                                                Vice President


                                   ADVENT PARTNERS HLS II LIMITED PARTNERSHIP

                                   By: Advent International Corporation, General
                                         Partner


                                         By:
                                            ------------------------------------
                                               Vice President/Senior
                                                Vice President

                                   ADVENT PARTNERS LIMITED PARTNERSHIP

                                   By: Advent International Corporation,
                                         General Partner


                                         By:
                                            ------------------------------------
                                              Vice President/Senior
                                               Vice President


                                      -15-
<PAGE>   16

                                   SCHEDULE A

                              SCHEDULE OF INVESTORS


<TABLE>
<CAPTION>
                                                                                   AGGREGATE
                                                        NUMBER OF SHARES           PURCHASE
              NAME AND ADDRESS                          TO BE PURCHASED            PRICE ($)
              ----------------                          ----------------          -----------
<S>                                                     <C>                       <C>
Alta BioPharma Partners, L.P.                                742,547              $ 6,215,859
Alta Embarcadero BioPharma, LLC                               27,988              $   234,288
ILEX Chase Partners (Alta Bio), LLC                          424,065              $ 3,549,852
Chase Venture Capital Associates, L.P.                       238,920              $ 2,000,000
B. J. McCombs                                                119,460              $ 1,000,000
Advent Health Care and Life Sciences II Limited
Partnership                                                  757,974              $ 6,345,000
Advent Health Care and Life Sciences II
Beteiligung GmbH & Co. KG                                     58,894              $   493,000
Advent Partners HLS II Limited Partnership                    16,844              $   141,000
Advent Partners Limited Partnership                            2,509              $    21,000
                                                           ---------              -----------
         TOTAL                                             2,389,201              $20,000,000
                                                           =========              ===========
</TABLE>


                                      A-1
<PAGE>   17

                               DISCLOSURE SCHEDULE
                                       to
                            Stock Purchase Agreement
                                      among
                          the Company and the Investors


                                   Section 2.9
                                 Certain Changes

On May 26, 1999 the Board of Directors of ILEX approved a write-off of up to $20
million in largely non-cash value of investments in affiliates and certain other
non-productive assets and commitments in the CRO business.



                                  Section 2.11
                               Registration Rights

Registration Rights Agreement dated July 16, 1999, among ILEX Oncology, Inc. and
Shareholders of Convergence Pharmaceuticals, Inc.

Registration Rights Agreement dated January 22, 1999, among ILEX Oncology, Inc.
and Eli Lilly and Company.

Registration Rights Agreement dated as of July 9, 1997, among ILEX Oncology,
Inc. and PRN Research, Inc.

Fourth Amended and Restated Registration Rights Agreement dated December 11,
1996.


                                      A-2