<PAGE>   1
                                                                    EXHIBIT 10.2

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                              XCYTE THERAPIES, INC.

                            SERIES D PREFERRED STOCK

                               PURCHASE AGREEMENT

                                  MAY 25, 2000


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<PAGE>   2


                               TABLE OF CONTENTS
<TABLE>
<CAPTION>
                                                                                          PAGE
                                                                                          ----
<S>                                                                                       <C>
1.   PURCHASE AND SALE OF STOCK                                                              3

   1.1    AUTHORIZATION, SALE AND ISSUANCE OF SHARES.........................................3
   1.2    CLOSING............................................................................3
   1.3    DELIVERY...........................................................................3
   1.4    ADDITIONAL CLOSINGS................................................................4

2.   REPRESENTATIONS AND WARRANTIES OF THE COMPANY...........................................4

   2.1    ORGANIZATION, GOOD STANDING AND QUALIFICATION......................................4
   2.2    AUTHORIZATION......................................................................4
   2.3    CAPITALIZATION.....................................................................5
   2.4    SUBSIDIARIES.......................................................................6
   2.5    GOVERNMENTAL CONSENTS..............................................................6
   2.6    PROPRIETARY INFORMATION AGREEMENT..................................................6
   2.7    PATENTS AND TRADEMARKS.............................................................6
   2.8    FINANCIAL STATEMENTS...............................................................7
   2.9    CHANGES............................................................................7
   2.10   LIABILITIES........................................................................8
   2.11   LITIGATION.........................................................................8
   2.12   COMPLIANCE WITH OTHER INSTRUMENTS..................................................8
   2.13   OFFERING...........................................................................9
   2.14   AGREEMENTS; ACTION.................................................................9
   2.15   LABOR AGREEMENTS AND ACTIONS......................................................10
   2.16   TAX RETURNS, PAYMENTS AND ELECTIONS...............................................10
   2.17   TITLE TO PROPERTY AND ASSETS......................................................10
   2.18   REGISTRATION RIGHTS...............................................................10
   2.19   EMPLOYEE BENEFIT PLANS............................................................10
   2.20   OBLIGATIONS OF MANAGEMENT.........................................................11
   2.21   ENVIRONMENTAL AND SAFETY LAWS.....................................................11
   2.22   DISCLOSURE........................................................................11
   2.23   SECTION 83(B) ELECTIONS...........................................................11
   2.24   REAL PROPERTY HOLDING CORPORATION.................................................11
   2.25   INSURANCE.........................................................................11
   2.26   INVESTMENT COMPANY ACT............................................................11

3.   REPRESENTATIONS AND WARRANTIES OF THE INVESTOR.........................................11

   3.1    AUTHORIZATION.....................................................................11
   3.2    PURCHASE ENTIRELY FOR OWN ACCOUNT.................................................12
   3.3    DISCLOSURE OF INFORMATION.........................................................12
   3.4    INVESTMENT EXPERIENCE.............................................................12
   3.5    REGULATION D......................................................................12
   3.6    RESTRICTED SECURITIES.............................................................12
   3.7    LEGENDS...........................................................................13
</TABLE>
<PAGE>   3

<TABLE>
<S>                                                                                       <C>
4.   CONDITIONS OF INVESTOR'S OBLIGATIONS AT CLOSING........................................13

   4.1    REPRESENTATIONS AND WARRANTIES....................................................13
   4.2    PERFORMANCE.......................................................................13
   4.3    CERTIFICATE.......................................................................13
   4.4    COMPLIANCE CERTIFICATE............................................................13
   4.5    PROCEEDINGS AND DOCUMENTS.........................................................13
   4.6    BOARD OF DIRECTORS................................................................14
   4.7    RIGHTS AGREEMENT..................................................................14
   4.8    CO-SALE AGREEMENT.................................................................14
   4.9    OPINION OF COMPANY COUNSEL........................................................14
   4.10   MINIMUM INVESTMENT................................................................14

5.   CONDITIONS OF THE COMPANY'S OBLIGATIONS AT CLOSING.....................................14

   5.1    REPRESENTATIONS AND WARRANTIES....................................................14
   5.2    LEGAL MATTERS.....................................................................14

6.   MISCELLANEOUS..........................................................................14

   6.1    SURVIVAL OF WARRANTIES............................................................15
   6.2    SUCCESSORS AND ASSIGNS............................................................15
   6.3    GOVERNING LAW.....................................................................15
   6.4    COUNTERPARTS......................................................................15
   6.5    TITLES AND SUBTITLES..............................................................15
   6.6    NOTICES...........................................................................15
   6.7    FINDER'S FEE......................................................................15
   6.8    AMENDMENTS AND WAIVERS............................................................16
   6.9    SEVERABILITY......................................................................16
   6.10   EXCULPATION AMONG INVESTORS.......................................................16
   6.11   EXPENSES..........................................................................16
</TABLE>


EXHIBITS

A      Schedule of Investors
B      Form of Amended and Restated Certificate of Incorporation
C      Schedule of Exceptions
D      Form of Proprietary Information Agreement
E      Form of Amended and Restated Investor Rights Agreement
F      Form of Amended and Restated Right of First Refusal and CoSale Agreement
G      Form of Opinion of Counsel to the Company


                                      -2-
<PAGE>   4

                              XCYTE THERAPIES, INC.

                            STOCK PURCHASE AGREEMENT

        THIS SERIES D PREFERRED STOCK PURCHASE AGREEMENT (the "Agreement") is
made as of the 25th day of May 2000, by and between Xcyte Therapies, Inc., a
Delaware corporation, located at 1124 Columbia Street, Suite 130, Seattle, WA
98104 (the "Company"), and the investors listed on Exhibit A hereto, each of
which is herein referred to as an "Investor."

        WHEREAS, the Company desires to issue and sell up to 7,194,245 shares of
        Series D Preferred Stock to the Investors; and

        WHEREAS, the Investors desire to purchase such shares from the Company
        on the terms and subject to the conditions of this Agreement.

        NOW THEREFORE, the parties hereby agree as follows:

        1. Purchase and Sale of Stock.

                1.1 Authorization, Sale and Issuance of Shares

                        (a) The Company has authorized the sale and issuance of
up to 7,194,245 shares of Series D Preferred Stock (the "Shares"), with the
Shares having the rights, preferences, privileges and restrictions as set forth
in the Company's Restated Certificate of Incorporation in the form satisfactory
to the Investors, a copy of which is attached hereto as Exhibit B (the
"Certificate"). The Common Stock issuable upon conversion of the Shares is
referred to hereinafter as the "Conversion Shares."

                        (b) Subject to the terms and conditions of this
Agreement, the Company shall sell and issue to each Investor, and each Investor
agrees, severally and not jointly, to purchase from the Company, that number of
Shares set forth opposite each Investor's name on Exhibit A attached hereto for
the purchase price of $2.78 per share as set forth thereon.

                1.2 Closing. The purchase and sale of the Shares shall take
place at the offices of Venture Law Group, 4750 Carillon Point, Kirkland,
Washington, at 10:00 a.m., on May 25, 2000, or at such other time and place as
the Company and Investors may agree (which time and place are designated as the
"Closing"). The date of such Closing is hereinafter referred to as the "Closing
Date."

                1.3 Delivery. At the Closing, the Company shall deliver to each
Investor a certificate representing the Shares which such Investor is purchasing
against delivery to the
<PAGE>   5

Company by such Investor of a check, wire transfer of immediately available
funds payable to the Company's order or cancellation of indebtedness (or any
combination thereof) in the aggregate amount of the purchase price therefor.

                1.4 Additional Closings. If the full number of Series D
Preferred Stock of the Company is not sold at the Closing, the Company shall
have the right, at any time prior to August 8, 2000 (the "Subsequent Closing
Date"), to sell the remaining authorized but unissued shares of Series D
Preferred Stock to one or more additional purchasers as determined by the
Company, or to any Purchaser hereunder who wishes to acquire additional shares
of Series D Preferred Stock at the price and on the terms set forth herein,
provided that any such additional purchaser shall be required to execute an
Addendum Agreement substantially in the form attached hereto as Exhibit H. Any
additional purchaser so acquiring shares of Series D Preferred Stock shall be
considered a "Purchaser" for purposes of this Agreement and an "Investor" for
the purposes of the Agreements (as defined below), and any Series D Preferred
Stock so acquired by such additional purchaser shall be considered "Shares" for
purposes of this Agreement and all other agreements contemplated hereby.

        2. Representations and Warranties of the Company. The Company hereby
represents and warrants to each Investor that, except as set forth on the
Schedule of Exceptions attached hereto as Exhibit C, which exceptions shall be
deemed to be representations and warranties as if made hereunder:

                2.1 Organization, Good Standing and Qualification. The Company
is a corporation duly organized, validly existing and in good standing under the
laws of the State of Delaware and has all requisite corporate power and
authority to carry on its business as now conducted and as proposed to be
conducted. The Company is duly qualified to transact business and is in good
standing in each jurisdiction in which the failure so to qualify would have a
material adverse effect on its business or properties. As of the Closing, the
Certificate shall be in the form attached hereto as Exhibit B and the Bylaws of
the Company shall be in the form provided to counsel for the Investors prior to
the Closing.

                2.2 Authorization.

                        (a) The Company has all requisite corporate power and
authority to execute and deliver, and to consummate the transactions
contemplated by this Agreement, the Amended and Restated Investor Rights
Agreement attached as Exhibit E ("Rights Agreement") and the Amended and
Restated Right of First Refusal and Co-Sale Agreement attached as Exhibit F (the
"Co-Sale Agreement" with the Agreement and Rights Agreement, the "Financing
Documents"). All corporate action on the part of the Company, its officers,
directors and stockholders necessary for the execution and delivery of, and the
consummation of the transactions contemplated by the Financing Documents, the
performance of all obligations of the

                                      -4-
<PAGE>   6

Company under the Financing Documents and the authorization, sale, issuance (or
reservation for issuance) and delivery of the Shares being sold hereunder and
the Conversion Shares has been taken or will be taken prior to the Closing. The
Financing Documents, upon execution and delivery by the Company and assuming the
due and proper execution and delivery by the other parties, constitute valid and
binding obligations of the Company enforceable in accordance with their
respective terms, except as such enforcement may be limited by bankruptcy,
insolvency, moratorium and other laws of general application affecting the
enforcement of creditors' rights.

                        (b) The Shares, when issued in compliance with the
provisions of this Agreement, will be validly issued, fully paid and
nonassessable and will be free of any liens or encumbrances known to, or caused
or created by, the Company; provided, however, that the Shares may be subject to
restrictions on transfer under state and/or federal securities laws as set forth
herein, as may be required by changes in such laws and as contemplated by the
Financing Documents. Upon conversion of the Shares into the Conversion Shares in
conformity with the Certificate, such Conversion Shares will be duly authorized,
validly issued, fully paid and nonassessable, and will be free of any liens or
encumbrances caused or created by the Company; provided, however, that the
Conversion Shares may be subject to restrictions on transfer under state and/or
federal securities laws as set forth herein, as may be required by changes in
such law and as contemplated by the Financing Documents.

                        (c) Except as set forth herein or in the Financing
Documents, no entity has any right of first refusal or any preemptive rights in
connection with the issuance of the Shares, the Conversion Shares or any future
issuances of securities by the Company.

                2.3 Capitalization.

                        (a) Immediately prior to the Closing, the authorized
capital of the Company shall consist of: (i) 40,000,000 shares of Common Stock,
and (ii), 25,909,976 shares of Preferred Stock (the "Preferred Stock"), of which
7,300,080 have been designated Series A Preferred Stock, 4,097,580 have been
designated Series B Preferred Stock, 7,212,316 have been designated Series C
Preferred Stock and 7,300,000 have been designated Series D Preferred Stock.
Immediately prior to the Closing, 5,964,247 shares of Common Stock, 6,860,512
shares of Series A Preferred Stock, warrants to purchase 439,568 shares of
Series A Preferred Stock, 3,903,080 shares of Series B Preferred Stock, warrants
to purchase 194,500 shares of Series B Preferred Stock, 7,185,630 shares of
Series C Preferred Stock, and warrants to purchase 26,686 shares of Series C
Preferred Stock and no shares of Series D Preferred Stock will be outstanding.

                        (b) Except as set forth in this Agreement and the
exhibits thereto, there are no outstanding options, warrants, rights (including
conversion or preemptive rights) or agreements for the purchase or acquisition
from the Company of any shares of its capital stock except that the Company has
reserved (i) the Shares for issuance at each Closing, (ii) the Common Stock
issuable upon conversion of the Preferred Stock, (iii) 2,500,000 shares of

                                      -5-
<PAGE>   7

Common Stock reserved for issuance pursuant to a stock option plan adopted by
the Company 992,441 options have been granted and remain outstanding, with
1,420,121 shares remaining for grant, (iv) 898,150 shares of Common Stock
reserved for issuance to scientific founders upon the achievement of certain
milestones, and (v) 157,890 shares reserved for issuance to Carl June or his
assignees upon the Company's acquisition of certain future technology.

                2.4 Subsidiaries. The Company does not presently own or
control, directly or indirectly, any interest in any other corporation,
association, or other business entity.

                2.5 Governmental Consents.

                        (a) No consent, approval, order or authorization of, or
registration, qualification, designation, declaration or filing with, any
federal, state or local governmental authority on the part of the Company is
required in connection with the consummation of the transactions contemplated by
the Financing Documents.

                        (b) No consent, approval, waiver or other action by any
person under any contract, agreement, indenture, lease, instrument or other
document to which the Company is a party or bound is required or necessary for
the execution, delivery and performance of, or the consummation of the
transactions contemplated by, any of the Financing Documents by the Company.

                2.6 Proprietary Information Agreement. Each former and present
employee, consultant and officer of the Company has executed and each future
employee, consultant and officer will execute, a Proprietary Information
Agreement in the form attached hereto as Exhibit D and no exceptions have been
taken by any such employee, consultant or officer to the terms of such
agreement. The Company, after reasonable investigation, is not aware that any of
its employees, officers or consultants are in violation thereof, and the Company
will use its best efforts to prevent any such violation.

               2.7 Patents and Trademarks. The Company has sufficient title and
ownership of all patents, trademarks, service marks, trade names, copyrights,
trade secrets, information, proprietary rights and processes necessary for its
business as now conducted and as proposed to be conducted without any conflict
with or infringement of the rights of others. There are no outstanding options,
licenses, or agreements of any kind relating to the foregoing, nor is the
Company bound by or a party to any options, licenses or agreements of any kind
with respect to the patents, trademarks, service marks, trade names, copyrights,
trade secrets, licenses, information, proprietary rights and processes of any
other person or entity. The Company has not received any communications alleging
that the Company has violated or, by conducting its business as proposed, would
violate any of the patents, trademarks, service marks, trade names, copyrights
or trade secrets or other proprietary rights of any other person or entity. The
Company is not aware that any of its employees is obligated under any contract
(including

                                      -6-
<PAGE>   8

licenses, covenants or commitments of any nature) or other agreement, or subject
to any judgment, decree or order of any court or administrative agency, that
would interfere with the use of his or her best efforts to promote the interests
of the Company or that would conflict with the Company's business as proposed to
be conducted. Neither the execution nor delivery of this Agreement, nor the
carrying on of the Company's business by the employees of the Company, nor the
conduct of the Company's business as proposed, will, to the best of the
Company's knowledge, conflict with or result in a breach of the terms,
conditions or provisions of, or constitute a default under, any contract,
covenant or instrument under which any of such employees is now obligated. The
Company does not believe it is or will be necessary to utilize any inventions of
any of its employees (or people it currently intends to hire) made prior to
their employment by the Company.

                2.8 Financial Statements. The Company has delivered to each
Investor (i) its unaudited balance sheet as of March 31, 2000 and unaudited
statement of income for the period from January 1, 2000 to March 31, 2000 and
unaudited financial statements as of December 31, 1999 (collectively the
"Financial Statements"). The Financial Statements, together with the notes
thereto, are complete and correct in all material respects and have been
prepared in accordance with generally accepted accounting principles applied on
a consistent basis throughout the periods indicated, except as disclosed
therein, and present fairly the financial condition and position of the Company
as of March 31, 2000; provided, however, that the unaudited financial statements
are subject to normal recurring year-end audit adjustments (which are not
expected to be material), and do not contain all footnotes required under
generally accepted accounting principles.

                2.9 Changes. Since March 31, 2000, there has not been:

                        (a) Any change in the assets, liabilities, financial
condition or operations of the Company from that reflected in the Financial
Statements, other than changes in the ordinary course of business, or any other
event or condition of any character, any of which individually or in the
aggregate has had or is expected to have a material adverse effect on such
assets, liabilities, financial condition or operations of the Company;

                        (b) Any resignation or termination of any key officers
of the Company; and the Company, to the best of its knowledge, does not know of
the impending resignation or termination of employment of any such officer;

                        (c) Any material change, except in the ordinary course
of business, in the contingent obligations of the Company by way of guaranty,
endorsement, indemnity, warranty or otherwise;

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<PAGE>   9

                        (d) Any damage, destruction or loss, whether or not
covered by insurance, materially and adversely affecting the properties,
business or prospects or financial condition of the Company;

                        (e) Any direct or indirect loans made by the Company to,
or any material change in, any compensation arrangement or agreement with, any
stockholder, employee, officer or director of the Company, other than advances
made in the ordinary course of business;

                        (f) Any declaration or payment of any dividend or other
distribution of the assets of the Company;

                        (g) Any debt, obligation or liability incurred, assumed
or guaranteed by the Company, except those for immaterial amounts and for
current liabilities incurred in the ordinary course of business; or any waiver
by the Company of a valuable right or of a material debt owed to it;

                        (h) Any sale, assignment or transfer of any patents,
trademarks, copyrights, trade secrets or other intangible assets; and

                        (i) To the Company's knowledge, any change in any
material agreement to which the Company is a party or by which it is bound which
materially and adversely affects the business, assets, liabilities, financial
condition, operations or prospects of the Company, including compensation
agreements with the Company's employees.

                2.10 Liabilities. The Company has no material liabilities and
knows of no material contingent liabilities not disclosed in the Financial
Statements, except current liabilities incurred in the ordinary course of
business subsequent to March 31, 2000, which have not been, either in any
individual case or in the aggregate, materially adverse.

                2.11 Litigation. There is no action, suit, proceeding or
investigation pending or currently threatened against the Company that questions
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 changes in the
assets, condition, affairs or prospects of the Company, financially or
otherwise, or any change in the current equity ownership of the Company, nor is
the Company aware that there is any basis for the foregoing. 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, their use in connection with the Company's business of any
information or techniques allegedly proprietary to any of their former
employers, or their obligations under any agreements with 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 government agency or

                                      -8-
<PAGE>   10

instrumentality. There is no action, suit, proceeding or investigation by the
Company currently pending or which the Company intends to initiate.

                2.12 Compliance with Other Instruments. The Company is not in
violation or default of any provision of its Certificate or Bylaws or any
provision of any mortgage, indenture, contract, agreement, instrument, judgment,
order, writ, or decree 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 would materially and adversely affect the
business, assets, liabilities, financial condition, operations or prospects of
the Company. The execution, delivery and performance of this Agreement, the
Rights Agreement and the Co-Sale Agreement and the consummation of the
transactions contemplated hereby and thereby will not result in any such
material violation or be in conflict with or constitute, with or without the
passage of time and giving of notice, either a default under any such provision,
instrument, judgment, order, writ, decree or contract or an event which results
in the creation of any lien, charge or encumbrance upon any assets of the
Company.

                2.13 Offering. Subject in part to the accuracy of the Investors'
representations set forth in Section 3 hereof, the offer, sale and issuance of
the Shares as contemplated by this Agreement and the issuance of the Conversion
Shares upon the conversion of such Shares are exempt from the registration
requirements of the Securities Act of 1933, as amended (the "Securities Act"),
and the registration, qualification or compliance requirements of any applicable
blue sky or other state securities laws, and neither the Company nor any
authorized agent acting on its behalf will take any action that would cause the
loss of any such exemption.

                2.14 Agreements; Action.

                        (a) There are no agreements, understandings or proposed
transactions between the Company and any of its officers, directors, affiliates,
or any affiliate thereof.

                        (b) There are no agreements, understandings,
instruments, contracts or proposed transactions to which the Company is a party
or by which it is bound which involve (i) obligations of, or payments to the
Company in excess of $25,000, or (ii) the license of any patent, copyright,
trade secret or other proprietary right to or from the Company (other than
licenses arising from the purchase of "off-the-shelf" products) or (iii)
obligations of, or payments by, the Company to any officer, director, employee
or family member of any such individual.

                        (c) The Company has not (i) declared or paid any
dividends, or authorized or made any distribution upon or with respect to any
class or series of its capital stock, (ii) incurred any indebtedness for money
borrowed or incurred any other liabilities individually in excess of $25,000 or
in excess of $75,000 in the aggregate, (iii) made any loans or advances to any
person, other than ordinary advances for travel expenses, or (iv) sold,
exchanged or otherwise disposed of any of its assets or rights, other than in
the ordinary course of business.

                                      -9-
<PAGE>   11

                        (d) The Company is not a party to and is not bound by
any contract, agreement or instrument, or subject to any restriction under its
Certificate or Bylaws, which materially adversely affects its business as now
conducted and as proposed to be conducted.

                        (e) The Company has not engaged in the past twelve (12)
months in any discussion (i) with any representative of any corporation or
corporations regarding the consolidation or merger of the Company with or into
any such corporation or corporations, (ii) with any corporation, partnership,
association or other business entity or any individual regarding the sale,
conveyance or disposition of all or substantially all of the assets of the
Company, or (iii) regarding any other form of liquidation, dissolution or
winding up of the Company.

                2.15 Labor Agreements and Actions. The Company is not bound by
or subject to (and none of its assets or properties is bound by or subject to)
any written or oral, express or implied, contract, commitment or arrangement
with any labor union, and no labor union has requested or, to the knowledge of
the Company, has sought to represent any of the employees, representatives or
agents of the Company. There is no strike or other labor dispute involving the
Company pending, or to the knowledge of the Company threatened, which could have
a material adverse effect on the assets, properties, financial condition,
operating results, or business of the Company (as such business is presently
conducted and as it is proposed to be conducted), nor is the Company aware of
any labor organization activity involving its employees. To the best of its
knowledge, the Company is not aware that any officer or key employee, or that
any group of key employees, intends to terminate their employment with the
Company, nor does the Company have a present intention to terminate the
employment of any of the foregoing. The employment of each officer and employee
of the Company is terminable at the will of the Company.

                2.16 Tax Returns, Payments and Elections. The Company has filed
all tax returns and reports as required by law. These returns and reports are
true and correct in all material respects. The Company has paid all taxes and
other assessments due, except those contested by it in good faith which are
listed in the Schedule of Exceptions, attached hereto as Exhibit C. The
provision for taxes of the Company as shown in the Balance Sheet is adequate for
taxes due or accrued as of the date thereof. The Company has not elected
pursuant to the Internal Revenue Code of 1986, as amended (the "Code"), to be
treated as a Subchapter S corporation or a collapsible corporation pursuant to
Section 1362(a) or Section 341(f) of the Code, respectively, nor has it made any
other elections pursuant to the Code (other than elections which relate solely
to methods of accounting, depreciation or amortization) which would have a
material effect on the Company, its financial condition, its business as
presently conducted or proposed to be conducted or any of its properties or
material assets.

                2.17 Title to Property and Assets. The Company owns its property
and assets free and clear of all mortgages, liens, loans and encumbrances,
except such encumbrances and liens which arise in the ordinary course of
business and do not materially impair the Company's

                                      -10-
<PAGE>   12

ownership or use of such property or assets. With respect to the property and
assets it leases, the Company is in compliance with such leases and, to the best
of its knowledge, holds a valid leasehold interest free of any liens, claims or
encumbrances.

                2.18 Registration Rights. Except as provided in the Rights
Agreement, a form of which is attached hereto as Exhibit E, the Company has not
granted or agreed to grant any registration rights, including piggyback rights,
to any person or entity.

                2.19 Employee Benefit Plans. The Company does not have any
Employee Benefit Plan as defined in the Employee Retirement Income Security Act
of 1974, as amended.

                2.20 Obligations of Management. Each officer of the Company is
currently devoting his or her full-time to the conduct of the business of the
Company. The Company is not aware of any officer or key employee or the Company
planning to work less than full-time at the Company in the future.

                2.21 Environmental and Safety Laws. To the best of its
knowledge, the Company is not in violation of any applicable statute, law or
regulation relating to the environment or occupational health and safety, and to
its knowledge, no material expenditures are or will be required in order to
comply with any such existing statute, law or regulation.

                2.22 Disclosure. The Company has fully provided each Investor
with all the information which such Investor has requested for deciding whether
to purchase the Shares and all information which the Company believes is
reasonably necessary to enable such Investor to make such decision. To the best
of the Company's knowledge, neither this Agreement, the Rights Agreement, the
Co-Sale Agreement nor any other statements or certificates made or delivered in
connection herewith, when taken as a whole, contains any untrue statement of a
material fact or omits to state a material fact necessary to make the statements
herein or therein not misleading.

                2.23 Section 83(b) Elections. To the Company's knowledge, all
elections and notices permitted by Section 83(b) of the Internal Revenue Code
and analogous provisions of applicable state tax laws have been timely filed by
all employees who have purchased shares of the Company's common stock under
agreements that provide for the vesting of such shares.

                2.24 Real Property Holding Corporation. The Company is not a
real property holding corporation within the meaning of Internal Revenue Code
Section 897(c)(2) and any regulations promulgated thereunder.

                2.25 Insurance. The Company has fire and casualty insurance
policies with coverage customary for companies similarly situated to the
Company.

                                      -11-
<PAGE>   13

                2.26 Investment Company Act. The Company is not an "investment
company", or a company "controlled" by an "investment", within the meaning of
the Investment Company Act of 1940, as amended.

        3. Representations and Warranties of the Investor. Each Investor hereby
severally and not jointly represents and warrants that:

                3.1 Authorization. This Agreement when executed and delivered by
such Investor shall constitute a valid and legally binding obligation,
enforceable in accordance with its terms, subject to the effect of applicable
bankruptcy, insolvency, reorganization, moratorium or other similar federal or
state laws affecting the rights of creditors and the effect of rules of law
governing specific performance, injunctive relief or other equitable remedies.

                3.2 Purchase Entirely for Own Account. This Agreement is made
with each Investor in reliance upon such Investor's representations and
warranties to the Company, which by such Investor's execution of this Agreement
such Investor hereby confirms, that the Shares to be received by such Investor
and the Conversion Shares (collectively, the "Securities") will be acquired for
investment for such 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 that such
Investor has no present intention of selling, granting any participation in, or
otherwise distributing the same. By executing this Agreement, each Investor
further represents that such Investor does not have any contract, undertaking,
agreement or arrangement with any person or entity to sell, transfer or grant
participation to such person or to any third person, with respect to any of the
Securities. Each Investor represents that it has full power and authority to
enter into this Agreement.

                3.3 Disclosure of Information. Each Investor believes it has
received all the information it considers necessary or appropriate for deciding
whether to purchase the Shares. Each Investor further represents that it has had
an opportunity to ask questions, if any, and receive answers from the Company
regarding the terms and conditions of the offering of the Shares. The foregoing,
however, does not limit or modify the representations and warranties of the
Company in Section 2 of this Agreement or the right of the Investors to rely
thereon.

                3.4 Investment Experience. Each Investor is an investor in
securities of companies in the development stage and acknowledges that it is
able to fend for itself, and bear the economic risk of its investment and has
such knowledge and experience in financial or business matters that it is
capable of evaluating the merits and risks of the investment in the Shares. If
other than an individual, Investor also represents it has not been organized for
the purpose of acquiring the Shares.

                3.5 Regulation D. Each Investor is an "Accredited Investor" as
that term is defined in Regulation D promulgated under the Securities Act.

                                      -12-
<PAGE>   14

                3.6 Restricted Securities. Each Investor understands that the
Shares it is purchasing (and the Conversion Shares) 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 such securities may be
resold without registration under the Securities Act only in certain limited
circumstances. In this connection, each Investor represents that it is familiar
with Rule 144, as presently in effect, and understands the resale limitations
imposed thereby and by the Securities Act.

                3.7 Legends. It is understood that the certificates evidencing
the Series D Preferred Stock (or the Conversion Shares) may bear one or all of
the following legends:

                        (a) "THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE
SECURITIES ACT OF 1933, AS AMENDED (THE "ACT"). THEY MAY NOT BE SOLD, OFFERED
FOR SALE, PLEDGED OR HYPOTHECATED IN THE ABSENCE OF A REGISTRATION STATEMENT IN
EFFECT WITH RESPECT TO THE SECURITIES UNDER SUCH ACT OR AN OPINION OF COUNSEL
SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT REQUIRED OR UNLESS
SOLD PURSUANT TO RULE 144 OF SUCH ACT. THESE SECURITIES ARE SUBJECT TO A CERTAIN
VOTING PROVISION ENTERED INTO BY AND AMONG THE INVESTORS."

                        (b) Any other legends required by the laws of the State
of Delaware or any other applicable blue sky or state securities laws.

        4. Conditions of Investor's Obligations at Closing. The obligations of
each Investor under this Agreement are subject to the fulfillment on or before
the Closing of each of the following conditions, any of which may be waived in
whole or in part by such Investor with respect to himself, herself or itself
unless required by state or federal law:

                4.1 Representations and Warranties. The representations and
warranties of the Company contained in Section 2 shall be true on and as of the
Closing Date with the same effect as though such representations and warranties
had been made on and as of the date of the Closing.

                4.2 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.

                4.3 Certificate. The Certificate shall have been filed with the
Secretary of State of the State of Delaware.

                                      -13-
<PAGE>   15

               4.4 Compliance Certificate. The President of the Company shall
deliver to counsel for the Investors at the Closing a certificate certifying
that the conditions specified in Sections 4.1, 4.2 and 4.3 have been fulfilled
and stating that there shall have been no adverse change in the business,
affairs, prospects, operations, properties, assets, liabilities or condition of
the Company since the date of this Agreement.

                4.5 Proceedings and Documents. All corporate and other
proceedings in connection with the transactions contemplated at the Closing and
all documents incident thereto shall be reasonably satisfactory in form and
substance to each Investor and counsel to any of the Investors, and they shall
have received all such counterpart original and certified or other copies of
such documents as they may reasonably request.

                4.6 Board of Directors. As of the Closing, the Board of
Directors will be comprised of seven members: Ronald J. Berenson, Robert Curry,
Jean Deleage, Steve Johnson, Peter Langecker, Robert Nelsen and Robert Williams.

                4.7 Rights Agreement. The Company and the Investors shall have
entered into the Rights Agreement in the form attached hereto as Exhibit E.

                4.8 Co-Sale Agreement. The Company, Ronald Berenson, Carl June,
Jeffrey Bluestone, Jeffrey Ledbetter and Craig Thompson and certain of the
Investors shall have entered into the Co-Sale Agreement in the form attached
hereto as Exhibit F.

                4.9 Opinion of Company Counsel. The Investors shall have
received from Venture Law Group, counsel to the Company, an opinion addressed to
them, dated the Closing Date, in the form attached hereto as Exhibit G.

                4.10 Minimum Investment. As of the Closing Date, the sale and
issuance of the Shares by the Company shall amount to a minimum investment by
the Investors of at least eleven million (11,000,000) dollars.

        5. Conditions of the Company's Obligations at Closing. The obligations
of the Company to each Investor under this Agreement are subject to the
fulfillment on or before the Closing of each of the following conditions any of
which may be waived in whole or in part by the Company unless required by state
or federal law:

                5.1 Representations and Warranties. The representations and
warranties of each Investor contained in Section 3 hereof shall be true and
correct on and as of the Closing Date with the same effect as though such
representations and warranties had been made on and as of that date; and each
Investor shall have performed all obligations and conditions required to be
performed or observed by he, she or it on or prior to the Closing Date.

                                      -14-
<PAGE>   16

                5.2 Legal Matters. All material matters of a legal nature which
pertain to this agreement and the transactions contemplated hereby, shall have
been reasonably approved by counsel to the Company.

        6. Miscellaneous.

                6.1 Survival of Warranties. The warranties, representations and
covenants of the Company and Investors contained in or made pursuant to this
Agreement shall survive the execution and delivery of this Agreement and the
Closing and shall in no way be affected by any investigation of the subject
matter thereof made by or on behalf of the Investors or the Company.

                6.2 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. 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, except as expressly provided
in this Agreement.

                6.3 Governing Law. This Agreement shall be governed by and
construed under the laws of the State of Washington.

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

                6.5 Titles and Subtitles. The titles and subtitles used in this
Agreement are used for convenience only and are not to be considered in
construing or interpreting this Agreement.

                6.6 Notices. Unless otherwise provided, any notice required or
permitted under this Agreement shall be given in writing and shall be deemed
effectively given upon personal deliver to the party to be notified, the refusal
of delivery by such person, or five (5) days after deposit with the United
States Post Office, by registered or certified mail, postage prepaid and
addressed to the party to be notified at the address indicated for such party in
Exhibit A attached hereto or in the case of the Company on the first page of
this Agreement, or at such other address as such party may designate by ten (10)
days' advance written notice to the other parties.

                6.7 Finder's Fee. Each party represents that it neither is nor
will be obligated for any finders' fee or commission in connection with this
transaction. Each Investor agrees to indemnify and to hold harmless the Company
from any liability for any commission or compensation in the nature of a
finders' fee (and the costs and expenses of defending against such liability or
asserted liability) for which the Investor or any of its officers, partners,
employees, or

                                      -15-
<PAGE>   17

representatives is responsible. The Company agrees to indemnify and hold
harmless each Investor from any liability for any commission or compensation in
the nature of a finders' fee (and the costs and expenses of defending against
such liability or asserted liability) for which the Company or any of its
officers, employees or representatives is responsible.

                6.8 Amendments and Waivers. Any term of this Agreement may be
amended 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 with the written consent of the Company and the holders of
a majority of the Shares. Any amendment or waiver effected in accordance with
this Section 6.8 shall be binding upon each holder of any securities purchased
under this Agreement at the time outstanding (including securities into which
such securities are convertible), each future holder of all such securities, and
the Company; provided, however, that no condition set forth in Section 4 hereof
may be waived with respect to any Investor who does not consent thereto.

                6.9 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 the Agreement shall be
interpreted as if such provision were so excluded and shall be enforceable in
accordance with its terms.

                6.10 Exculpation Among Investors. Each Investor acknowledges
that it is not relying upon any person, firm or corporation, other than the
Company and its officers and directors, in making its investment decision to
invest in the Company. Each Investor agrees that no other Investor nor the
respective controlling persons, officers, directors, partners, agents or
employees of any such other Investor shall be liable for any action heretofore
or hereafter taken or omitted to be taken by any of them in connection with each
Investor's purchase of the Shares and Conversion Shares.

                6.11 Expenses. Upon the Closing of the purchase and sale of
securities as contemplated by this Agreement and the exhibits thereto, the
Company shall pay the fees and reasonable expenses of counsel for the Investors,
which fees shall not exceed $15,000.00.

                            (signature page follows)

                                      -16-
<PAGE>   18

        IN WITNESS WHEREOF, the parties have executed this Agreement as of the
date first above written.


                                       XCYTE THERAPIES, INC.


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

                                       Name:
                                            ------------------------------------
                                                          (print)
                                       Title:
                                             -----------------------------------

                                       PURCHASERS:


                                       -----------------------------------------
                                       (Print name of Purchaser)

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

                                       Name:
                                            ------------------------------------
                                                          (print)
                                       Title:
                                             -----------------------------------

     [SIGNATURE PAGE TO XCYTE THERAPIES, INC. SERIES D PURCHASE AGREEMENT]
<PAGE>   19

                                    EXHIBIT A

                              SCHEDULE OF INVESTORS

<TABLE>
<CAPTION>
                                                NUMBER OF SERIES D
INVESTOR NAME AND ADDRESS                        PREFERRED SHARES          AMOUNT OF INVESTMENT
<S>                                             <C>                        <C>
DLJ CAPITAL CORP.                                      6,475                         $18,000.50
3000 Sand Hill Road
Building Three, Suite 170
Menlo Park, CA  94025
Attn:  Philippe Chambon, M.D. Ph.D.

DLJ FIRST ESC L.P.                                    32,374                         $89,999.72
3000 Sand Hill Road
Building Three, Suite 170
Menlo Park, CA  94025
Attn:  Philippe Chambon, M.D. Ph.D.

SPROUT CAPITAL VII, L.P.                              281,622                       $782,909.16
3000 Sand Hill Road
Building Three, Suite 170
Menlo Park, CA  94025
Attn:  Philippe Chambon, M.D. Ph.D.

THE SPROUT CEO FUND, L.P.                              3,270                          $9,090.60
3000 Sand Hill Road
Building Three, Suite 170
Menlo Park, CA  94025
Attn:  Philippe Chambon, M.D. Ph.D.

ARCH VENTURE FUND III, L.P.                           962,230                     $2,674,999.40
1000 Second Avenue, Suite 3700
Seattle, WA  98104-1053
Attn:  Bob Nelsen

ALTA CALIFORNIA PARTNERS, L.P.                        571,491                     $1,588,744.98
One Embarcadero Center, Suite 4050
San Francisco, CA  94111
Attn: Jean Deleage

ALTA EMBARCADERO PARTNERS, LLC                        13,056                         $36,295.68
One Embarcadero Center, Suite 4050
San Francisco, CA  94111
</TABLE>
<PAGE>   20

<TABLE>
<CAPTION>
                                                NUMBER OF SERIES D
INVESTOR NAME AND ADDRESS                        PREFERRED SHARES          AMOUNT OF INVESTMENT
<S>                                             <C>                        <C>
Attn: Jean Deleage

TGI FUND II, LC                                       286,022                       $795,141.16
6501 Columbia Center
701 - 5th Avenue Seattle, WA 98104
Attn:  Michael Beblo and Steven Johnson

FALCON TECHNOLOGY PARTNERS, L.P.                      95,341                        $265,047.98
600 Dorset Road
Devon, PA  19333
Attn: Jim Rathman

VULCAN VENTURES INC.                                  719,424                     $1,999,998.72
110 110th Avenue, NE, Suite 550
Bellevue, WA  98004
Attn:  Ruth B. Kunath

FLUKE CAPITAL MANAGEMENT, L.P.                        89,928                        $249,999.84
11400 SE 6th Street, Suite 230
Bellevue, WA  98004
Attn:  Dennis Weston

TOM ALBERG                                            719,424                     $1,999,998.72
c/o Madrona Investment Group
1000 2nd Avenue
Seattle, WA  98104

MGN OPPORTUNITY GROUP LLC                             359,712                       $999,999.36
Matthew G. Norton Company
The Norton Building
801 Second Avenue, Suite 1300
Seattle, WA  98104
Attn:  Stephen Humphreys
</TABLE>

                                      -2-
<PAGE>   21

<TABLE>
<CAPTION>
                                                NUMBER OF SERIES D
INVESTOR NAME AND ADDRESS                        PREFERRED SHARES          AMOUNT OF INVESTMENT
<S>                                             <C>                        <C>
ARNOLD L. HOLM, JR.                                   36,000                        $100,080.00
Holm Construction Services
310 3rd Avenue NE, Suite 103
Issaquah, WA  98027

HENRY JAMES                                           89,928                        $249,999.84
22420 North Dogwood Lane
Woodway, WA  98020

OKI ENTERPRISES, LLC                                  359,712                       $999,999.36
c/o Scott Oki
10838 Main Street
Bellevue, WA  98004

VLG INVESTMENTS LLC                                   12,619                         $35,080.82
c/o Elias J. Blawie
2800 Sand Hill Road
Menlo Park, CA 94025

VLG ASSOCIATES 2000                                    1,770                          $4,920.60
c/o Elias J. Blawie
2800 Sand Hill Road
Menlo Park, CA 94025

SONYA F. ERICKSON                                      1,799                           $5001.22
4750 Carillon Point
Kirkland, WA 98033

TOTAL                                                4,642,197                   $12,905,307.66
</TABLE>

                                      -3-
<PAGE>   22

                                    EXHIBIT B

                          FORM OF AMENDED AND RESTATED
                          CERTIFICATE OF INCORPORATION
                                 (SEE TAB NO. 4)

<PAGE>   23

                                    EXHIBIT C

                             SCHEDULE OF EXCEPTIONS

<PAGE>   24

                                    EXHIBIT D

                    FORM OF PROPRIETARY INFORMATION AGREEMENT

<PAGE>   25

                                    EXHIBIT E

                          FORM OF AMENDED AND RESTATED
                            INVESTOR RIGHTS AGREEMENT
                                 (SEE TAB NO. 2)

<PAGE>   26

                                    EXHIBIT F

                          FORM OF AMENDED AND RESTATED
                  RIGHT OF FIRST REFUSAL AND CO-SALE AGREEMENT
                                 (SEE TAB NO. 3)

<PAGE>   27

                                    EXHIBIT G

                    FORM OF OPINION OF COUNSEL TO THE COMPANY
                                (SEE TAB NO. 11)