<PAGE>   1
                                                               EXHIBIT 10.10 (f)

                         INVESTMENT MANAGEMENT AGREEMENT

AGREEMENT made as of the 1st day of February, l999, by and between NUVEEN MONEY
MARKET TRUST, a Massachusetts business trust (the "Trust"), and NUVEEN ADVISORY
CORP., a Delaware corporation (the "Adviser").

                                   WITNESSETH

In consideration of the mutual covenants hereinafter contained, it is hereby
agreed by and between the parties hereto as follows:

1. The Trust hereby employs the Adviser to act as the investment adviser for,
and to manage the investment and reinvestment of the assets of each of the
Trust's series as set forth on Exhibit A attached hereto (the "Funds") or as may
exist from time to time in accordance with the Trust's investment objective and
policies and limitations relating to such Fund, and to administer the Trust's
affairs to the extent requested by and subject to the supervision of the Board
of Trustees of the Trust for the period and upon the terms herein set forth. The
investment of the assets of each Fund shall be subject to the Trust's policies,
restrictions and limitations with respect to securities investments as set forth
in the Trust's registration statement on Form N-1A under the Securities Act of
1933 and the Investment Company Act of l940 covering the Trust's Funds' shares
of beneficial interest, including the Prospectus and Statement of Additional
Information forming a part thereof, all as filed with the Securities and
Exchange Commission and as from time to time amended, and


<PAGE>   2


all applicable laws and the regulations of the Securities and Exchange
Commission relating to the management of registered open-end, management
investment companies.

The Adviser accepts such employment and agrees during such period to render such
services, to furnish office facilities and equipment and clerical, bookkeeping
and administrative services (other than such services, if any, provided by the
Trust's custodian, transfer agent and shareholder service agent, and the like)
for the Trust, to permit any of its officers or employees to serve without
compensation as trustees or officers of the Trust if elected to such positions,
and to assume the obligations herein set forth for the compensation herein
provided. The Adviser shall, for all purposes herein provided, be deemed to be
an independent contractor and, unless otherwise expressly provided or
authorized, shall have no authority to act for nor represent the Trust in any
way, nor otherwise be deemed an agent of the Trust.

2. For the services and facilities described in Section l, the Trust will pay to
the Adviser, at the end of each calendar month, an investment management fee
related to each of the Trust's Funds. For each Fund, calculated separately,
except the Nuveen Municipal Money Market Fund and Nuveen Money Market Fund, the
fees shall be computed at the rate of:

                    RATE                      NET ASSETS
                    ----                      ----------
                   .4000%            For the first $125 million
                   .3875%            For the next $125 million
                   .3750%            For the next $250 million
                   .3625%            For the next $500 million
                   .3500%            For the next $1 billion
                   .3250%            For assets over $2 billion

For Nuveen Money Market Fund, the fees shall be computed at the rate of:

                                                                               2
<PAGE>   3

                     RATE                     NET ASSETS
                     ----                     ----------
                    .4500%           For the first $125 million
                    .4375%           For the next $125 million
                    .4250%           For the next $250 million
                    .4125%           For the next $500 million
                    .4000%           For the next $1 billion
                    .3750%           For assets over $2 billion

For Nuveen Municipal Money Market Fund, the fees shall be computed at the rate
of:
                     RATE                     NET ASSETS
                     ----                     ----------
                    .5000%           For the first $125 million
                    .4875%           For the next $125 million
                    .4750%           For the next $250 million
                    .4625%           For the next $500 million
                    .4500%           For the next $1 billion
                    .4250%           For assets over $2 billion

For the month and year in which this Agreement becomes effective or terminates,
and for any month and year in which a Fund is added or eliminated from the
Trust, there shall be an appropriate proration on the basis of the number of
days that the Agreement shall have been in effect, or the Fund shall have
existed, during the month and year, respectively. The services of the Adviser to
the Trust under this Agreement are not to be deemed exclusive, and the Adviser
shall be free to render similar services or other services to others so long as
its services hereunder are not impaired thereby.

3. The net asset value of each Fund shall be calculated as provided in the
Declaration of Trust of the Trust. On each day when net asset value is not
calculated, the net asset value of a share of beneficial interest of a Fund
shall be deemed to be the net asset value of such share as of the close of


                                                                               3
<PAGE>   4


business on the last day on which such calculation was made for the purpose of
the foregoing computations.

4. Regardless of any of the above provisions, the Adviser guarantees that the
total expenses of each Fund in any fiscal year, exclusive of taxes, interest,
brokerage commissions, and extraordinary expenses such as litigation costs,
shall not exceed, and the Adviser undertakes to pay or refund to the Fund any
amount up to but not greater than the aggregate fees received by the Adviser
under this Agreement for such fiscal year, the limitation imposed by any
jurisdiction in which the Trust continues to offer and sell shares of the Fund
after exceeding such limitation. Except as otherwise agreed to by the Trust or
the Adviser or unless otherwise required by the law or regulation of any state,
any reimbursement by the Adviser to a Fund under this section shall not exceed
the management fee payable to the Adviser by a Fund under this Agreement.

5. The Adviser shall arrange for officers or employees of the Adviser to serve,
without compensation from the Trust, as trustees, officers or agents of the
Trust, if duly elected or appointed to such positions, and subject to their
individual consent and to any limitations imposed by law.

6. Subject to applicable statutes and regulations, it is understood that
officers, trustees, or agents of the Trust are, or may be, interested in the
Adviser as officers, directors, agents, shareholders or otherwise, and that the
officers, directors, shareholders and agents of the Adviser may be interested in
the Trust otherwise than as trustees, officers or agents.


                                                                               5
<PAGE>   5

7. The Adviser shall not be liable for any loss sustained by reason of the
purchase, sale or retention of any security, whether or not such purchase, sale
or retention shall have been based upon the investigation and research made by
any other individual, firm or corporation, if such recommendation shall have
been selected with due care and in good faith, except loss resulting from
willful misfeasance, bad faith, or gross negligence on the part of the Adviser
in the performance of its obligations and duties, or by reason of its reckless
disregard of its obligations and duties under this Agreement.

8. The Adviser currently manages other investment accounts and Trusts, including
those with investment objectives similar to the Trust, and reserves the right to
manage other such accounts and funds in the future. Securities considered as
investments for a Fund of the Trust may also be appropriate for other Funds or
for other investment accounts and funds that may be managed by the Adviser.
Subject to applicable laws and regulations, the Adviser will attempt to allocate
equitably portfolio transactions among the Trust's Funds and the portfolios of
its other investment accounts and funds purchasing securities whenever decisions
are made to purchase or sell securities by a Fund and another fund's portfolio
or one or more of such other accounts or funds simultaneously. In making such
allocations, the main factors to be considered by the Adviser will be the
respective investment objectives of the Trust's Fund or Funds purchasing such
securities and such other accounts and funds, the relative size of portfolio
holdings of the same or comparable securities, the availability of cash for
investment by the Trust's Funds and such other accounts and funds, the size of
investment commitments generally held by the Trust's Funds and such accounts and
funds, and



                                                                               6
<PAGE>   6


the opinions of the persons responsible for recommending investments to the
Trust and such other accounts and funds.

9. This Agreement shall continue in effect until August 1, 2000, unless and
until terminated by either party as hereinafter provided, and shall continue in
force from year to year thereafter, but only as long as such continuance is
specifically approved, at least annually, in the manner required by the
Investment Company Act of l940.

This Agreement shall automatically terminate in the event of its assignment, and
may be terminated at any time without the payment of any penalty by the Trust or
by the Adviser upon sixty (60) days' written notice to the other party. The
Trust may effect termination by action of the Board of Trustees, or, with
respect to any Trust Fund, by vote of a majority of the outstanding voting
securities of that Fund, accompanied by appropriate notice.

This Agreement may be terminated, at any time, without the payment of any
penalty, by the Board of Trustees of the Trust, or, with respect to any Trust
Fund, by vote of a majority of the outstanding voting securities of that Fund,
in the event that it shall have been established by a court of competent
jurisdiction that the Adviser, or any officer or director of the Adviser, has
taken any action which results in a breach of the covenants of the Adviser set
forth herein.

Termination of this Agreement shall not affect the right of the Adviser to
receive payments on any unpaid balance of the compensation, described in Section
2, earned prior to such termination.


                                                                               6
<PAGE>   7


10. If any provision of this Agreement shall be held or made invalid by a court
decision, statute, rule, or otherwise, the remainder shall not be thereby
affected.

11. The Adviser and its affiliates reserve the right to grant, at any time, the
use of the name "Nuveen", or any approximation or abbreviation thereof, to any
other investment company or business enterprise. Upon termination of this
Agreement by either party, or by its terms, the Trust shall thereafter refrain
from using any name of the Trust which includes "Nuveen" or any approximation or
abbreviation thereof, or is sufficiently similar to such name as to be likely to
cause confusion with such name, and shall not allude in any public statement or
advertisement to the former association.

12. Any notice under this Agreement shall be in writing, addressed and delivered
or mailed, postage prepaid, to the other party at such address as such other
party may designate for receipt of such notice.





                                                                               7
<PAGE>   8


13. The Trust's Declaration of Trust is on file with the Secretary of the
Commonwealth of Massachusetts. This Agreement is executed on behalf of the Trust
by the Trust's officers as officers and not individually and the obligations
imposed upon the Trust by this Agreement are not binding upon any of the Trust's
Trustees, officers or shareholders individually but are binding only upon the
assets and property of the Trust.

         IN WITNESS WHEREOF, the Trust and the Adviser have caused this
Agreement to be executed on the day and year above written.

                                             NUVEEN MONEY MARKET TRUST



                                             by:
                                                -------------------------
                                                     Vice President



Attest:
        --------------------
         Assistant Secretary


                                             NUVEEN ADVISORY CORP.



                                             by:
                                                -------------------------
                                                     Vice President



Attest:
        --------------------
         Assistant Secretary




                                                                               8
<PAGE>   9
                                                                       Exhibit A


                        Nuveen Money Market Fund
                        Nuveen Municipal Money Market Fund
                        Nuveen Institutional Tax-Exempt Money Market Fund
                        Nuveen California Tax-Exempt Money Market Fund
                        Nuveen New York Tax-Exempt Money Market Fund








                                                                               9