SCHEDULE 14A
(RULE 14A-101)
INFORMATION REQUIRED IN PROXY STATEMENT
SCHEDULE 14A INFORMATION
PROXY STATEMENT PURSUANT TO SECTION 14(A) OF THE SECURITIES
EXCHANGE ACT OF 1934 (AMENDMENT NO. )

Filed by the registrant /X/

Filed by a party other than the registrant / /

Check the appropriate box:

/ / Preliminary proxy statement / / Confidential, for Use of the
Commission Only (as permitted by
Rule 14a-6(e)(2))

/X/ Definitive proxy statement

/ / Definitive additional materials

/ / Soliciting material pursuant to Rule 14a-11(c) or Rule 14a-12
NUVEEN SELECT MATURITIES MUNICIPAL FUND
- --------------------------------------------------------------------------------
(Name of Registrant as Specified in Its Charter)

- --------------------------------------------------------------------------------
(Name of Person(s) Filing Proxy Statement, if other than the Registrant)

Payment of filing fee (Check the appropriate box):

/X/ $125 per Exchange Act Rule 0-11(c)(1)(ii), 14a-6(i)(1), or 14a-6(i)(2) or
Item 22(a)(2) of Schedule 14A.

/ / $500 per each party to the controversy pursuant to Exchange Act Rule
14a-6(i)(3).

/ / Fee computed on table below per Exchange Act Rules 14a-6(i)(4) and 0-11.

(1) Title of each class of securities to which transaction applies:

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

(2) Aggregate number of securities to which transaction applies:

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

(3) Per unit price or other underlying value of transaction computed pursuant to
Exchange Act Rule 0-11 (Set forth the amount on which the filing fee is
calculated and state how it was determined):

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

(4) Proposed maximum aggregate value of transaction:

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

(5) Total fee paid:

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

/ / Fee paid previously with preliminary materials.

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

/ / Check box if any part of the fee is offset as provided by Exchange Act Rule
0-11(a)(2) and identify the filing for which the offsetting fee was paid
previously. Identify the previous filing by registration statement number, or
the form or schedule and the date of its filing.

(1) Amount previously paid:

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

(2) Form, schedule or registration statement no.:

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

(3) Filing party:

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

(4) Date filed:

- --------------------------------------------------------------------------------
2

NOTICE OF ANNUAL MEETING 333 West Wacker Drive
OF SHAREHOLDERS - JULY 25, 1996 Chicago, Illinois
60606
(800) 257-8787

NUVEEN SELECT MATURITIES MUNICIPAL FUND

June 7, 1996

TO THE SHAREHOLDERS OF NUVEEN SELECT MATURITIES MUNICIPAL FUND:

Notice is hereby given that the Annual Meeting of Shareholders of Nuveen Select
Maturities Municipal Fund, a Massachusetts business trust (the "Fund"), will be
held in the 6th floor auditorium of The Northern Trust Company, 50 South LaSalle
Street, Chicago, Illinois, on Thursday, July 25, 1996, at 10:30 a.m., Chicago
time, for the following purposes:

1. To elect six (6) trustees to serve until the next Annual Meeting and
until their successors shall have been duly elected and qualified.

2. To ratify the selection of Ernst & Young LLP as independent auditors for
the fiscal year ending May 31, 1997.

3. To transact such other business as may properly come before the Annual
Meeting.

Shareholders of record at the close of business on May 28, 1996 are entitled to
notice of and to vote at the Annual Meeting.

IN ORDER TO AVOID DELAY AND ADDITIONAL EXPENSE FOR THE FUND, AND TO ASSURE THAT
YOUR SHARES ARE REPRESENTED, IF YOU DO NOT EXPECT TO BE PRESENT IN PERSON AT
YOUR ANNUAL MEETING, YOU ARE REQUESTED TO FILL IN, SIGN AND MAIL THE ENCLOSED
PROXY AS PROMPTLY AS POSSIBLE. NO POSTAGE IS REQUIRED IF MAILED IN THE UNITED
STATES.

James J. Wesolowski
Secretary
3

PROXY STATEMENT 333 West Wacker Drive
JUNE 7, 1996 Chicago, Illinois
60606
(800) 257-8787

NUVEEN SELECT MATURITIES MUNICIPAL FUND

GENERAL INFORMATION

This Proxy Statement is furnished in connection with the solicitation by the
Board of Trustees of Nuveen Select Maturities Municipal Fund (the "Fund") of
proxies to be voted at the Annual Meeting of Shareholders of the Fund to be held
on July 25, 1996 (the "Annual Meeting"), and at any and all adjournments
thereof.

On the matters coming before the Annual Meeting as to which a choice has been
specified by the shareholders on the proxy, the shares will be voted
accordingly. If no choice is so specified, the shares will be voted FOR the
election of the six nominees for trustee, as listed in this Proxy Statement, and
FOR ratification of the selection of Ernst & Young LLP as the Fund's independent
auditors. Shareholders who execute proxies may revoke them at any time before
they are voted by filing with the Fund a written notice of revocation, by
delivering a duly executed proxy bearing a later date, or by attending the
Annual Meeting and voting in person.

A quorum of shareholders is required to take action at the Annual Meeting. A
majority of the shares entitled to vote at the Annual Meeting, represented in
person or by proxy, will constitute a quorum of shareholders at the Annual
Meeting. Votes cast by proxy or in person at the Annual Meeting will be
tabulated by the inspectors of election appointed for the Annual Meeting. The
inspectors of election will determine whether or not a quorum is present at the
Annual Meeting. The inspectors of election will treat abstentions and "broker
non-votes" (i.e., shares held by brokers or nominees, typically in "street
name," as to which (i) instructions have not been received from the beneficial
owners or persons entitled to vote and (ii) the broker or nominee does not have
discretionary voting power on a particular matter) as present for purposes of
determining a quorum.

For purposes of determining the approval of the matters submitted to the
shareholders for a vote, abstentions and broker non-votes will have no effect on
the election of trustees (the six nominees receiving the largest number of votes
will be elected) and will be treated as shares voted against ratification of the
selection of independent auditors. The details of both proposals to be voted on
by the Fund's shareholders and the vote required for approval of each proposal
are set forth under the description of each proposal below.

As of May 28, 1996, there were issued and outstanding 12,370,635 shares of
beneficial interest of the Fund (the "Shares"). Those persons who were
shareholders of record at the close of business on May 28, 1996 will be entitled
to one vote for each Share held.

This Proxy Statement is first being mailed to shareholders of the Fund on or
about June 7, 1996.

1
5

1. ELECTION OF TRUSTEES

At the Annual Meeting, six (6) trustees are to be elected to serve until the
next Annual Meeting and until their successors shall have been duly elected and
qualified. The affirmative vote of a plurality of the shares present and
entitled to vote will be required to elect the trustees of the Fund.

It is the intention of the persons named in the enclosed proxy to vote the
shares represented thereby for the election of the nominees listed below unless
the proxy is marked otherwise. Each of the nominees has agreed to serve as a
trustee if elected; however, should any nominee become unable or unwilling to
accept nomination or election, the proxies will be voted for one or more
substitute nominees designated by the present Board of Trustees.

The table below shows each nominee's age, principal occupations and other
business affiliations, the year in which each nominee was first elected or
appointed a trustee of the Fund, and the number of Shares of the Fund and the
common shares of all funds managed by Nuveen Advisory Corp. (excluding money
market funds) which each nominee beneficially owned as of April 30, 1996. All of
the nominees were last elected to the Board of Trustees at the 1995 annual
meeting of shareholders, except Anthony T. Dean, who will be standing for
election by the Fund's shareholders for the first time at the Annual Meeting to
fill a vacancy that will occur upon the retirement of Richard J. Franke from
John Nuveen & Co. Incorporated and the Board of Trustees of the Fund on June 30,
1996. Mr. Franke's contributions to the Fund are greatly appreciated. As of
April 30, 1996, Mr. Franke owned 1,000 shares of the Fund. In addition to the
vacancy that will occur upon the retirement of Mr. Franke, there is currently
another vacancy on the Board. The Fund's nominating committee is considering
candidates for that vacancy.

THE BOARD OF TRUSTEES UNANIMOUSLY RECOMMENDS THAT SHAREHOLDERS VOTE FOR THE
ELECTION OF THE NOMINEES NAMED BELOW.

2
6

NOMINEES FOR TRUSTEE

- ---------------------------------------------------------------------------------------
FULL SHARES
BENEFICIALLY OWNED
APRIL 30, 1996
--------------------
ALL
NAME, AGE AND PRINCIPAL OCCUPATIONS OF YEAR FIRST ELECTED THE NUVEEN
NOMINEES AS OF APRIL 30, 1996(1) OR APPOINTED A TRUSTEE FUND(2) FUNDS(3)
- ---------------------------------------------------------------------------------------

Lawrence H. Brown (61) 1993 950 3,637
Trustee of the Fund; retired in August
1989 as Senior Vice President of The
Northern Trust Company.
*Anthony T. Dean (51) Nominee 0 5,695
Trustee nominee of the Fund and
President-elect (effective July 1,
1996); President, Chairman-elect
(effective July 1, 1996) and Trustee of
the Select Tax-Free Portfolios advised
by Nuveen Institutional Advisory Corp.
(since July 1994); President-elect
(effective July 1, 1996) and Executive
Vice President and Director of The John
Nuveen Company (since March 1992), John
Nuveen & Co. Incorporated, Nuveen
Advisory Corp. (since October 1992) and
Nuveen Institutional Advisory Corp.
(since October 1992).
Anne E. Impellizzeri (63) 1994 0 2,000
Trustee of the Fund; President and Chief
Executive Officer of Blanton-Peale,
Institutes of Religion and Health (since
December 1990); prior thereto, Vice
President of New York City Partnership
(from 1987 to 1990) and Vice President
of Metropolitan Life Insurance Company
(from 1980 to 1987).
Margaret K. Rosenheim (69) 1992 0 5,329
Trustee of the Fund; Helen Ross
Professor of Social Welfare Policy,
School of Social Service Administration,
University of Chicago.
Peter R. Sawers (63) 1992 1,000 8,281
Trustee of the Fund; Adjunct Professor
of Business and Economics, University
of Dubuque, Iowa (since January 1991);
Adjunct Professor, Lake Forest Graduate
School of Management, Lake Forest,
Illinois (since January 1992); prior
thereto, Executive Director, Towers
Perrin Australia (management
consultant); Chartered Financial
Analyst; Certified Management
Consultant.
*Timothy R. Schwertfeger (47) 1994 0 94,921
President and Trustee of the Fund (since
July 1994), Chairman-elect (effective
July 1, 1996); Chairman-elect (effective
July 1, 1996) and Executive Vice
President and Director of The John
Nuveen Company (since March 1992), John
Nuveen & Co. Incorporated, Nuveen
Advisory Corp. (since October 1992) and
Nuveen Institutional Advisory Corp.
(since October 1992).
- ---------------------------------------------------------------------------------------

(*) "Interested person" as defined in the Investment Company Act of 1940, as
amended, by reason of being an officer or director of the Fund's investment
adviser, Nuveen Advisory Corp.

3
7

(1) The trustee nominees of the Fund, except Anthony T. Dean, are board members
of 21 Nuveen open-end funds and 53 closed-end funds managed by Nuveen Advisory
Corp. ("NAC Funds"). Mr. Dean is a board member nominee of 18 closed-end NAC
Funds and is a board member of five closed-end funds managed by Nuveen
Institutional Advisory Corp. ("NIAC Funds"). Mr. Schwertfeger is a board member
nominee of each of the NIAC Funds.

(2) In addition to the Shares shown in this column, Nuveen Advisory Corp., of
which Messrs. Dean, Franke and Schwertfeger are directors, beneficially owned on
April 30, 1996, 17,689 Shares. No trustee nominee beneficially owned as much as
1% of the outstanding Shares. The above persons have sole voting power and sole
investment power as to the Shares listed.

(3) The number shown reflects the aggregate number of common shares beneficially
owned in all of the NAC Funds referred to in note (1) above (excluding money
market funds).

The trustees affiliated with John Nuveen & Co. Incorporated ("Nuveen") or Nuveen
Advisory Corp. (the "Adviser") serve without any compensation from the Fund.
Trustees who are not affiliated with Nuveen or the Adviser receive a $45,000
annual retainer for serving as a trustee or director, as the case may be, of all
funds sponsored by Nuveen and managed by the Adviser and a $1,000 fee per day
plus expenses for attendance at all meetings held on a day on which a regularly
scheduled Board meeting is held, a $1,000 fee per day plus expenses for
attendance in person or a $500 fee per day plus expenses for attendance by
telephone at a meeting held on a day on which no regular Board meeting is held,
and a $250 fee per day plus expenses for attendance in person or by telephone at
a meeting of the executive committee. The annual retainer, fees and expenses are
allocated among the funds managed by the Adviser on the basis of relative net
asset sizes. The Fund has adopted a Directors' Deferred Compensation Plan
pursuant to which a trustee of the Fund may elect to have all or a portion of
the trustee's fee deferred. Trustees may defer fees for any calendar year by the
execution of a Participation Agreement prior to the beginning of the calendar
year during which the trustee wishes to begin deferral.

The table below shows, for each trustee who is not affiliated with Nuveen or the
Adviser, the aggregate compensation paid by the Fund for its fiscal year ended
May 31, 1996 and the total compensation that the Nuveen funds accrued for each
trustee during the calendar year 1995, including any interest accrued for
trustees on deferred compensation. The rate of earnings on deferred compensation
is equivalent to the average net earnings rate, computed on a quarterly basis,
on the shares of such Nuveen fund.

- ---------------------------------------------------------------------------------------
AGGREGATE TOTAL COMPENSATION
COMPENSATION NUVEEN FUNDS
NAME OF TRUSTEE FROM THE FUND ACCRUED FOR TRUSTEES(1)
- ---------------------------------------------------------------------------------------

Lawrence H. Brown $385 $55,500
Anne E. Impellizzeri $385 $63,000
Margaret K. Rosenheim $403 $62,322(2)
Peter R. Sawers $385 $55,500
- ---------------------------------------------------------------------------------------

(1) Includes compensation for service on the boards of the NAC Funds.

(2) Includes $1,572 in interest accrued on deferred compensation from prior
years.

Richard J. Franke, Margaret K. Rosenheim and Timothy R. Schwertfeger currently
serve as members of the executive committee of the Board of Trustees. The
executive committee, which meets between regular meetings of the Board of
Trustees, is authorized to exercise all

4
8

of the powers of the Board of Trustees. The executive committee held twelve
meetings during the fiscal year ended May 31, 1996.

The Fund's Board of Trustees has an audit committee composed of Lawrence H.
Brown, Anne E. Impellizzeri, Margaret K. Rosenheim and Peter R. Sawers, trustees
of the Fund who are not "interested persons." The audit committee reviews the
work and any recommendations of the Fund's independent auditors. Based on such
review, it is authorized to make recommendations to the Board of Trustees. The
audit committee held two meetings during the fiscal year ended May 31, 1996.

Nomination of those trustees who are not "interested persons" of the Fund is
committed to a nominating committee composed of the trustees who are not
"interested persons" of the Fund. It identifies and recommends individuals to be
nominated for election as non-interested trustees. The nominating committee held
one meeting during the fiscal year ended May 31, 1996. No policy or procedure
has been established as to the recommendation of trustee nominees by
shareholders.

The Board of Trustees held six meetings during the fiscal year ended May 31,
1996. During the last fiscal year, each trustee attended 75% or more of the
Fund's Board meetings and the committee meetings (if a member thereof), except
that Mr. Franke was unable to attend certain executive committee meetings held
solely to declare dividends. His attendance at all executive committee meetings
which he was scheduled to attend was less than 75%.

The following table sets forth information as of April 30, 1996 with respect to
each executive officer of the Fund, other than executive officers who are
trustees and reflected above. Officers of the Fund receive no compensation from
the Fund. The term of office of all officers will expire at the first meeting of
the Board of Trustees of the Fund after the Annual Meeting, which Board of
Trustees' meeting is presently scheduled to be held on July 25, 1996; however,
as previously mentioned, Mr. Franke will be retiring from the Board of Trustees
effective June 30, 1996.

- ------------------------------------------------------------------------------
NAME, AGE AND PRINCIPAL OCCUPATIONS FOR PAST POSITIONS AND OFFICES WITH
FIVE YEARS FUND
- ------------------------------------------------------------------------------

William M. Fitzgerald, 32 Vice President
Vice President of Nuveen Advisory Corp. (since (since 1996)
December 1995); prior thereto, Assistant
Vice President (from September 1992 to
December 1995) and Assistant Portfolio Manager
(from June 1988 to September 1992) of Nuveen
Advisory Corp.
Kathleen M. Flanagan, 48 Vice President
Vice President of John Nuveen & Co. (since 1994)
Incorporated.
Richard J. Franke, 64 Chairman of the Board
Chairman of the Board and Director of The John (since the Fund's
Nuveen Company (since March 1992), John organization)
Nuveen & Co. Incorporated, Nuveen Advisory
Corp. and Nuveen Institutional Advisory Corp.;
formerly Chairman of the Board and Board
Member of the Nuveen Funds advised by Nuveen
Institutional Advisory Corp. (from inception
to August 1994); Certified Financial Planner.

5
9

J. Thomas Futrell, 40 Vice President
Vice President of Nuveen Advisory Corp. (since 1992)
Steven J. Krupa, 38 Vice President
Vice President of Nuveen Advisory Corp. (since 1992)
Anna R. Kucinskis, 50 Vice President
Vice President of John Nuveen & Co. (since 1992)
Incorporated.
Larry W. Martin, 44 Vice President (since 1993) &
Vice President (since September 1992), Assistant Secretary (since
Assistant Secretary and Assistant General 1992)
Counsel of John Nuveen & Co. Incorporated;
Vice President (since May 1993) and Assistant
Secretary of Nuveen Advisory Corp.; Vice
President (since May 1993) and Assistant
Secretary (since January 1992) of Nuveen
Institutional Advisory Corp.; Assistant
Secretary (since February 1993) of The John
Nuveen Company; Director of Nuveen, Duff &
Phelps Investment Advisors (since January
1995).
O. Walter Renfftlen, 56 Vice President & Controller
Vice President and Controller of The John (since 1992)
Nuveen Company (since March 1992), John
Nuveen & Co. Incorporated, Nuveen Advisory
Corp. and Nuveen Institutional Advisory Corp.
Thomas C. Spalding, Jr., 44 Vice President
Vice President of Nuveen Advisory Corp. and (since 1992)
Nuveen Institutional Advisory Corp.;
Chartered Financial Analyst.
H. William Stabenow, 61 Vice President & Treasurer
Vice President and Treasurer of The John (since 1992)
Nuveen Company (since March 1992), John
Nuveen & Co. Incorporated, Nuveen Advisory
Corp. and Nuveen Institutional Advisory Corp.
(since January 1992).
James J. Wesolowski, 45 Vice President & Secretary
Vice President, General Counsel and Secretary (since 1992)
of The John Nuveen Company (since March
1992), John Nuveen & Co. Incorporated, Nuveen
Advisory Corp. and Nuveen Institutional
Advisory Corp.
Gifford R. Zimmerman, 39 Vice President (since 1993) &
Vice President (since September 1992), Assistant Secretary (since
Assistant Secretary and Assistant General 1992)
Counsel of John Nuveen & Co. Incorporated;
Vice President (since May 1993) and Assistant
Secretary of Nuveen Advisory Corp.; Vice
President (since May 1993) and Assistant
Secretary (since January 1992) of Nuveen
Institutional Advisory Corp.

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

On April 30, 1996, trustees and executive officers of the Fund as a group
beneficially owned 2,950 Shares (less than 1%). On April 30, 1996, trustees,
trustee nominees and executive officers of the Fund as a group beneficially
owned 315,656 common shares of all funds

6
10

managed by the Adviser (excluding money market funds). As of April 30, 1996, no
person is known to the Fund to have owned beneficially more than five percent of
the shares of the Fund.

Section 30(f) of the Investment Company Act of 1940, as amended (the "1940
Act"), and Section 16(a) of the Securities Exchange Act of 1934, as amended,
require the Fund's officers and trustees, investment adviser, affiliated persons
of the investment adviser and persons who own more than ten percent of a
registered class of the Fund's equity securities to file forms reporting their
affiliation with the Fund and reports of ownership and changes in ownership of
Fund shares with the Securities and Exchange Commission (the "SEC") and the New
York Stock Exchange. These persons and entities are required by SEC regulation
to furnish the Fund with copies of all Section 16(a) forms they file. Based on a
review of these forms furnished to the Fund, the Fund believes that during the
fiscal year ended May 31, 1996, all Section 16(a) filing requirements applicable
to the Fund's officers and trustees, investment adviser and affiliated persons
of the investment adviser were complied with.

2. SELECTION OF INDEPENDENT AUDITORS

The members of the Fund's Board who are not "interested persons" of the Fund
have unanimously selected Ernst & Young LLP, independent public accountants, as
independent auditors, to audit the books and records of the Fund for the fiscal
year ending May 31, 1997. Ernst & Young LLP has served the Fund in this capacity
since the Fund was organized and has no direct or indirect financial interest in
the Fund except as independent auditors. The selection of Ernst & Young LLP as
independent auditors of the Fund is being submitted to the shareholders for
ratification, which requires the affirmative vote of a majority of the Shares of
the Fund present and entitled to vote on the matter. A representative of Ernst &
Young LLP is expected to be present at the Annual Meeting and will be available
to respond to any appropriate questions raised at the Annual Meeting and to make
a statement if he or she wishes.

THE BOARD OF TRUSTEES UNANIMOUSLY RECOMMENDS THAT SHAREHOLDERS VOTE FOR THE
RATIFICATION OF THE SELECTION OF INDEPENDENT AUDITORS.

INFORMATION ABOUT THE FUND'S INVESTMENT ADVISER

The Adviser, located at 333 West Wacker Drive, Chicago, Illinois, serves as
investment adviser and manager for the Fund since it was organized. The Adviser
is a wholly-owned subsidiary of Nuveen, 333 West Wacker Drive, Chicago, Illinois
60606. Nuveen is a subsidiary of The John Nuveen Company which in turn is
approximately 78% owned by The St. Paul Companies, Inc., ("St. Paul"). St. Paul
is located at 385 Washington Street, St. Paul, Minnesota 55102, and is
principally engaged in providing property-liability insurance through
subsidiaries. Nuveen acted as co-managing underwriter for the Fund in its
initial public offering of Shares in September 1992.

SHAREHOLDER PROPOSALS

To be considered for presentation at the Annual Meeting of Shareholders to be
held in 1997, a shareholder proposal must be received at the offices of the
Fund, 333 West Wacker Drive, Chicago, Illinois 60606, not later than February 7,
1997.

7
11

EXPENSES OF PROXY SOLICITATION

The cost of preparing, printing and mailing the enclosed proxy, accompanying
notice and proxy statement, and all other costs in connection with the
solicitation of proxies, will be paid by the Fund. Additional solicitation may
be made by letter, telephone or telegraph by officers of the Fund, by officers
or employees of John Nuveen & Co. Incorporated or Nuveen Advisory Corp., or by
dealers and their representatives. The Fund has engaged Tritech Services to
assist in the solicitation of proxies at a total estimated cost of $2,000.

ANNUAL REPORT DELIVERY

The Fund's annual report for the fiscal year ended May 31, 1995 was sent to
shareholders of record following the Fund's fiscal year end. THE FUND WILL
FURNISH, WITHOUT CHARGE, A COPY OF ITS MAY 31, 1995 ANNUAL REPORT AND ITS MORE
RECENT SEMI ANNUAL REPORT UPON REQUEST. SUCH WRITTEN OR ORAL REQUEST SHOULD BE
DIRECTED TO THE FUND AT 333 WEST WACKER DRIVE, CHICAGO, ILLINOIS 60606 OR BY
CALLING 1-800-257-8787.

GENERAL

Management does not intend to present and does not have reason to believe that
others will present any other items of business at the Annual Meeting. However,
if other matters are properly presented to the Annual Meeting for a vote, the
proxies will be voted upon such matters in accordance with the judgment of the
persons acting under the proxies.

A list of shareholders entitled to be present and to vote at the Annual Meeting
will be available at the offices of the Fund, 333 West Wacker Drive, Chicago,
Illinois, for inspection by any shareholder during regular business hours for
ten days prior to the date of the Annual Meeting.

Failure of a quorum to be present at the Annual Meeting will necessitate
adjournment and will subject the Fund to additional expense. The persons named
in the enclosed proxy may also move for an adjournment of the Annual Meeting to
permit further solicitation of proxies with respect to any of the proposals if
they determine that adjournment and further solicitation is reasonable and in
the best interests of the shareholders. Under the Fund's By-Laws, an adjournment
of a meeting requires the affirmative vote of a majority of the shares present
in person or represented by proxy at the meeting.

IF YOU CANNOT BE PRESENT IN PERSON, YOU ARE REQUESTED TO FILL IN, SIGN AND
RETURN THE ENCLOSED PROXY PROMPTLY. NO POSTAGE IS REQUIRED IF MAILED IN THE
UNITED STATES.

James J. Wesolowski
Secretary

8
12

NIM796
13
PROXY BALLOT

NUVEEN SELECT MATURITIES MUNICIPAL FUND

COMMON SHARES
PROXY SOLICITED BY THE BOARD OF TRUSTEES
FOR ANNUAL MEETING OF SHAREHOLDERS
TO BE HELD ON JULY 25, 1996

The undersigned hereby appoints Timothy R. Schwertfeger and James J.
Wesolowski, and each of them, with full power of substitution, Proxies for
the undersigned to represent and vote the common shares of the undersigned at
the Annual Meeting of Shareholders of Nuveen Select Maturities Municipal Fund
to be held on July 25, 1996, or any adjournment or adjournments thereof:

1. Election of Trustees:

NOMINEES: Lawrence H. Brown, Anthony T. Dean, Anne E. Impellizzeri,
Margaret K. Rosenheim, Peter R. Sawers, and Timothy R. Schwertfeger.

2. Ratification of the selection of Ernst & Young LLP as independent auditors
for the fiscal year ending May 31, 1997.

3. In their discretion, the Proxies are authorized to vote upon such other
business as may properly come before the Annual Meeting.

------------------------------------------------------------------------
You are encouraged to specify your choices by marking the appropriate
boxes ON THE REVERSE SIDE. If you do not mark any boxes, your Proxy
will be voted in accordance with the Board of Trustees' recommendations.
Please sign, date and return this Proxy card promptly using the enclosed
envelope.
------------------------------------------------------------------------
SEE REVERSE SIDE
NIM796

THE BOARD OF TRUSTEES RECOMMENDS A VOTE FOR ALL NOMINEES AND THE PROPOSAL: Please mark your votes as in this example. [X]
- ------------------------------------------------------------------------------------------------------------------------------------

1. ELECTION OF TRUSTEES: [ ] FOR [ ] WITHHOLD authority [ ] WITHHOLD authority
(SEE REVERSE FOR NOMINEES) all nominees to vote for all nominees to vote for nominees
as indicated below:

INSTRUCTIONS:
To grant authority to vote FOR ALL nominees, mark the box on the left above OR do not mark any box above. -----------------------
To WITHHOLD authority to vote FOR ALL nominees, mark the box in the middle above.
To WITHHOLD authority to vote FOR ANY ONE OR MORE of the nominees, mark the box on the right above AND write each nominee's
name in the space provided.

2. RATIFICATION OF THE SELECTION OF ERNST & YOUNG LLP AS INDEPENDENT AUDITORS FOR THE FISCAL YEAR ENDING MAY 31, 1997.

FOR AGAINST ABSTAIN
[ ] [ ] [ ]

3. IN THEIR DISCRETION, THE PROXIES ARE AUTHORIZED TO VOTE UPON SUCH OTHER BUSINESS AS MAY PROPERLY COME BEFORE THE
ANNUAL MEETING.

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

THE SHARES TO WHICH THIS PROXY RELATES WILL BE VOTED AS SPECIFIED. IF NO SPECIFICATION IS MADE, SUCH SHARES WILL BE VOTED FOR THE
ELECTION OF TRUSTEES AND FOR THE PROPOSAL SET FORTH ON THIS PROXY.

-Please be sure to sign and date this Proxy.

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

Shareholder sign here----------------------Date--------------

Co-owner sign here-------------------------Date--------------

NOTE: Please sign exactly as your name appears on this Proxy.
If signing for estates, trusts or corporations, title or capacity
should be stated. If shares are held jointly, each holder
should sign.

[ ] BK NIM796 NIM796