NUVEEN SELECT MATURITIES MUNICIPAL FUND
DEF 14A, 1995-06-14
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<PAGE>
                           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 Section 240.14a-11(c) or Section 240.14a-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 Rules 0-11(c)(1)(ii), 14a-6(i)(1), 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:

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

Notes:
<PAGE>
 
                            NUVEEN SELECT MATURITIES
                                 MUNICIPAL FUND
 
                 333 WEST WACKER DRIVE, CHICAGO, ILLINOIS 60606
                            TELEPHONE (312) 917-7700
 
                    NOTICE OF ANNUAL MEETING OF SHAREHOLDERS
 
                                 JULY 26, 1995
 
                                                                   June 16, 1995
 
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 Wednesday, July 26, 1995, 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 or reject the selection of Ernst & Young LLP as independent
  auditors for the fiscal year ending May 31, 1996.
 
    3. To transact such other business as may properly come before the
  Annual Meeting.
 
  Shareholders of record at the close of business on May 31, 1995 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
<PAGE>
 
                            NUVEEN SELECT MATURITIES
                                 MUNICIPAL FUND
 
                 333 WEST WACKER DRIVE, CHICAGO, ILLINOIS 60606
                            TELEPHONE (312) 917-7700
 
                                PROXY STATEMENT
 
                                                                   June 16, 1995
 
                              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 26, 1995 (the "Annual Meeting"), and at any and all adjournments
thereof. 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. The Fund's annual report for the fiscal year ended May 31, 1994 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, 1994 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.
 
  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.
 
                                       1
<PAGE>
 
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 31, 1995, there were issued and outstanding 12,365,146 shares of
beneficial interest of the Fund (the "Shares"). Those persons who were
shareholders of record at the close of business on May 31, 1995 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 16, 1995.
 
                            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 May 15, 1995. All of
the nominees were last elected to the Board of Trustees at the 1994 annual
meeting of shareholders.
 
  The members of the Board of Trustees mourn the recent passing of John E.
O'Toole, a trustee since the Fund's organization. There is currently a vacancy
on the Board. The Fund's nominating committee is considering candidates for the
vacancy, and will report to the full Board later this summer.
 
                                       2
<PAGE>
 
                             NOMINEES FOR TRUSTEE
 
<TABLE>
<CAPTION>
                                                                       FULL SHARES
                                                                    BENEFICIALLY OWNED
                                                                       MAY 15, 1995
                                                        YEAR FIRST  ------------------
                                                         ELECTED                ALL
NAME AND AGE OF NOMINEES                               OR APPOINTED   THE     NUVEEN
   AS OF MAY 15, 1995       PRINCIPAL OCCUPATIONS(1)    A TRUSTEE   FUND (2) FUNDS (3)
- ------------------------    ------------------------   ------------ -------- ---------
<S>                       <C>                          <C>          <C>      <C>
*Richard J. Franke (63)   Chairman of the Board and        1992      1,000    20,625
                            Trustee of the Fund;
                            Chairman of the Board and
                            Director of The John
                            Nuveen Company (since
                            March 1992), John Nuveen
                            & Co. Incorporated,
                            Nuveen Advisory Corp. and
                            Nuveen Institutional Ad-
                            visory Corp.; formerly
                            Chairman of the Board and
                            Board Member of the
                            Nuveen Funds advised by
                            Nuveen Institutional Ad-
                            visory Corp. (from incep-
                            tion to August 1994);
                            Certified Financial Plan-
                            ner.
*Timothy R. Schwertfeger  President and Trustee of         1994          0    88,620
 (46)                       the Fund (since July
                            1994); Executive Vice
                            President and Director of
                            The John Nuveen Company
                            (since March 1992) and
                            John Nuveen & Co. Incor-
                            porated; Director of
                            Nuveen Advisory Corp.
                            (since October 1992) and
                            Nuveen Institutional Ad-
                            visory Corp. (since Octo-
                            ber 1992).
Lawrence H. Brown (60)    Trustee of the Fund; re-         1993        899     3,445
                            tired in August 1989 as
                            Senior Vice President of
                            The Northern Trust Compa-
                            ny.
Anne E. Impellizzeri      Trustee of the Fund; Presi-      1994          0     2,000
(62)                        dent and Chief Executive
                            Officer of Blanton-Peale,
                            Institutes of Religion
                            and Health (since Decem-
                            ber 1990); prior thereto,
                            Vice President of New
                            York City Partnership
                            (from 1987 to 1990) and
                            Vice President of Metro-
                            politan Life Insurance
                            Company (from 1980 to
                            1987).
Margaret K. Rosenheim     Trustee of the Fund; Helen       1992          0     5,015
(68)                        Ross Professor of Social
                            Welfare Policy, School of
                            Social Service
                            Administration, Univer-
                            sity of Chicago.
</TABLE>
- -----------
  (*) "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
<PAGE>
 
<TABLE>
<CAPTION>
                                                          FULL SHARES
                                                       BENEFICIALLY OWNED
 NAME AND                                                 MAY 15, 1995
  AGE OF                                   YEAR FIRST  ------------------
NOMINEES AS                                 ELECTED                ALL
OF MAY 15,                                OR APPOINTED   THE     NUVEEN
   1995        PRINCIPAL OCCUPATIONS(1)    A TRUSTEE   FUND (2) FUNDS (3)
- -----------    ------------------------   ------------ -------- ---------
<S>          <C>                          <C>          <C>      <C>
Peter R.     Trustee of the Fund; Ad-         1992      1,000     7,825
Sawers (62)    junct Professor of Busi-
               ness and Economics, Uni-
               versity of Dubuque, Iowa
               (since January 1991); Ad-
               junct Professor, Lake
               Forest Graduate School of
               Management, Lake Forest,
               Illinois (since January
               1992); prior thereto, Ex-
               ecutive Director, Towers
               Perrin Australia (manage-
               ment consultant); Chart-
               ered Financial Analyst;
               Certified Management Con-
               sultant.
</TABLE>
 
  (1) The trustee nominees of the Fund are trustees or directors, as the case
may be, of 21 Nuveen open-end funds and 55 Nuveen closed-end funds.
 
  (2) In addition to the Shares shown in this column, Nuveen Advisory Corp.,
of which Richard J. Franke and Timothy R. Schwertfeger are directors,
beneficially owned on May 15, 1995, 17,689 full 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 by the nominee in all of the funds managed by Nuveen
Advisory Corp. and 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
 
                                       4
<PAGE>
 
May 31, 1995 and the total compensation that the Nuveen funds accrued for each
trustee during the calendar year 1994, 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.
 
<TABLE>
<CAPTION>
                           AGGREGATE     TOTAL COMPENSATION
                         COMPENSATION       NUVEEN FUNDS
NAME OF TRUSTEE          FROM THE FUND ACCRUED FOR TRUSTEES(1)
- ---------------          ------------- -----------------------
<S>                      <C>           <C>
Lawrence H. Brown           $336.76            56,500
Anne E. Impellizzeri(2)     $336.76            48,750
Margaret K. Rosenheim       $352.96            64,404(3)
Peter R. Sawers             $336.76            56,000
</TABLE>
- -----------
 
  (1) Includes compensation for service on the boards of 21 Nuveen open-end
funds and 55 Nuveen closed-end funds. Also includes amounts for Nuveen funds
that existed for part of the year, estimated as if the funds had existed for
the entire year.
 
  (2) Anne E. Impellizzeri was appointed a trustee in April 1994.
 
  (3) Includes $1,404 in interest accrued on deferred compensation from prior
years.
 
  Richard J. Franke, Margaret K. Rosenheim and Timothy R. Schwertfeger 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 of the powers of the Board of Trustees. The
executive committee held thirteen meetings during the fiscal year ended May
31, 1995.
 
  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, 1995.
 
  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, 1995. 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,
1995. 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 only which he was scheduled to attend was less than 75%.
 
                                       5
<PAGE>
 
  The following table sets forth information as of May 15, 1995 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 26, 1995.
 
<TABLE>
<CAPTION>
                             POSITIONS AND
        NAME          AGE  OFFICES WITH FUND    PRINCIPAL OCCUPATIONS
        ----          ---  -----------------    ---------------------
<S>                   <C> <C>                 <C>
Kathleen M. Flanagan   48 Vice President      Vice President of John
                          (since 1994)          Nuveen & Co. Incorporat-
                                                ed.
J. Thomas Futrell      39 Vice President      Vice President of Nuveen
                          (since 1992)          Advi-sory Corp. (since
                                                February 1991); prior
                                                thereto, Assistant Vice
                                                President of Nuveen Ad-
                                                visory Corp. (from Au-
                                                gust 1988 to February
                                                1991); Chartered Finan-
                                                cial Analyst.
Steven J. Krupa        37 Vice President      Vice President of Nuveen
                          (since 1992)          Advi-sory Corp. (since
                                                October 1990); prior
                                                thereto, Vice President
                                                of John Nuveen & Co. In-
                                                corporated (from January
                                                1989 to October 1990).
Anna R. Kucinskis      49 Vice President      Vice President of John
                          (since 1992)          Nuveen & Co. Incorporat-
                                                ed.
Larry W. Martin        43 Vice President      Vice President (since Sep-
                          (since 1993) &        tember 1992), Assistant
                          Assistant Secretary   Secretary and Assistant
                          (since 1992)          General Counsel of John
                                                Nuveen & Co. Incorpo-
                                                rated; Vice President
                                                (since May 1993) and As-
                                                sistant Secretary of
                                                Nuveen Advisory Corp.;
                                                Vice President (since
                                                May 1993) and Assistant
                                                Secretary (since January
                                                1992) of Nuveen Institu-
                                                tional Advisory Corp.;
                                                Assistant Secretary
                                                (since February 1993) of
                                                The John Nuveen Company;
                                                Director of Nuveen, Duff
                                                & Phelps Investment Ad-
                                                visors (since January
                                                1995).
O. Walter Renfftlen    55 Vice President &    Vice President and Con-
                          Controller (since     troller of The John
                          1992)                 Nuveen Company (since
                                                March 1992), John Nuveen
                                                & Co. Incorporated,
                                                Nuveen Advisory Corp.
                                                and Nuveen Institutional
                                                Advisory Corp.
</TABLE>
 
 
                                       6
<PAGE>
 
<TABLE>
<CAPTION>
                               POSITIONS AND
         NAME            AGE OFFICES WITH FUND   PRINCIPAL OCCUPATIONS
         ----            --- -----------------   ---------------------
<S>                      <C> <C>               <C>
Thomas C. Spalding, Jr.   43 Vice President    Vice President of Nuveen
                             (since 1992)        Advisory Corp. and
                                                 Nuveen Institutional Ad-
                                                 visory Corp.; Chartered
                                                 Financial Analyst.
H. William Stabenow       60 Vice President &  Vice President and Trea-
                             Treasurer           surer of The John Nuveen
                             (since 1992)        Company (since March
                                                 1992), John Nuveen & Co.
                                                 Incorporated, Nuveen Ad-
                                                 visory Corp. and Nuveen
                                                 Institutional Advisory
                                                 Corp. (since January
                                                 1992).
George P. Thermos         63 Vice President    Vice President of John
                             (since 1992)        Nuveen & Co. Incorporat-
                                                 ed.
James J. Wesolowski       44 Vice President &  Vice President, General
                             Secretary           Counsel and Secretary of
                             (since 1992)        The John Nuveen Company
                                                 (since March 1992), John
                                                 Nuveen & Co. Incorporat-
                                                 ed, Nuveen Advisory
                                                 Corp. and Nuveen Insti-
                                                 tutional Advisory Corp.
Gifford R. Zimmerman      38 Vice President    Vice President (since Sep-
                             (since 1993) &      tember 1992), Assistant
                             Assistant           Secretary and Assistant
                             Secretary (since    General Counsel of John
                             1992)               Nuveen & Co. Incorporat-
                                                 ed; Vice President
                                                 (since May 1993) and As-
                                                 sistant Secretary of
                                                 Nuveen Advisory Corp.;
                                                 Vice President (since
                                                 May 1993) and Assistant
                                                 Secretary (since January
                                                 1992) of Nuveen Institu-
                                                 tional Advisory Corp.
</TABLE>
 
  On May 15, 1995, trustees and executive officers of the Fund as a group
beneficially owned 2,899 Shares (less than 1%). On May 15, 1995, trustees and
executive officers of the Fund as a group beneficially owned 204,005 common
shares of all funds managed by the Adviser (excluding money market funds). As
of May 15, 1995, 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
 
                                       7
<PAGE>
 
these forms furnished to the Fund, the Fund believes that during the fiscal
year ended May 31, 1995, 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, 1996. 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 75% 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 1996, a shareholder proposal must be received at the offices of the
Fund, 333 West Wacker Drive, Chicago, Illinois 60606, not later than February
16, 1996.
 
                                    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.
 
                                       8
<PAGE>
 
  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
 
                                       9
<PAGE>
 
 
 
 
 
 
 
 
 
 
                                                                          NIM795
<PAGE>
 
                                                                   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 26, 1995
 
The undersigned hereby appoints Richard J. Franke, 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 26, 1995, or any adjournment or adjournments
thereof:
1. Election of Trustees:
 NOMINEES: Lawrence H. Brown, Richard J. Franke, 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, 1996.
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                          NIM795
<PAGE>
 
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:         
    (SEE REVERSE FOR NOMINEES)

    [_] FOR             [_] WITHHOLD authority         [_] WITHHOLD authority to
        all nominees        to vote for all nominees       vote for nominees 
                                                           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, 1996.
 
                          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 NIM795                                      NIM795



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