NUVEEN SELECT MATURITIES MUNICIPAL FUND
N-30D, 1996-07-31
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Nuveen Exchange-Traded Funds
Providing tax-free income to help you live your dreams
NUVEEN SELECT MATURITIES MUNICIPAL FUND (NIM)
ANNUAL REPORT/MAY 31, 1996
Photographic image of couple walking on beach.
<PAGE>
CONTENTS
 3  Dear shareholder
 5  Answering your questions
 8  Fund performance
 9  Commonly used terms
11  Portfolio of investments
17  Statement of net assets
18 Statement of operations 
19 Statement of changes in net assets 
20 Notes to financial statements 
28 Financial highlights 
30 Report to independent auditors
<PAGE>
Dear shareholder

Photographic image of head shot of Chairman and Chief Executive Officer
of Nuveen.

"Municipal bonds continue to play an important role in meeting the investment
goals of conservative investors."

As I begin my duties as the new chairman and chief executive officer of
John Nuveen & Co. Incorporated and chairman of the board of the Nuveen
exchange-traded funds, I am pleased to report to you on the performance of
your fund. My experience with Nuveen over 19 years has reinforced my
commitment to maintaining Nuveen's successful tradition of value investing and
prudent management, helping our shareholders meet their need for tax-free
investment income with a full range of investment choices. Our focus will
continue to be on building shareholder value, providing research-oriented
management, and delivering dependable performance. With this focus, we
anticipate many more years of progress and accomplishment for fund
shareholders and our firm.

  Municipal bonds continue to play an important role in meeting the investment
goals of conservative investors. The performance of the Nuveen Select
Maturities Municipal Fund demonstrates how quality investments can provide
attractive tax-free income while delivering the relative stability of an
intermediate-term investment. As of May 31, 1996, the current annualized yield
on share price was 5.82%. To match this yield, investors in the 36% federal
income tax bracket would have had to earn 9.09% on taxable alterna tives.
Without question, taxable yields at this level on investments of comparable
quality can be difficult to achieve in today's markets.

  With the strength of the bond market last year, the fund also continued to
produce attractive returns. The change in net asset value, including the
reinvestment of all dividends and capital gains, for the Nuveen Select
Maturities Municipal Fund was 4.76%, equivalent to taxable investments with
total returns of 7.95%.

  The years ahead present opportunities as well as challenges for all of
us. I want to thank you for your continued confidence in Nuveen
exchange-traded funds, and I look forward to sharing reports of continued
progress with you.

Sincerely,

Timothy R. Schwertfeger
Chairman of the Board
July 15, 1996
<PAGE>
Answering your questions

Tom Spalding, head of Nuveen's portfolio management team, discusses investment
performance and recent factors affecting the municipal market.

What are the best measures of fund performance?

Fund performance can be gauged in many ways, with each method providing
certain insights. Among these various measures of performance, total return is
generally recognized as one of the more compre hensive. We use the term "total
return" to refer to a share's appreciation plus reinvested dividend income and
capital gains distributions, if applicable. In 1994, total returns for
municipal bond funds--and the entire bond market--declined, in one of the most
difficult period for bonds in decades. This was immediately followed by 1995's
exceptional market recovery, which resulted in a rebound in total returns.
During the first part of 1996, municipal bond funds have continued to provide
solid total returns, although at a slightly lower level than during 1995's
bull market.

  The events of these past few years illustrate the importance of considering
risk, or variability of returns, when comparing total returns. Over this time
period, Nuveen's prudent approach to management has protected investors from
wide swings in performance by maintaining a higher level of value than peer
group funds during 1994's bear market and participating only slightly less in
1995's recovery.

  Another important measure of fund performance involves assessing whether a
fund has met its stated investment goals. At Nuveen, we continue to empha size
our fund's goals of providing dependable tax-free dividends and adhering to a
value investing approach. In this regard, the steadiness of dividends over the
long term is a good practical measure of success.
<PAGE>
Photographic image of Tom Spalding, Portfolio Manager at Nuveen. 

Tom Spalding, head of Nuveen's portfolio management team, answers
investors' questions on develop ments in the municipal market.

What has been Nuveen's investment approach during this period?

Because we believe that a value approach offers investors greater price
stability in uncertain markets, Nuveen continues to pursue value investing as
the optimal way to meet our investors' objectives. We define value investing
as a disciplined approach to security selection and portfolio construction
designed to deliver above-market performance by identifying individual bonds
with current yields, prices, credit quality, and future prospects that are
exceptionally attractive in relation to other bonds in the market. This
approach was rewarded over the past year, as many of our portfolio holdings
were upgraded by the national rating agencies, indicating that our Research
Department's judgments about credit quality were on target.

  As opportunity allowed, we moved to protect current income by investing a
larger percentage of our portfolios in non-callable bonds. Because these bonds
cannot be redeemed before maturity, their yield is assured for the long term
even if interest rates decline. As another measure of income protec tion, we
also purchased an increased number of bonds at discounts from their par value.
These bonds, which are yielding slightly below market levels due to their
current coupon, are less likely to be called from our portfolios, assuring
more stable yields for our investors.
<PAGE>
<TABLE>
NUVEEN SELECT MATURITIES MUNICIPAL FUND
NIM
Shareholders enjoyed 12 months of steady dividends, in accordance with the
Fund's goal of providing attractive, dependable tax-free income. Shareholders
also received a capital gains distribution in December.

12 MONTH DIVIDEND HISTORY
<CAPTION>
Date       Monthly Dividends  Supplemental Dividends    Capital Gains
<S>        <C>                <C>                       <C>
 6/94      $0.0540
 7/94      $0.0540
 8/94      $0.0540
 9/94      $0.0540
10/94      $0.0540
11/94      $0.0540
12/94      $0.0540                                      $0.0433
 1/95      $0.0540
 3/95      $0.0540
 3/95      $0.0540
 5/94      $0.0540
 6/95      $0.0540
<CAPTION>
FUND HIGHLIGHTS 5/31/96
<S>                                         <C>
Yield                                         5.82%
Taxable-equivalent yield                      9.09%
Annual total return on NAV                    4.76%
Taxable-equivalent total return               7.95%
Share price                                 $11.125
NAV                                         $11.59
The price, net asset value and dividend history used in this chart constitute
past performance and do not necessarily predict the future price, net asset
value or dividends of the Fund or of any other Nuveen Fund.
</TABLE>
<PAGE>
Commonly used terms

Yield
An exchange-traded fund's annualized monthly dividend on a given date (in the
case of this report, May 31, 1996) divided by its closing price per share on
that date.

Taxable equivalent yield
The return an investor subject to a given federal income tax rate would need
to obtain from a fully taxable investment to equal the fund's stated
annualized yield on share price. In this report, this tax rate is assumed to
be 36% for shareholders, based on incomes of $121,300-$263,750 for investors
filing singly, $147,700-$263,750 for those filing jointly.

Net Asset Value (NAV)
The market value of all securities and other assets held by an exchange-traded
fund, minus any liabilities. The NAV per share is the fund's net assets,
divided by its total number of shares outstanding.

<PAGE>
Total return on NAV
The percentage change in a fund's NAV per common share for a given period,
assuming reinvestment of all dividends and capital gains distributions, if
any.

Taxable equivalent total return
The total return an investor subject to a given income tax rate would need to
obtain from a fully taxable investment to equal the fund's stated total return
on NAV.

The Fund intends to repurchase shares of its own common stock in the future at
such times and in such amounts as are deemed advisable. No shares were
repurchased during the 12 months ended May 31, 1996. Any future repurchases
will be reported to shareholders in the next annual or semiannual report.
<PAGE>
<TABLE>
PORTFOLIO OF INVESTMENTS
<CAPTION>
       PRINCIPAL                                                                     OPT. CALL                             MARKET
          AMOUNT   DESCRIPTION                                                     PROVISIONS*       RATINGS**              VALUE
<S>                <C>                                                             <C>                    <C>         <C>
                   ARIZONA - 1.8%
     $ 2,470,000   Arizona Educational Loan Marketing Corporation,
                    Educational Loan Revenue Bonds, 6.375%, 9/01/05
                    (Alternative Minimum Tax)                                      9/02 at 101             Aa         $ 2,546,175
- ---------------------------------------------------------------------------------------------------------------------------------
                   ARKANSAS - 1.1%
       1,500,000   Arkansas Student Loan Authority, 6.750%, 6/01/06
                    (Alternative Minimum Tax)                                      6/01 at 102              A           1,584,120
- ---------------------------------------------------------------------------------------------------------------------------------
                   COLORADO - 6.6%
       5,500,000   City and County of Denver, Colorado, Airport System
                    Revenue Bonds, Series 1991A, 8.750%, 11/15/23
                    (Alternative Minimum Tax)                                     11/01 at 102            Baa           6,571,180
       1,611,133   El Paso County, Colorado, Single Family Mortgage
                    Revenue Taxable Refunding Bonds, Series 1992A
                    Class A-2, 8.750%, 6/01/11                                    No Opt. Call            Aaa           1,722,832
       1,000,000   Summit County, Colorado, Sports Facilities Refunding
                    Revenue Bonds (Keystone Resorts Management, Inc.
                    Project), Series 1990, 7.750%, 9/01/06                        No Opt. Call             A-           1,164,980
- ---------------------------------------------------------------------------------------------------------------------------------
                   DISTRICT OF COLUMBIA - 3.9%
       5,400,000   District of Columbia (Washington, D.C.), General
                    Obligation Refunding Bonds, Series 1993A,
                    6.000%, 6/01/07                                               No Opt. Call            Aaa           5,557,734
- ---------------------------------------------------------------------------------------------------------------------------------
                   FLORIDA - 4.3%
       2,000,000   State of Florida, Faith and Credit, State Board of
                    Education, Public Education Capital Outlay Bonds,
                    Series 1986-C, 7.100%, 6/01/07                                No Opt. Call            Aaa           2,107,740
       3,500,000   Hillsborough County Industrial Development
                    Authority, Pollution Control Revenue Refunding
                    Bonds (Tampa Electric Company Project),
                    Series 1992, 8.000%, 5/01/22                                   5/02 at 103            Aa2           4,098,010
- ---------------------------------------------------------------------------------------------------------------------------------
                   GEORGIA - 8.8%
       2,540,000   Municipal Electric Authority of Georgia, General
                    Power Revenue Bonds, 1992B Series,
                    7.500%, 1/01/07                                               No Opt. Call            Aaa           2,941,091
       1,800,000   State of Georgia, General Obligation Bonds, 1994-D,
                    6.700%, 8/01/09                                               No Opt. Call            Aaa           2,021,022
         945,000   Urban Residential Finance Authority of the City of
                    Atlanta, Revenue Bonds (Landrum Arms Project),
                    Series 1994, 6.750%, 7/01/04                                  No Opt. Call            N/R             976,374
       5,755,000   Development Authority of Burke County, Georgia,
                    Pollution Control Revenue Bonds (Oglethorpe
                    Power Corporation Vogtle Project) Series 1992,
                    8.000%, 1/01/15                                                1/03 at 103            Aaa           6,732,832
<PAGE>
<CAPTION>
       PRINCIPAL                                                                     OPT. CALL                             MARKET
          AMOUNT   DESCRIPTION                                                     PROVISIONS*       RATINGS**              VALUE
<S>                <C>                                                            <C>                     <C>         <C>
                   ILLINOIS - 11.6%
     $ 2,615,000   Illinois Housing Development Authority, Section 8
                    Elderly Housing Revenue Bonds (Skyline Tower
                    Apartments), Series 1992B, 6.625%, 11/01/07                   11/02 at 102              A         $ 2,721,614
       4,700,000   The Illinois Development Finance Authority, Child
                    Care Facility Revenue Bonds (The Illinois Facilities
                    Fund Project), Series 1992, 7.400%, 9/01/04                    9/02 at 102            N/R           4,848,191
       1,300,000   General Obligation Lease Certificates, 1992 Series A
                    (Board of Education of the City of Chicago), Illinois,
                    6.125%, 1/01/07                                               No Opt. Call            Aaa           1,372,475
       2,765,000   Chicago Metropolitan Housing Development
                    Corporation (Chicago, Illinois), Housing
                    Development Revenue Refunding Bonds, (FHA-
                    Insured Mortgage Loan-Section 8 Assisted Project),
                    Series 1993B, 5.700%, 1/01/13                                  7/03 at 100            Aaa           2,698,281
       3,000,000   City of Chicago, Illinois, Tax Increment Allocation
                    Revenue and Refunding Bonds (Stockyards
                    Industrial - Commercial Redevelopment Project),
                    Series 1994A, 9.250%, 1/01/12                                 No Opt. Call            N/R           3,289,590
         745,000   City of Danville, Vermilion County, Illinois, Single
                    Family Mortgage Revenue Refunding Bonds,
                    Series 1993, 7.300%, 11/01/10                                 11/03 at 102             A1             777,475
         925,000   City of Rock Island, Illinois, Residential Mortgage
                    Revenue Refunding Bonds, Series 1992,
                    7.700%, 9/01/08                                                9/02 at 102             Aa             985,042
- ---------------------------------------------------------------------------------------------------------------------------------
                   INDIANA - 5.6%
                   The Indianapolis Local Public Improvement Bond
                    Bank, Series 1992 D Bonds:
       1,000,000    6.400%, 2/01/05                                               No Opt. Call             A+           1,066,970
       1,000,000    6.600%, 2/01/07                                               No Opt. Call             A+           1,076,070
       2,100,000   The Indianapolis Local Public Improvement Bond
                    Bank, Transportation Revenue Bonds, Series 1992,
                    6.000%, 7/01/10                                                7/03 at 102             Aa           2,153,802
       1,540,000   The Trustees of Indiana University, Indiana University
                    Facility Revenue Bonds, Series 1994A,
                    6.000%, 11/15/06                                              No Opt. Call            Aaa           1,622,482
       2,000,000   Hospital Authority of Elkhart County, Indiana,
                    Hospital Revenue Bonds, Series 1992 (Elkhart
                    General Hospital, Inc.), 7.000%, 7/01/08                       7/02 at 102             A1           2,137,440
- ---------------------------------------------------------------------------------------------------------------------------------
                   LOUISIANA - 1.5%
       2,000,000   Louisiana Public Facilities Authority, Student Loan
                    Revenue Bonds, 6.750%, 9/01/06 (Alternative
                    Minimum Tax)                                                   9/02 at 102            Aaa           2,102,220
<PAGE>
<CAPTION>
       PRINCIPAL                                                                     OPT. CALL                             MARKET
          AMOUNT   DESCRIPTION                                                     PROVISIONS*       RATINGS**              VALUE
<S>                <C>                                                             <C>                    <C>         <C>
                   MAINE - 1.1%
     $ 1,500,000   Maine Educational Loan Marketing Corporation,
                    Student Loan Revenue Refunding Bonds, Series 1992,
                    Student Loan Revenue Refunding Bonds,
                    Subordinate Series 1992A-2, 6.600%, 5/01/05
                    (Alternative Minimum Tax)                                      5/02 at 101              A         $ 1,558,155
- ---------------------------------------------------------------------------------------------------------------------------------
                   MARYLAND - 1.5%
       2,000,000   Anne Arundel County, Maryland, Multifamily Housing
                    Revenue Bonds (Woodside Apartments Project), Series
                    1994, 7.450%, 12/01/24 (Alternative Minimum Tax)
                    (Mandatory put 12/01/03)                                      No Opt. Call           BBB+           2,089,700
- ---------------------------------------------------------------------------------------------------------------------------------
                   MASSACHUSETTS - 1.2%
       1,760,000   Massachusetts Municipal Wholesale Electric Company,
                    Power Supply System Revenue Bonds, 1994 Series B,
                    4.700%, 7/01/06                                               No Opt. Call            Aaa           1,664,168
- ---------------------------------------------------------------------------------------------------------------------------------
                   MICHIGAN - 2.8%
       3,800,000   Greater Detroit Resource Recovery Authority,
                    Michigan, Resource Revenue Refunding Bonds,
                    Series 1996-A, 6.250%, 12/13/07                               No Opt. Call            Aaa           4,020,932
- ---------------------------------------------------------------------------------------------------------------------------------
                   NEBRASKA - 4.2%
                   Nebraska Public Gas Agency, Gas Supply System
                    Revenue Bonds, 1995 Series A:
       1,000,000    5.250%, 4/01/02                                               No Opt. Call           Baa1             984,170
       1,250,000    5.300%, 4/01/03                                               No Opt. Call           Baa1           1,222,750
       1,000,000    5.400%, 4/01/04                                               No Opt. Call           Baa1             975,260
       2,400,000   Airport Authority of the City of Omaha (Nebraska),
                    Airport Facilities Revenue Refund Bonds,
                    Series 1991, 8.375%, 1/01/14                                   1/02 at 102              A           2,780,112
- ---------------------------------------------------------------------------------------------------------------------------------
                   NEW JERSEY - 0.7%
       1,000,000   The Essex County Utilities Authority (Essex County,
                    New Jersey), Solid Waste System Revenue Bonds,
                    Series 1996A, 5.500%, 4/01/02                                 No Opt. Call            Aaa           1,030,310
- ---------------------------------------------------------------------------------------------------------------------------------
                   NEW YORK - 10.7%
       2,000,000   New York State Medical Care, Facilities Finance
                    Agency, FHA-Insured Mortgage Project Revenue
                    Bonds, 1995 Series D, 6.100%, 8/15/15                          2/06 at 102            AA+           2,000,600
       4,000,000   The City of New York, General Obligation Bonds,
                    Fiscal 1991 Series D, 9.500%, 8/01/02                      8/01 at 101 1/2           Baa1           4,710,440
       2,000,000   The City of New York, General Obligation Bonds,
                    Fiscal 1996 Series B, 6.750%, 8/15/03                         No Opt. Call           Baa1           2,121,240
<PAGE>
<CAPTION>
       PRINCIPAL                                                                     OPT. CALL                             MARKET
          AMOUNT   DESCRIPTION                                                     PROVISIONS*       RATINGS**              VALUE
<S>                <C>                                                             <C>                    <C>         <C>
                   NEW YORK (CONTINUED)
     $ 4,000,000   New York City Housing Development Corporation,
                    Multi-Family Housing Revenue Bonds, 1993
                    Series A, 5.700%, 11/01/13                                     5/03 at 102             Aa         $ 3,934,760
       2,130,000   City of Niagara Falls, Niagara County, New York,
                    Water Treatment Plant (Serial) Bonds, 1994,
                    8.500%, 11/01/07 (Alternative Minimum Tax)                    No Opt. Call            Aaa           2,669,401
- ---------------------------------------------------------------------------------------------------------------------------------
                   NORTH CAROLINA - 1.9%
       3,000,000   North Carolina Municipal Power Agency Number 1,
                    Catawba Electric Revenue Bonds, Series 1993,
                    4.100%, 1/01/05                                               No Opt. Call            Aaa           2,714,610
- ---------------------------------------------------------------------------------------------------------------------------------
                   OHIO - 5.4%
       2,000,000   Akron, Bath and Copley Joint Township Hospital
                    District, Ohio, Hospital Facilities Revenue Bonds,
                    Series 1992, (Summa Health System Project),
                    6.250%, 11/15/07                                              11/02 at 102              A           2,040,000
       4,500,000   County of Hamilton, Ohio, Hospital Facilities
                    Revenue, Refunding Bonds, Series 1992A
                    (Bethesda Hospital, Inc.), 6.250%, 1/01/06                    No Opt. Call             A1           4,618,710
       1,000,000   Oxford Water Supply System Mortgage Revenue,
                    6.000%, 12/01/14                                              12/02 at 102            Aaa           1,017,630
- ---------------------------------------------------------------------------------------------------------------------------------
                   PENNSYLVANIA - 1.6%
       1,930,000   Pennsylvania Higher Educational Facilities Authority,
                    7.625%, 7/01/15                                               No Opt. Call            Aaa           2,261,478
- ---------------------------------------------------------------------------------------------------------------------------------
                   RHODE ISLAND - 2.1%
       3,000,000   Rhode Island Housing and Mortgage Finance
                    Corporation, Homeownership Opportunity Bonds,
                    Series 7, 6.500%, 4/01/25, (Alternative
                    Minimum Tax)                                                   4/02 at 102            AA+           3,055,620
- ---------------------------------------------------------------------------------------------------------------------------------
                   SOUTH DAKOTA - 2.6%
       3,595,000   South Dakota Student Loan Assistance Corporation,
                    7.400%, 8/01/99 (Alternative Minimum Tax)                     No Opt. Call              A           3,770,436
- ---------------------------------------------------------------------------------------------------------------------------------
                   TENNESSEE - 0.7%
       1,000,000   Tennessee Housing Development Agency,
                    Homeownership Program Bonds, Issue WR,
                    Series 1992, 6.400%, 7/01/06                                   7/02 at 102             Aa           1,026,550
- ---------------------------------------------------------------------------------------------------------------------------------
                   TEXAS - 3.9%
         625,000   Austin-Travis County Mental Health Centers,
                    6.500%, 3/01/15                                                3/05 at 102            Aaa             652,938
<PAGE>
<CAPTION>
       PRINCIPAL                                                                     OPT. CALL                             MARKET
          AMOUNT   DESCRIPTION                                                     PROVISIONS*       RATINGS**              VALUE
<S>                <C>                                                             <C>                    <C>         <C>
                   TEXAS (CONTINUED)
     $ 1,290,000   City of Galveston Property Finance Authority, Inc.,
                    Single Family Mortgage Revenue Bonds,
                    Series 1991A, 8.500%, 9/01/11                                  9/01 at 103              A         $ 1,400,656
       1,185,000   Texas Community MHMR Centers Revenue Bonds
                    (Mental Health and Mental Retardation Center
                    Facilities Acquisition Program), Series 1995 A-E,
                    6.500%, 3/01/15                                                3/05 at 102            Aaa           1,238,799
       1,400,000   Travis County Health Facilities Development
                    Corporation (Daughters of Charity Health System),
                    5.900%, 11/15/07                                              11/03 at 102             Aa           1,426,236
         855,000   Tri-County Mental Health and Retardation Center,
                    6.500%, 3/01/15                                                3/05 at 102            Aaa             897,399
- ---------------------------------------------------------------------------------------------------------------------------------
                   VIRGINIA - 1.5%
       2,000,000   Hampton Redevelopment and Housing Authority
                    Multifamily Housing Revenue Refunding Bonds,
                    Series 1994 (Chase Hampton II Apartments),
                    7.000%, 7/01/24 (Mandatory put 7/01/04)                        7/02 at 104           Baa3           2,129,120
- ---------------------------------------------------------------------------------------------------------------------------------
                   WASHINGTON - 10.3%
                   Washington Health Care Facilities Authority, Revenue Bonds,
                    Series 1996 (Yakima Valley Memorial Hospital Association,
                    Yakima):
       1,880,000    6.000%, 12/01/09                                              No Opt. Call            AAA           1,921,942
       1,500,000    6.000%, 12/01/10                                              No Opt. Call            AAA           1,524,735
                   Washington Public Power Supply System, Nuclear
                    Project No. 1 Refunding Revenue Bonds
                    Series 1993A:
       2,500,000    7.000%, 7/01/07                                               No Opt. Call             Aa           2,712,750
       3,000,000    7.000%, 7/01/08                                               No Opt. Call             Aa           3,290,250
       7,000,000   Washington Public Power Supply System, Nuclear
                    Project No. 3 Refunding Revenue Bonds,
                    Series 1990B, 0.000%, 7/01/06                                 No Opt. Call             Aa           3,909,920
       1,255,000   Public Utility District No. 1, of Douglas County,
                    Washington, Wells Hydroelectric Revenue Bonds,
                    Series of 1990, 7.700%, 9/01/08 (Alternative
                    Minimum Tax)                                                   9/00 at 102             A+           1,379,910
- ---------------------------------------------------------------------------------------------------------------------------------
    $134,066,133   Total Investments - (cost $135,102,331) - 97.4%                                                    139,627,429
    ============
<PAGE>
<CAPTION>
       PRINCIPAL                                                                     OPT. CALL                             MARKET
          AMOUNT   DESCRIPTION                                                     PROVISIONS*       RATINGS**              VALUE
<S>                <C>                                                             <C>                    <C>         <C>
                   TEMPORARY INVESTMENTS IN SHORT-TERM
                   MUNICIPAL SECURITIES - 1.2%
     $ 1,000,000   Clark County, Nevada, Industrial Development
                    Revenue Bonds, (Nevada Cogeneration
                    Associates I Project), Series 1990, Variable Rate
                    Demand Bonds, 3.800%, 11/01/20+
                    (Alternative Minimum Tax)                                                          VMIG-1         $ 1,000,000
         700,000   County of Daviess, Kentucky, Solid Waste Disposal
                    Facilities Revenue Bonds (Scott Paper Company
                    Project), Variable Rate Demand Bonds,
                    3.850%, 12/01/23+ (Alternative Minimum Tax)                                          A-1+             700,000
     $ 1,700,000   Total Temporary Investments - 1.2%                                                                   1,700,000
     ===========
                   Other Assets Less Liabilities - 1.4%                                                                 2,036,306
                   Net Assets - 100%                                                                                 $143,363,735
                                                                                                                     ============
<CAPTION>
                                                                          NUMBER           MARKET          MARKET
                   STANDARD & POOR'S                        MOODY'S    OF ISSUES            VALUE         PERCENT
<S>                      <C>              <C>                                 <C>    <C>                      <C>
  SUMMARY OF                         AAA                    Aaa               22     $ 50,493,051             36%
  RATINGS**                 AA+, AA, AA-      Aa1, Aa, Aa2, Aa3               12       31,139,715              22
  PORTFOLIO OF                        A+                     A1                6       11,056,575               8
  INVESTMENTS                      A, A-              A, A2, A3                8       17,020,073              12
  (INCLUDING             BBB+, BBB, BBB-  Baa1, Baa, Baa2, Baa3                8       20,803,860              15
  TEMPORARY                    Non-rated              Non-rated                3        9,114,155               7
  INVESTMENTS):
  TOTAL                                                                       59     $139,627,429            100%
<FN>
* Optional Call Provisions (not covered by the report of independent
auditors): Dates (month and year) and prices of the earliest optional call or
redemption. There may be other call provisions at varying prices at later
dates.
** Ratings (not covered by the report of independent auditors): Using the
higher of Standard & Poor's or Moody's rating.
N/R - Investment is not rated.
+ The security has a maturity of more than one year, but has variable rate and
demand features which qualify it as a short-term security. The rate disclosed
is that currently in effect. This rate changes periodically based on market
conditions or a specified market index.

See accompanying notes to financial statements.
</TABLE>
<PAGE>
<TABLE>
<CAPTION>
STATEMENT OF NET ASSETS
<S>                                                                 <C>
ASSETS
Investments in municipal securities, at market
   value (note 1)                                                   $139,627,429
Temporary investments in short-term municipal
   securities, at amortized cost (note 1)                              1,700,000
Cash                                                                     189,275
Receivables:
   Interest                                                            2,588,436
   Investments sold                                                       20,385
Other assets                                                              47,919
                                                                    ------------
     Total assets                                                    144,173,444
                                                                    ------------
LIABILITIES
Accrued expenses:
   Management fees (note 6)                                               60,600
   Other                                                                  81,095
Dividends payable                                                        668,014
                                                                    ------------
     Total liabilities                                                   809,709
                                                                    ------------
Net assets (note 7)                                                 $143,363,735
                                                                    ============
Shares outstanding                                                    12,370,635
                                                                    ============
Net asset value per share outstanding (net assets
   divided by shares outstanding)                                   $      11.59
                                                                    ============

See accompanying notes to financial statements.
</TABLE>
<PAGE>
<TABLE>
<CAPTION>
STATEMENT OF OPERATIONS
Year ended May 31, 1996
<S>                                                                 <C>
   INVESTMENT INCOME
   Tax-exempt interest income (note 1)                              $ 8,853,072
                                                                    -----------
   Expenses:
      Management fees (note 6)                                          725,139
      Shareholders' servicing agent fees and expenses                    24,910
      Custodian's fees and expenses                                      45,637
      Trustees' fees and expenses (note 6)                                2,466
      Professional fees                                                  16,346
      Shareholders' reports--printing and mailing expenses               60,338
      Stock exchange listing fees                                        23,347
      Investor relations expense                                          9,629
      Other expenses                                                      6,467
                                                                    -----------
        Total expenses                                                  914,279
                                                                    -----------
          Net investment income                                       7,938,793
                                                                    -----------
   REALIZED AND UNREALIZED GAIN (LOSS)
   FROM INVESTMENTS
   Net realized gain from investment transactions, net
      of taxes (notes 1 and 3)                                          922,639
   Net change in unrealized appreciation (depreciation)
      of investments                                                 (2,000,905)
                                                                    -----------
          Net gain (loss) from investments                           (1,078,266)
                                                                    -----------
   Net increase in net assets from operations                       $ 6,860,527
                                                                    ===========

See accompanying notes to financial statements.
</TABLE>
<PAGE>
<TABLE>
<CAPTION>
STATEMENT OF CHANGES IN NET ASSETS
                                                                           Year ended                Year ended
                                                                            5/31/96                    5/31/95
<S>                                                                   <C>                       <C>
OPERATIONS
Net investment income                                                 $   7,938,793             $   7,862,011
Net realized gain from investment transactions, net
   of taxes, if applicable                                                  922,639                   204,387
Net change in unrealized appreciation (depreciation)
   of investments                                                        (2,000,905)                4,606,003
                                                                      -------------             -------------
     Net increase in net assets from operations                           6,860,527                12,672,401
                                                                      -------------             -------------
DISTRIBUTIONS TO SHAREHOLDERS (note 1)
From undistributed net investment income                                 (8,031,140)               (8,012,616)
From accumulated net realized gains from
   investment transactions                                                 (517,776)                 (198,988)
In excess of accumulated net realized gains from
   investment transactions                                                     --                     (75,518)
                                                                      -------------             -------------
     Decrease in net assets from distributions
       to shareholders                                                   (8,548,916)               (8,287,122)
                                                                      -------------             -------------
CAPITAL SHARE TRANSACTIONS (note 2)
Net proceeds from shares issued to shareholders due
   to reinvestment of distributions                                          65,320                      --
                                                                      -------------             -------------
Net increase in net assets derived from capital
   share transactions                                                        65,320                      --
                                                                      -------------             -------------
   Net increase (decrease) in net assets                                 (1,623,069)                4,385,279
Net assets at beginning of year                                         144,986,804               140,601,525
                                                                      -------------             -------------
Net assets at end of year                                             $ 143,363,735             $ 144,986,804
                                                                      =============             =============
Balance of undistributed net investment income
   at end of year                                                     $     348,240             $     440,587
                                                                      =============             =============

See accompanying notes to financial statements.
</TABLE>
<PAGE>
NOTES TO FINANCIAL STATEMENTS

1. GENERAL INFORMATION AND SIGNIFICANT ACCOUNTING POLICIES
At May 31, 1996, the Fund covered in this report and its corresponding New
York Stock Exchange symbol is Nuveen Select Maturities Municipal Fund (NIM).

The Fund has invested in a diversified, investment-grade quality portfolio of
municipal obligations with intermediate characteristics having an initial
average effective maturity of approximately ten years. In assembling and
managing its portfolio, the Fund has purchased municipal obligations having
remaining effective maturities of no more than fifteen years, that in the
opinion of the Fund's investment adviser, represent the best value in terms of
the balance between yield and capital preservation currently available from
the intermediate sector of the municipal market. The Fund's investment
adviser, Nuveen Advisory Corp. (the "Adviser"), a wholly owned subsidiary of
The John Nuveen Company, will actively monitor the effective maturities of the
Fund's investments in response to prevailing market conditions, and will
adjust its portfolio consistent with its investment policy of maintaining an
average effective remaining maturity for the Fund's portfolio of between eight
and twelve years.

The Fund is registered under the Investment Company Act of 1940 as a
closed-end, diversified management investment company.

The following is a summary of significant accounting policies followed by the
Fund in the preparation of its financial statements in accordance with
generally accepted accounting principles.

Securities Valuation

Portfolio securities for which market quotations are readily available are
valued at the mean between the quoted bid and asked prices or the yield
equivalent. Portfolio securities for which market quotations are not readily
available are valued at fair value by consistent application of methods
determined in good faith by the Board of Trustees. Temporary investments in
securities that have variable rate and demand features qualifying them as
short-term securities are traded and valued at amortized cost.
<PAGE>
Securities Transactions

Securities transactions are recorded on a trade date basis. Realized gains and
losses from such transactions are determined on the specific identification
method. Securities purchased or sold on a when-issued or delayed delivery
basis may be settled a month or more after the transaction date. The
securities so purchased are subject to market fluctuation during this period.
The Fund has instructed the custodian to segregate assets in a separate
account with a current value at least equal to its purchase commitments. At
May 31, 1996, there were no such purchase commitments in the Fund.

Interest Income

Interest income is determined on the basis of interest accrued, adjusted for
amortization of premiums and accretion of discounts on long-term debt
securities when required for federal income tax purposes.

Federal Income Taxes

The Fund intends to comply with the requirements of the Internal Revenue Code
applicable to regulated investment companies by distributing to shareholders
all of its tax-exempt net investment income, in addition to any significant
amounts of net realized capital gains from investments and/or market discount
realized upon the sale of securities. The Fund currently considers significant
net realized capital gains and/or market discount as amounts in excess of
$.001 per share. Furthermore, the Fund intends to satisfy conditions which
will enable interest from municipal securities, which is exempt from regular
federal income tax, to retain such tax-exempt status when distributed to
shareholders of the Fund. All income dividends paid during the year ended May
31, 1996, have been designated Exempt Interest Dividends which are entirely
exempt from federal income taxes.

Dividends and Distributions to Shareholders

Net investment income is declared as a dividend monthly and payment is made or
reinvestment is credited to shareholder accounts after month-end. Net realized
capital gains from securities transactions are distributed to shareholders not
less frequently than annually only to the extent they exceed available capital
loss carryovers.

Distributions to shareholders of net investment income and net realized
capital gains are recorded on the ex-dividend date. The amount and timing of
such distributions are determined in accordance with federal income tax
regulations, which may differ from generally accepted accounting principles.
Accordingly, temporary over-distributions as a result of these differences may
result and will be classified as either distributions in excess of net
investment income or distributions in excess of net realized gains, if
applicable.
<PAGE>
Derivative Financial Instruments

In October 1994, the Financial Accounting Standards Board (FASB) issued
Statement of Financial Accounting Standards No. 119 Disclosure about
Derivative Financial Instruments and Fair Value of Financial Instruments which
prescribes disclosure requirements for transactions in certain derivative
financial instruments including futures, forward, swap, and option contracts,
and other financial instruments with similar characteristics. Although the
Fund is authorized to invest in such financial instruments, and may do so in
the future, the Fund did not make any such investments during the year ended
May 31, 1996.

Use of Estimates

The preparation of financial statements in conformity with generally accepted
accounting principles requires management to make estimates and assumptions
that affect the reported amounts of assets and liabilities at the date of the
financial statements and the reported amounts of increases and decreases in
net assets from operations during the reporting period.
<PAGE>
<TABLE>
2. FUND SHARES

The Fund issued 5,489 shares due to reinvestment of distribution during
the year ended May 31, 1996. There were no share transactions during the year
ended May 31, 1995.

3. SECURITIES TRANSACTIONS
Purchases and sales (including maturities) of investments in municipal
securities and temporary municipal investments during the year ended May 31,
1996, were as follows:
<CAPTION>
<S>                                                  <C>
PURCHASES
Investments in municipal securities                  $36,217,514
Temporary municipal investments                       13,800,000
SALES AND MATURITIES
Investments in municipal securities                   37,501,986
Temporary municipal investments                       12,800,000
                                                      ==========

At May 31, 1996, the identified cost of investments owned for federal income
tax purposes was the same as the cost for financial reporting purposes.
</TABLE>
<PAGE>
<TABLE>
4. DISTRIBUTIONS TO SHAREHOLDERS
On June 3, 1996, the Fund declared a dividend distribution of $.0540 per share
from its ordinary income which was paid July 1, 1996, to shareholders of
record on June 15, 1996.

5. UNREALIZED APPRECIATION (DEPRECIATION)
Gross unrealized appreciation and gross unrealized depreciation of investments
at May 31, 1996, were as follows:
<CAPTION>
<S>                                                                 <C>
Gross unrealized:
      Appreciation                                                  $ 4,982,572
      Depreciation                                                     (457,474)
                                                                    -----------
Net unrealized appreciation                                         $ 4,525,098
                                                                    ===========

6. MANAGEMENT FEES AND OTHER TRANSACTIONS WITH AFFILIATES
Under the Fund's investment management agreement with the Adviser, the Fund
pays to the Adviser an annual management fee, payable monthly, at the rates
set forth below, which are based upon the average daily net asset value of the
Fund:
<CAPTION> 
<S>                                          <C>
AVERAGE DAILY NET ASSET VALUE                MANAGEMENT FEE
For the first $125,000,000                      .5 of 1%
For the next $125,000,000                    .4875 of 1
For the next $250,000,000                     .475 of 1
For the next $500,000,000                    .4625 of 1
For the next $1,000,000,000                    .45 of 1
For net assets over $2,000,000,000           .4375 of 1

The fee compensates the Adviser for overall investment advisory and
administrative services and general office facilities. The Fund pays no
compensation directly to those Trustees who are affiliated with the Adviser or
to their officers, all of whom receive remuneration for their services to the
Fund from the Adviser.
</TABLE>
<PAGE>
<TABLE>
7. COMPOSITION OF NET ASSETS
At May 31, 1996, net assets consisted of:
<CAPTION>
<S>                                                                 <C>
Common shares, $.01 par value per share                             $    123,706
Paid-in surplus                                                      138,037,346
Balance of undistributed net investment income                           348,240
Accumulated net realized gain from
      investment transactions                                            329,345
Net unrealized appreciation of investments                             4,525,098
                                                                    ------------
        Net assets                                                  $143,363,735
                                                                    ============
Authorized shares:
      Common                                                           Unlimited
                                                                    ============
</TABLE>
<PAGE>
<TABLE>
8. INVESTMENT COMPOSITION
The Fund invests in municipal securities which include general obligation,
escrowed and revenue bonds. At May 31, 1996, the revenue sources by municipal
purpose for these investments, expressed as a percent of total investments,
were as follows:
<CAPTION>
<S>                                                                         <C>
 Revenue Bonds:
      Housing Facilities                                                     17%
      Electric Utilities                                                     16
      Health Care Facilities                                                 13
      Pollution Control Facilities                                            9
      Educational Facilities                                                  8
      Transportation                                                          8
      Lease Rental Facilities                                                 4
      Water/Sewer Facilities                                                  1
      Other                                                                   8
General Obligation Bonds                                                     13
Escrowed Bonds                                                                3
                                                                            ---
                                                                            100%
                                                                            ===

In addition, 32% of the long-term and intermediate-term investments owned by
the Fund are either backed by insurance issued by several private insurers or
are backed by an escrow or trust containing U.S. Government or U.S. Government
agency securities, both of which ensure the timely payment of principal and
interest in the event of default. Such insurance or escrow, however, does not
guarantee the market value of the municipal securities or the value of the
Fund's shares.

All of the temporary investments in short-term municipal securities have
credit enhancements (letters of credit, guarantees or insurance) issued by
third party domestic or foreign banks or other institutions.

For additional information regarding each investment security, refer to the
Portfolio of Investments of the Fund.
</TABLE>
<PAGE>
<TABLE>
FINANCIAL HIGHLIGHTS
SELECTED DATA FOR A SHARE OUTSTANDING THROUGHOUT EACH PERIOD IS AS FOLLOWS:
<CAPTION>
                                Operating performance
                                                   Net
                                                   realized &
                      Net asset                    unrealized    Dividends
                      value           Net          gain (loss)   from net          Distributions
                      beginning       investment   from          investment        from net
                      of period       income       investments++ income            realized gains
<S>                   <C>             <C>          <C>           <C>               <C>
Year Ended 5/31,
         1996         $11.730         $.641        $(.090)       $(.648)           $(.043)
         1995          11.370          .643          .387         (.648)            (.022)**
         1994          11.710          .616         (.275)        (.646)            (.035)
9/18/92 to
         5/31/93       11.300          .392          .455         (.322)              --
<PAGE>
<CAPTION>
                                                                   Total
                                                    Per share      investment     Total
                         Organization  Net asset    market         return         return on
                         and           value end    value end      on market      net asset
                         offering costsof period    of period      value+         value+
<S>                      <C>           <C>          <C>            <C>            <C>
Year Ended 5/31,
         1996            $ --          $11.590      $11.125        6.14%          4.76%
         1995              --           11.730       11.125        7.67           9.51
         1994              --           11.370       11.000       (1.90)          2.86
9/18/92 to
         5/31/93         (.115)         11.710       11.875        1.74           6.54
<PAGE>
<CAPTION>
                                               Ratios/Supplemental data
                                                              Ratio of
                                                              net
                               Net assets      Ratio of       investment
                               end of          expenses       income               Portfolio
                               period (in      to average     to average           turnover
                               thousands)      net assets     net assets           rate
<S>                            <C>             <C>            <C>                  <C>
Year Ended 5/31,
         1996                  $143,364        .63%           5.45%                25%
         1995                   144,987        .65            5.64                 38
         1994                   140,602        .72            5.26                 11
9/18/92 to
         5/31/93                 91,599        .75*           5.11*                25
<FN>
* Annualized.
** The amount shown reflects a distribution in excess of net realized gains
from investment transactions of $.006 per share.
+ Total Investment Return on Market Value is the combination of reinvested
dividend income, reinvested capital gains distributions, if any, and changes
in stock price per share. Total Return on Net Asset Value is the combination
of reinvested dividend income, reinvested capital gains distributions, if any,
and changes in net asset value per share.
++ Net of taxes, if applicable.
</TABLE>
<PAGE>
REPORT OF INDEPENDENT AUDITORS

The Boards of Trustees and Shareholders
Nuveen Select Maturities Municipal Fund

We have audited the accompanying statement of net assets, including the
portfolio of investments, of Nuveen Select Maturities Municipal Fund as of May
31, 1996, and the related statements of operations, changes in net assets and
the financial highlights for the periods indicated therein. These financial
statements and financial highlights are the respon sibility of the Fund's
management. Our responsibility is to express an opinion on these financial
statements and financial highlights based on our audits.

We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to
obtain reasonable assurance about whether the financial statements and
financial highlights are free of material misstatement. An audit includes
examining, on a test basis, evidence supporting the amounts and disclosures in
the financial statements. Our procedures included confirmation of investments
owned as of May 31, 1996, by correspondence with the custodian. An audit also
includes assessing the accounting principles used and significant estimates
made by management, as well as evaluating the overall financial statement
presentation. We believe that our audits provide a reasonable basis for our
opinion.

In our opinion, the financial statements and financial highlights referred to
above present fairly, in all material respects, the financial position of
Nuveen Select Maturities Municipal Fund at May 31, 1996, and the results of
its operations, changes in its net assets and financial highlights for the
periods indicated therein in conformity with generally accepted accounting
principles.

Ernst & Young LLP
Chicago, Illinois
July 12, 1996
<PAGE>
Your investment partners

Photographic image of John Nuveen, Sr., founder of Nuveen.

For nearly 100 years, Nuveen has earned its reputation as a tax-free income
specialist by focusing on municipal bonds.

Since 1898, John Nuveen & Co. Incorporated has worked to bring together the
various participants in the municipal bond industry and build strong
partnerships that benefit all concerned. Investors, financial advisers,
municipal officials, investment bankers--Nuveen believes that forging
relationships within these groups based on trust and value is the key to
successful investing.

  As the oldest and largest municipal bond special ist in the United States,
Nuveen's investment bankers work with issuers to understand and meet their
needs in structuring and selling their bond issues.

  Nuveen also works closely with financial advisers around the country,
including brokerage firms, banks, insurance companies, and independent
financial planners, to bring the benefits of tax-free investing to you. These
advisers are experts at identifying your needs and recommending the best
solutions for your situation. Together we make a powerful team, helping you
create a successful investment plan that meets your needs today and in the
future.

John Nuveen & Co. Incorporated
333 West Wacker Drive
Chicago, Illinois 60606-1286

ETF1-JULY 96


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