QUARTERLY SCHEDULE OF PORTFOLIO HOLDINGS OF REGISTERED MANAGEMENT INVESTMENT COMPANY

Investment Company Act file number 811-7056

Nuveen Select Maturities Municipal Fund
(Exact name of registrant as specified in charter)

333 West Wacker Drive, Chicago, Illinois 60606
(Address of principal executive offices) (Zip code)

Jessica R. Droeger—Vice President and Secretary
333 West Wacker Drive, Chicago, Illinois 60606
(Name and address of agent for service)

Registrant's telephone number, including area code: 312-917-7700

Date of fiscal year end: 09/30

Date of reporting period: 12/31/04

Form N-Q is to be used by management investment companies, other than small business investment companies registered on Form N-5 (§§ 239.24 and 274.5 of this chapter), to file reports with the Commission, not later than 60 days after the close of the first and third fiscal quarters, pursuant to rule 30b1-5 under the Investment Company Act of 1940 (17 CFR 270.30b1-5). The Commission may use the information provided on Form N-Q in its regulatory, disclosure review, inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-Q, and the Commission will make this information public. A registrant is not required to respond to the collection of information contained in Form N-Q unless the Form displays a currently valid Office of Management and Budget (“OMB”) control number. Please direct comments concerning the accuracy of the information collection burden estimate and any suggestions for reducing the burden to the Secretary, Securities and Exchange Commission, 450 Fifth Street, NW, Washington, DC 20549-0609. The OMB has reviewed this collection of information under the clearance requirements of 44 U.S.C. § 3507.

Item 1. Schedule of Investments

Portfolio of Investments (Unaudited)
Nuveen Select Maturities Municipal Fund (NIM)
December 31, 2004

	Principal		Optional Call		Market
	Amount (000)	Description	Provisions*	Ratings**	Value

		Alabama - 2.1%

$	2,000	Alabama 21st Century Authority, Tobacco Settlement Revenue Bonds, Series 2001, 5.750%, 12/01/17	12/11 at 101.00	A-	$ 2,082,460

	500	Marshall County Healthcare Authority, Alabama, Revenue Bonds, Series 2002A, 6.250%, 1/01/22	1/12 at 101.00	A-	548,920

		Arizona - 3.9%

	2,470	Arizona Educational Loan Marketing Corporation, Educational Loan Revenue Bonds, Series 1992,	3/05 at 100.00	Aaa	2,478,398
		6.375%, 9/01/05 (Alternative Minimum Tax)

	1,570	Phoenix Industrial Development Authority, Arizona, Statewide Single Family Mortgage Revenue Bonds,	4/08 at 101.50	AAA	1,618,890
		Series 1998C, 6.650%, 10/01/29 (Alternative Minimum Tax)

	975	Industrial Development Authority, Winslow, Arizona, Hospital Revenue Bonds, Winslow Memorial	No Opt. Call	N/R	945,331
		Hospital Project, Series 1998, 5.750%, 6/01/08

		Arkansas - 3.0%

	1,000	Fort Smith, Arkansas, Water and Sewer Revenue Refunding and Construction Bonds, Series 2002A,	10/11 at 100.00	AAA	1,103,710
		5.250%, 10/01/17 - FSA Insured

	1,000	Jonesboro, Arkansas, Industrial Development Revenue Bonds, Anheuser Busch Inc. Project, Series	No Opt. Call	A+	1,056,390
		2002, 4.600%, 11/15/12

	1,380	North Little Rock, Arkansas, Electric Revenue Refunding Bonds, Series 1992A, 6.500%, 7/01/15 -	No Opt. Call	AAA	1,679,805
		MBIA Insured

		California - 1.8%

	2,115	Vernon, California, Electric System Revenue Bonds, Malburg Generating Station Project, Series	4/08 at 100.00	Aaa	2,311,653
		2003C, 5.250%, 4/01/17 (Pre-refunded to 4/01/08)

		Colorado - 9.3%

	1,475	Colorado Educational and Cultural Facilities Authority, Charter School Revenue Bonds, Douglas	7/12 at 100.00	BBB	1,486,505
		County School District RE-1 - DCS Montessori School, Series 2002A, 6.000%, 7/15/22

	1,175	Colorado Educational and Cultural Facilities Authority, Charter School Revenue Bonds, Classical	12/13 at 100.00	AAA	1,203,153
		Academy, Series 2003, 4.500%, 12/01/18 - XLCA Insured

	660	Colorado Housing Finance Authority, Single Family Program Senior Bonds, Series 2000D-2, 6.900%,	4/10 at 105.00	AA	677,312
		4/01/29 (Alternative Minimum Tax)

	1,000	Denver Health and Hospitals Authority, Colorado, Healthcare Revenue Bonds, Series 2001A, 6.000%,	12/11 at 100.00	BBB	1,049,830
		12/01/23

	1,465	Denver West Metropolitan District, Colorado, General Obligation Refunding and Improvement Bonds,	12/13 at 100.00	AA	1,474,581
		Series 2003, 4.500%, 12/01/18 - RAAI Insured

	199	El Paso County, Colorado, FNMA Mortgage-Backed Single Family Revenue Refunding Bonds, Series	No Opt. Call	Aaa	201,058
		1992A-2, 8.750%, 6/01/11

	5,875	Northwest Parkway Public Highway Authority, Colorado, Senior Lien Revenue Bonds, Series 2001B,	6/11 at 38.04	AAA	1,676,079
		0.000%, 6/15/27 - AMBAC Insured

	1,000	Summit County, Colorado, Sports Facilities Revenue Refunding Bonds, Keystone Resorts Management,	No Opt. Call	AAA	1,085,350
		Inc. Project, Series 1990, 7.750%, 9/01/06

	2,845	University of Colorado Hospital Authority, Hospital Revenue Bonds, Series 2001A, 5.600%, 11/15/21	11/11 at 100.00	A3	3,000,735

		Connecticut - 1.7%

		Eastern Connecticut Resource Recovery Authority, Solid Waste Revenue Bonds, Wheelabrator Lisbon
		Project, Series 1993A:
	500	5.500%, 1/01/14 (Alternative Minimum Tax)	1/05 at 100.00	BBB	509,400
	1,570	5.500%, 1/01/15 (Alternative Minimum Tax)	1/05 at 100.00	BBB	1,606,503

		District of Columbia - 4.1%

		District of Columbia, General Obligation Refunding Bonds, Series 1993A:
	900	6.000%, 6/01/07 - MBIA Insured	No Opt. Call	AAA	950,814
	4,105	6.000%, 6/01/07 - MBIA Insured	No Opt. Call	AAA	4,322,647

		Florida - 2.1%

	2,400	Deltona, Florida, Utility Systems Water and Sewer Revenue Bonds, Series 2003, 5.250%, 10/01/17 -	10/13 at 100.00	AAA	2,665,536
		MBIA Insured

		Illinois - 11.4%

	895	Chicago, Illinois, Tax Increment Allocation Bonds, Irving/Cicero Redevelopment Project, Series	1/09 at 100.00	N/R	916,059
		1998, 7.000%, 1/01/14

	2,000	Illinois Development Finance Authority, Revenue Refunding Bonds, Olin Corporation Project, Series	4/10 at 102.00	BBB-	2,102,260
		1993D, 6.750%, 3/01/16

	4,965	Illinois Development Finance Authority, GNMA Collateralized Mortgage Revenue Bonds, Greek American	4/11 at 105.00	Aaa	5,429,674
		Nursing Home Project, Series 2000A, 7.600%, 4/20/40

	2,000	Illinois Educational Facilities Authority, Revenue Bonds, Art Institute of Chicago, Series 2000,	No Opt. Call	A1	2,008,180
		4.450%, 3/01/34 (Mandatory put 3/01/15)

	1,000	Illinois Health Facilities Authority, Revenue Refunding Bonds, Edward Hospital, Series 1993A,	2/05 at 101.00	A+	1,022,660
		6.000%, 2/15/19

	1,210	Illinois Health Facilities Authority, Revenue Bonds, Silver Cross Hospital and Medical Centers,	8/09 at 101.00	A-	1,251,588
		Series 1999, 5.500%, 8/15/19

	850	Illinois Housing Development Authority, Section 8 Elderly Housing Revenue Bonds, Skyline Towers	5/05 at 100.00	A-	851,683
		Apartments, Series 1992B, 6.625%, 11/01/07

	1,000	Illinois Educational Facilities Authority, Student Housing Revenue Bonds, Educational Advancement	5/12 at 101.00	Baa2	1,127,400
		Foundation Fund, University Center Project, Series 2002, 6.625%, 5/01/17

		Indiana - 0.8%

	1,000	Indianapolis Local Public Improvement Bond Bank, Indiana, Series 1992D, 6.600%, 2/01/07	No Opt. Call	AA	1,084,890

		Iowa - 2.1%

	1,000	Iowa Finance Authority, Healthcare Revenue Bonds, Genesis Medical Center, Series 2000, 6.250%,	7/10 at 100.00	A1	1,082,150
		7/01/25

	1,800	Iowa Tobacco Settlement Authority, Tobacco Settlement Asset-Backed Revenue Bonds, Series 2001B,	6/11 at 101.00	BBB	1,590,012
		5.300%, 6/01/25

		Kansas - 2.9%

	3,500	Wichita, Kansas, Hospital Revenue Refunding and Improvement Bonds, Via Christi Health System Inc.,	11/11 at 101.00	A+	3,738,000
		Series 2001-III, 5.500%, 11/15/21

		Maryland - 0.9%

	1,100	Maryland Energy Financing Administration, Revenue Bonds, AES Warrior Run Project, Series 1995,	9/05 at 102.00	N/R	1,125,245
		7.400%, 9/01/19 (Alternative Minimum Tax)

		Massachusetts - 2.0%

	1,000	Massachusetts Industrial Finance Agency, Resource Recovery Remarketed Revenue Refunding Bonds,	No Opt. Call	BBB	1,009,880
		Ogden Haverhill Project, Series 1992A, 4.850%, 12/01/05

	1,490	Massachusetts Housing Finance Agency, Rental Housing Mortgage Revenue Bonds, Series 2000H, 6.650%,	7/10 at 100.00	AAA	1,598,308
		7/01/41 (Alternative Minimum Tax) - MBIA Insured

		Michigan - 2.7%

	1,000	Cornell Township Economic Development Corporation, Michigan, Environmental Improvement Revenue	5/12 at 100.00	BBB	1,073,130
		Refunding Bonds, MeadWestvaco Corporation-Escanaba Project, Series 2002, 5.875%, 5/01/18

	1,326	Michigan State Hospital Finance Authority, Collateralized Loan, Detroit Medical Center, Series	No Opt. Call	Baa2	1,336,662
		2001, 7.360%, 4/01/07

	470	Michigan State Hospital Finance Authority, Revenue Refunding Bonds, Detroit Medical Center, Series	No Opt. Call	Ba3	470,564
		1988A, 8.125%, 8/15/12

	600	Michigan State Hospital Finance Authority, Hospital Revenue Refunding Bonds, Sinai Hospital, Series	1/06 at 102.00	Ba3	591,504
		1995, 6.625%, 1/01/16

		Minnesota - 0.9%

	1,000	White Earth Band of Chippewa Indians, Minnesota, Revenue Bonds, Series 2000A, 7.000%, 12/01/11 -	No Opt. Call	A	1,122,390
		ACA Insured

		Nebraska - 0.8%

	1,000	Dodge County School District 1, Nebraska, Fremont Public Schools, General Obligation Bonds, Series	12/14 at 100.00	Aaa	1,078,460
		2004, 5.000%, 12/15/19 - FSA Insured

		New York - 9.2%

	1,000	Dormitory Authority of the State of New York, Revenue Bonds, Brooklyn Law School, Series 2003A,	7/13 at 100.00	AA	1,115,960
		5.500%, 7/01/15 - RAAI Insured

	1,500	New York State Energy Research and Development Authority, Facilities Revenue Bonds, Consolidated	10/05 at 100.00	A1	1,508,280
		Edison Company Inc., Series 2001A, 4.700%, 6/01/36 (Alternative Minimum Tax) (Mandatory put
		10/01/12)

	1,415	New York State Medical Care Facilities Finance Agency, FHA-Insured Mortgage Hospital and Nursing	2/06 at 102.00	AA+	1,493,688
		Home Revenue Bonds, Series 1995C, 6.100%, 8/15/15

	2,130	Niagara Falls, Niagara County, New York, General Obligation Water Treatment Plant Bonds, Series	No Opt. Call	AAA	2,458,041
		1994, 8.500%, 11/01/07 (Alternative Minimum Tax) - MBIA Insured

	4,300	Port Authority of New York and New Jersey, Special Project Bonds, JFK International Air Terminal	No Opt. Call	AAA	5,168,428
		LLC, Sixth Series 1997, 7.000%, 12/01/12 (Alternative Minimum Tax) - MBIA Insured

		North Carolina - 1.6%

	1,880	Union County, North Carolina, Certificates of Participation, Series 2003, 5.000%, 6/01/18 - AMBAC	6/13 at 101.00	AAA	2,030,137
		Insured

		Ohio - 1.6%

	970	Hamilton County, Ohio, Hospital Facilities Revenue Refunding Bonds, Bethesda Hospital Inc., Series	No Opt. Call	A***	987,916
		1992A, 6.250%, 1/01/06

	1,000	Toledo-Lucas County Port Authority, Ohio, Port Revenue Bonds, Cargill Inc. Project, Series 2004B,	No Opt. Call	A+	1,031,950
		4.500%, 12/01/15

		Oklahoma - 1.0%

	1,150	Oklahoma State Industries Authority, Health System Revenue Refunding Bonds, Baptist Medical Center,	8/06 at 102.00	AAA	1,215,492
		Series 1995D, 5.000%, 8/15/14 - AMBAC Insured

		Pennsylvania - 2.5%

	1,500	Pennsylvania Economic Development Financing Authority, Resource Recovery Revenue Bonds, Colver	12/05 at 101.00	BBB-	1,535,715
		Project, Series 1994D, 7.150%, 12/01/18 (Alternative Minimum Tax)

	1,390	Pennsylvania Higher Educational Facilities Authority, College Revenue Bonds, Ninth Series 1976,	No Opt. Call	Aaa	1,676,020
		7.625%, 7/01/15

		South Carolina - 4.0%

		Piedmont Municipal Power Agency, South Carolina, Electric Revenue Bonds, Series 1991:
	1,040	6.750%, 1/01/19 - FGIC Insured	No Opt. Call	AAA	1,351,522
	1,460	6.750%, 1/01/19 - FGIC Insured	No Opt. Call	AAA	1,860,916

	1,250	South Carolina JOBS Economic Development Authority, Hospital Revenue Bonds, Palmetto Health	No Opt. Call	BBB	1,452,125
		Alliance, Series 2000A, 7.000%, 12/15/10

	500	Tobacco Settlement Revenue Management Authority, South Carolina, Tobacco Settlement Asset-Backed	5/11 at 101.00	BBB	494,910
		Bonds, Series 2001B, 6.000%, 5/15/22

		Tennessee - 1.8%

		Shelby County Health, Educational and Housing Facilities Board, Tennessee, Hospital Revenue Bonds,
		Methodist Healthcare, Series 2002:
	750	6.000%, 9/01/17	9/12 at 100.00	A-***	878,385
	1,250	6.000%, 9/01/17 (Pre-refunded to 9/01/12)	9/12 at 100.00	A-***	1,467,750

		Texas - 7.1%

	1,055	Austin, Texas, General Obligation Bonds, Series 2004, 5.000%, 9/01/20 - MBIA Insured	9/14 at 100.00	AAA	1,129,662

	445	Austin-Travis County Mental Health Center, Texas, Revenue Bonds, Mental Health and Mental	3/05 at 101.00	AAA	452,311
		Retardation Center Facilities Acquisition Program, Series 1995A, 6.500%, 3/01/15 - FSA Insured

	2,000	Brazos River Authority, Texas, Collateralized Revenue Refunding Bonds, CenterPoint Energy Inc.,	6/14 at 100.00	AAA	2,018,500
		Series 2004B, 4.250%, 12/01/17 - FGIC Insured

	210	Galveston Property Finance Authority Inc., Texas, Single Family Mortgage Revenue Bonds, Series	3/05 at 100.00	A3	210,678
		1991A, 8.500%, 9/01/11

	770	Gulf Coast Mental Health Centers, Texas, Revenue Bonds, Mental Health and Mental Retardation	3/05 at 101.00	AAA	782,651
		Facilities Acquisition Program, Series 1995C, 6.500%, 3/01/15 - FSA Insured

	2,500	Matagorda County Navigation District 1, Texas, Pollution Control Revenue Refunding Bonds, Central	No Opt. Call	BBB+	2,577,300
		Power and Light Company, Series 2001A, 4.550%, 11/01/29 (Mandatory put 11/01/06)

	900	Tom Green County Health Facilities Development Corporation, Texas, Hospital Revenue Bonds, Shannon	No Opt. Call	Baa3	922,644
		Health System Project, Series 2001, 5.600%, 5/15/06

	300	Travis County Health Facilities Development Corporation, Texas, Hospital Revenue Bonds, Daughters	5/05 at 101.00	Aaa	303,591
		of Charity National Health System, Series 1993B, 5.900%, 11/15/07

	610	Tri-County Mental Health and Retardation Center, Texas, Revenue Bonds, Facilities Acquisition	3/05 at 101.00	AAA	620,022
		Program, Series 1995E, 6.500%, 3/01/15 - FSA Insured

		Utah - 1.7%

	2,055	Bountiful, Davis County, Utah, Hospital Revenue Refunding Bonds, South Davis Community Hospital	No Opt. Call	N/R	2,121,767
		Project, Series 1998, 6.000%, 12/15/10

		Washington - 9.6%

		Washington State Public Power Supply System, Nuclear Project 1 Revenue Refunding Bonds, Series
		1993A:
	160	7.000%, 7/01/07	No Opt. Call	Aaa	177,446
	1,340	7.000%, 7/01/07	No Opt. Call	Aaa	1,492,680
	1,130	7.000%, 7/01/08	No Opt. Call	Aaa	1,302,472
	1,870	7.000%, 7/01/08	No Opt. Call	Aaa	2,140,533

	7,000	Washington Public Power Supply System, Revenue Refunding Bonds, Nuclear Project 3, Series 1990B,	No Opt. Call	Aaa	6,746,950
		0.000%, 7/01/06

	295	Washington Public Power Supply System, Revenue Refunding Bonds, Nuclear Project 3, Series 1989B,	No Opt. Call	AAA	381,217
		7.125%, 7/01/16 - MBIA Insured

		West Virginia - 1.6%

	2,000	Harrison County Commission, West Virginia, Solid Waste Disposal Revenue Bonds, West Penn Power	8/06 at 100.00	AAA	2,047,220
		Company, Series 1994C, 6.750%, 8/01/24 (Alternative Minimum Tax) - MBIA Insured

		Wisconsin - 3.6%

		Badger Tobacco Asset Securitization Corporation, Wisconsin, Tobacco Settlement Asset-Backed Bonds,
		Series 2002:
	930	6.125%, 6/01/27	6/12 at 100.00	BBB	928,819
	1,480	6.375%, 6/01/32	6/12 at 100.00	BBB	1,420,785

	1,000	Wisconsin Health and Educational Facilities Authority, Revenue Bonds, Agnesian Healthcare Inc.,	7/11 at 100.00	A-	1,070,070
		Series 2001, 6.000%, 7/01/21

	1,150	Wisconsin Health and Educational Facilities Authority, Revenue Bonds, Aurora Health Care Inc.,	2/09 at 101.00	A	1,195,632
		Series 1999A, 5.500%, 2/15/20 - ACA Insured

$	122,070	Total Long-Term Investments (cost $120,251,487) - 97.8%			125,115,944

		Other Assets Less Liabilities - 2.2%			2,768,484

		Net Assets - 100%			$127,884,428


*	Optional Call Provisions: 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: Using the higher of Standard & Poor's or Moody's rating.
***	Securities are backed by an escrow or trust containing sufficient U.S. Government or U.S. Government agency
	securities which ensures the timely payment of principal and interest. Such securities are normally considered
	to be equivalent to AAA rated securities.
N/R	Investment is not rated.

	Income Tax Information

	The following information is presented on an income tax basis. Differences between amounts for financial statement
	and federal income tax purposes are primarily due to timing differences in recognizing income on taxable market
	discount securities and timing differences in recognizing certain gains and losses on security transactions.

	At December 31, 2004, the cost of investments was $120,168,205.

	Gross unrealized appreciation and gross unrealized depreciation of investments at December 31, 2004, were as
	follows:

	Gross unrealized:
	Appreciation	$5,148,349
	Depreciation	(200,610)

	Net unrealized appreciation of investments	$4,947,739

Item 2. Controls and Procedures.

The registrant's principal executive and principal financial officers, or persons performing similar functions, have concluded that the registrant's disclosure controls and procedures (as defined in Rule 30a-3(c) under the Investment Company Act of 1940, as amended (the "1940 Act") (17 CFR 270.30a-3(c))) are effective, as of a date within 90 days of the filing date of this report that includes the disclosure required by this paragraph, based on their evaluation of the controls and procedures required by Rule 30a-3(b) under the 1940 Act (17 CFR 270.30a-3(b)) and Rule 13a-15(b) or 15d-15(b) under the Securities Exchange Act of 1934 (17 CFR 240.13a-15(b) or 240.15d-15(b)).
There were no changes in the registrant's internal control over financial reporting (as defined in Rule 30a-3(d) under the 1940 Act (17 CFR 270.30a-3(d)) that occurred during the registrant's last fiscal quarter that have materially affected, or are reasonably likely to materially affect, the registrant's internal control over financial reporting.

Item 3. Exhibits.

File as exhibits as part of this Form a separate certification for each principal executive officer and principal financial officer of the registrant as required by Rule 30a-2(a) under the 1940 Act (17 CFR 270.30a-2(a)), exactly as set forth below: EX-99 CERT Attached hereto.

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

(Registrant) Nuveen Select Maturities Municipal Fund

By (Signature and Title)* /s/ Jessica R. Droeger--Vice President and Secretary

Date 02/28/05

Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, this report has been signed below by the following persons on behalf of the registrant and in the capacities and on the dates indicated.

By (Signature and Title)* /s/ Gifford R. Zimmerman--Chief Administrative Officer (principal executive officer)

Date 02/28/05

By (Signature and Title)* /s/ Stephen D. Foy--Vice President and Controller (principal financial officer)

Date 02/28/05

* Print the name and title of each signing officer under his or her signature.

UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, DC 20549 FORM N-Q

QUARTERLY SCHEDULE OF PORTFOLIO HOLDINGS OF REGISTERED MANAGEMENT INVESTMENT COMPANY

SIGNATURES

UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, DC 20549

FORM N-Q