-----BEGIN PRIVACY-ENHANCED MESSAGE-----
Proc-Type: 2001,MIC-CLEAR
Originator-Name: webmaster@www.sec.gov
Originator-Key-Asymmetric:
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 TWSM7vrzLADbmYQaionwg5sDW3P6oaM5D3tdezXMm7z1T+B+twIDAQAB
MIC-Info: RSA-MD5,RSA,
 VLlrjW/lF3N5im82h9QIlFaoru8JhRp6kjNfHgirsbOAHoGckhK5UMoRXBK/2AoY
 1JQSTxvcwwJ8B72uZSQiug==

<SEC-DOCUMENT>0001189642-04-000198.txt : 20040305
<SEC-HEADER>0001189642-04-000198.hdr.sgml : 20040305
<ACCEPTANCE-DATETIME>20040305120401
ACCESSION NUMBER:		0001189642-04-000198
CONFORMED SUBMISSION TYPE:	3
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20040223
FILED AS OF DATE:		20040305

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			STEEVES CATHRYN
		CENTRAL INDEX KEY:			0001281059

	FILING VALUES:
		FORM TYPE:		3
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	811-07484
		FILM NUMBER:		04651012

	MAIL ADDRESS:	
		STREET 1:		333 W WACKER CRIVE
		STREET 2:		C/O NUVEEN INVESTMENTS
		CITY:			CHICAGO
		STATE:			IL
		ZIP:			60606

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			NUVEEN MASSACHUSETTS PREMIUM INCOME MUNICIPAL FUND
		CENTRAL INDEX KEY:			0000897419
		STANDARD INDUSTRIAL CLASSIFICATION:	UNKNOWN SIC - 0000 [0000]
		IRS NUMBER:				367032570
		STATE OF INCORPORATION:			MA
		FISCAL YEAR END:			0531

	BUSINESS ADDRESS:	
		STREET 1:		333 WEST WACKER DR
		CITY:			CHICAGO
		STATE:			IL
		ZIP:			60606
		BUSINESS PHONE:		3129178200

	MAIL ADDRESS:	
		STREET 1:		333 WEST WACKER DRIVE
		STREET 2:		333 WEST WACKER DRIVE
		CITY:			CHICAGO
		STATE:			IL
		ZIP:			60606
</SEC-HEADER>
<DOCUMENT>
<TYPE>3
<SEQUENCE>1
<FILENAME>ste8.xml
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0201</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2004-02-23</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0000897419</issuerCik>
        <issuerName>NUVEEN MASSACHUSETTS PREMIUM INCOME MUNICIPAL FUND</issuerName>
        <issuerTradingSymbol>NMT</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001281059</rptOwnerCik>
            <rptOwnerName>STEEVES CATHRYN</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>333 W. WACKER DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 2900</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60606</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Portfolio Manager</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value></value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes></footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By: Walter M. Kelly/Signed under POA</signatureName>
        <signatureDate>2004-03-02</signatureDate>
    </ownerSignature>
</ownershipDocument>

</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
-----END PRIVACY-ENHANCED MESSAGE-----