-----BEGIN PRIVACY-ENHANCED MESSAGE-----
Proc-Type: 2001,MIC-CLEAR
Originator-Name: webmaster@www.sec.gov
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MIC-Info: RSA-MD5,RSA,
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 v6e90NYZfg7QLZ6AqCv4vw==

<SEC-DOCUMENT>0001140361-10-015228.txt : 20100405
<SEC-HEADER>0001140361-10-015228.hdr.sgml : 20100405
<ACCEPTANCE-DATETIME>20100405112005
ACCESSION NUMBER:		0001140361-10-015228
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20100331
FILED AS OF DATE:		20100405
DATE AS OF CHANGE:		20100405

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			CLEVELAND RUSSELL
		CENTRAL INDEX KEY:			0001132090

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	000-30099
		FILM NUMBER:		10729746

	MAIL ADDRESS:	
		STREET 1:		8080 N CENTRAL EXPWY
		STREET 2:		STE 210 LB 59
		CITY:			DALLAS
		STATE:			TX
		ZIP:			75206

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			Access Plans Inc
		CENTRAL INDEX KEY:			0001087216
		STANDARD INDUSTRIAL CLASSIFICATION:	SERVICES-DIRECT MAIL ADVERTISING SERVICES [7331]
		IRS NUMBER:				582445301

	BUSINESS ADDRESS:	
		STREET 1:		900 36TH AVENUE
		STREET 2:		NW
		CITY:			NORMAN
		STATE:			OK
		ZIP:			73072
		BUSINESS PHONE:		4055798525

	MAIL ADDRESS:	
		STREET 1:		900 36TH AVENUE
		STREET 2:		NW
		CITY:			NORMAN
		STATE:			OK
		ZIP:			73072

	FORMER COMPANY:	
		FORMER CONFORMED NAME:	ALLIANCE HEALTHCARD INC
		DATE OF NAME CHANGE:	20000315

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			RENN Global Entrepreneurs Fund, Inc.
		CENTRAL INDEX KEY:			0000919567
		STATE OF INCORPORATION:			TX
		FISCAL YEAR END:			1231

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	000-30099
		FILM NUMBER:		10729747

	BUSINESS ADDRESS:	
		STREET 1:		8080 N CENTRAL EXPRWY
		STREET 2:		STE 210 LB59
		CITY:			DALLAS
		STATE:			TX
		ZIP:			75206
		BUSINESS PHONE:		2148918294

	MAIL ADDRESS:	
		STREET 1:		8080 N CENTRAL EXPWY., SUITE 210 LB 59
		CITY:			DALLAS
		STATE:			TX
		ZIP:			75206

	FORMER NAME:	
		FORMER CONFORMED NAME:	RENAISSANCE CAPITAL GROWTH & INCOME FUND III INC
		DATE OF NAME CHANGE:	19940228

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			RENN Capital Group, Inc.
		CENTRAL INDEX KEY:			0001353068
		STATE OF INCORPORATION:			TX
		FISCAL YEAR END:			1231

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	000-30099
		FILM NUMBER:		10729745

	BUSINESS ADDRESS:	
		STREET 1:		8080 N. CENTRAL EXPRESSWAY
		STREET 2:		SUITE 210, LB-59
		CITY:			DALLAS
		STATE:			TX
		ZIP:			75204
		BUSINESS PHONE:		214-891-8294

	MAIL ADDRESS:	
		STREET 1:		8080 N. CENTRAL EXPRESSWAY
		STREET 2:		SUITE 210, LB-59
		CITY:			DALLAS
		STATE:			TX
		ZIP:			75204
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>doc1.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2010-03-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001087216</issuerCik>
        <issuerName>Access Plans Inc</issuerName>
        <issuerTradingSymbol>ALHC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001132090</rptOwnerCik>
            <rptOwnerName>CLEVELAND RUSSELL</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>8080 N. CENTRAL EXPRESSWAY SUITE 210 LB</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75206</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0000919567</rptOwnerCik>
            <rptOwnerName>RENN Global Entrepreneurs Fund, Inc.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>8080 N CENTRAL EXPRWY</rptOwnerStreet1>
            <rptOwnerStreet2>STE 210 LB59</rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75206</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001353068</rptOwnerCik>
            <rptOwnerName>RENN Capital Group, Inc.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>8080 N. CENTRAL EXPRESSWAY</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75206</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle></officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2010-03-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>11390</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>369436</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>RENN Global  Entrepreneurs Fund Inc</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Shares are held in RENN Global Entrepreneurs Fund Inc.</footnote>
        <footnote id="F2">Russell Cleveland is President of RENN Capital Group, Inc. Investment Advisor to RENN Global Entrepreneurs Fund, Inc., and therefore may be considered to be beneficial owner of such shares.  Russell Cleveland disclaims such beneficial ownership.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Russell Cleveland</signatureName>
        <signatureDate>2010-04-05</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
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