<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2014-05-12</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000799231</issuerCik>
        <issuerName>ALMOST FAMILY INC</issuerName>
        <issuerTradingSymbol>AFAM</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001557543</rptOwnerCik>
            <rptOwnerName>NORTH TIDE CAPITAL, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>500 BOYLSTON STREET</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 310</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02116</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>2014-05-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>19000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>24.18</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1072100</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2014-05-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>18400</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>23.76</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1090500</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Shares reported herein represent: as of May 12, 2014, (i) 964,890 shares held by North Tide Capital Master, LP and (ii) 107,210 shares held by a managed account client; and as of May 13, 2014, (i) 981,450 shares held by North Tide Capital Master, LP and (ii) 109,050 shares held by a managed account client. North Tide Capital, LLC (&quot;North Tide&quot;) serves as investment manager for North Tide Capital Master, LP and the managed account client.  Mr. Laughlin serves as manager of North Tide.  Each of the Reporting Persons disclaims beneficial ownership of the shares reported herein except to the extent of its or his pecuniary interest therein, and the filing of this Form 4 shall not be construed as an admission that any of the Reporting Persons is the beneficial owner of any such shares for purposes of Section 16(a) of the Securities Exchange Act of 1934 or for any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ NORTH TIDE CAPITAL MASTER, LP - Conan Laughlin, Manager</signatureName>
        <signatureDate>2014-05-14</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ CONAN LAUGHLIN</signatureName>
        <signatureDate>2014-05-14</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ North Tide Capital, LLC - Conan Laughlin, Manager</signatureName>
        <signatureDate>2014-05-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
