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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2021-02-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000313616</issuerCik>
        <issuerName>DANAHER CORP /DE/</issuerName>
        <issuerTradingSymbol>DHR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001015014</rptOwnerCik>
            <rptOwnerName>RALES MITCHELL P</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>11790 GLEN ROAD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>POTOMAC</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>20854</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chairman of Exec. Committee</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Danaher deferred contribution programs - Danaher Stock Fund</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>0.00</value>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2021-02-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>83</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>237.84</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F3"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock, par value $.01</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>83</value>
                    <footnoteId id="F1"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1674.901</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Represents the Company's annual contribution to the Danaher stock fund (the &quot;ECP Stock Fund&quot;) in the Reporting Person's Excess Contribution Program (the &quot;ECP&quot;) account. The Company contributions are deemed to be invested in a number of unfunded, notional shares of Danaher common stock, calculated by dividing the contribution amount by the closing price of Danaher common stock as reported on the NYSE as of the day before the contribution is credited and then the number of shares is rounded to the next full share. The price shown in Table II, Column 8 is the closing price per share of Danaher common stock as reported on the NYSE on the date the contribution was actually made (or the closing price for the immediately preceding business day, if such date is not a business day).</footnote>
        <footnote id="F2">The notional shares convert on a one-for-one basis.</footnote>
        <footnote id="F3">Company contributions to the ECP consist of matching contributions (based on amounts the reporting person voluntary defers into the Danaher Deferred Compensation Plan) and non-elective contributions. A participant vests in the matching contribution in the ECP made each year on the first anniversary after it is credited to the participant's account. A participant vests in the non-elective contribution in the ECP made each year on the later of the first anniversary after it is credited to the participant's account, or the date the participant has completed three years of service with Danaher.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>By: /s/ Mitchell P. Rales</signatureName>
        <signatureDate>2021-02-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
