<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-08-21</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000773660</issuerCik><issuerName>UICI</issuerName>        <issuerTradingSymbol>UCI</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001230556</rptOwnerCik><rptOwnerName>JOSEPHSON MURAL R</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>124 RONAN ROAD</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>HIGHWOOD</rptOwnerCity><rptOwnerState>IL</rptOwnerState><rptOwnerZipCode>60040</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-08-21</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>P</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>1714</value></transactionShares><transactionPricePerShare><value>13.0824</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1714</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><derivativeTable><derivativeTransaction><securityTitle><value>Stock Option</value></securityTitle><conversionOrExercisePrice><value>13.07</value></conversionOrExercisePrice><transactionDate><value>2003-08-21</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>1714</value></transactionShares><transactionPricePerShare><value>13.07</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2004-08-21</value><footnoteId id="F1" /></exerciseDate><expirationDate><value>2008-09-20</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>1714</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1714</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">Options vest over a five-year period in 20% annual increments</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>Mural R.  Josephson by /s/ Peggy G. Simpson, POA</signatureName><signatureDate>2003-08-25</signatureDate></ownerSignature></ownershipDocument>

