Amodifiedsequentiallinearprogrammingalgorithmispresented,whosesubproblemisalwayssolvable,fortheextendedlinearcomplementarityproblem(XLCP),theglobalconvergenceofthealgorithmunderassumptionofX-rowsufficiencyorX-columnmonotonicityisproved.Asaresult,asufficientconditionforexistenceandboundednessofsolutiontotheXLCPareobtained.