Inthispaperweconsidertheeffectivereducibilityofthefollowinglineardifferentialequation:x=(A+∈Q(t,∈))x,|∈|≤∈0,whereAisaconstantmatrix,Q(t,e)isquasiperiodicint,andeisasmallperturbationparameter.WeprovethatiftheeigenvaluesofAandthebasicfrequenciesofQsatisfysomenon-resonantconditions,thelineardifferentialequationcanbereducedtoy=(A^*(∈)+R^*(t,∈))y,|∈|≤∈o,whereR^*isexponentiallysmallin∈.
