Thestationarycorrelationfunctionandtheassociatedrelaxationtimeforageneralsystemdrivenbycrosscorrelatedwhitenoisesarederived,byvirtueofaStratonovich-likeansatz.Theeffectsofcorrelatednoisesontherelaxationtimeofabistablekineticmodelcoupledtoanadditiveandamultiplicativewhitenoisesarestudied.ItisprovedthatforsmallfluctuationstherelaxationtimeTcasafunctionofλ(thecorrelatedintensitybetweennoises)exhibitsverydifferentbehavioursforαD(αandD,respectively,standfortheintensitiesofadditiveandmultiplicativenoises).Whenα>D,Tcincreaseswithincreasingλ.Butwhenα