Abstract: Discusses the stability of semilinar stochastic evolution equations on Hilbert Space dY(t)=AY(t) +f(Y(t))dt + G(Y(t))dw(t). At first, in order to Study Stochatic asymp-totically stability, some concepts for mild-solution,, and the sufficiently conditions for this stability are obtained. Secondly, some new concepts of stability are defined. The main results make the finite dimensions extention and Ichika' results development.