For nonlinear stochastic equations dx(t) = [Ax(t) + f (t, x(t), λ)] dt + g(t, x(t), λ) dω(t) with parameter λ in a Hilbert space, we show the existence and uniqueness of mild solutions. Provided that f satisfies a locally Lipschitz condition and g is a uniformly Lipschitz function, some sufficient conditions for p (p ≥ 2) moment locally exponential stability as well as almost surely exponential stability of mild solutions are obtained under a sufficiently small initial value ξ . Meanwhile, we

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... so consider parameter dependence of stable mild solutions for the stochastic system if f , g are sufficiently small Lipschitz perturbations in the parameter λ.