The exponential stability in the mean square sense (MSS), stability in probability and exponential ultimate boundedness (EUB in the MSS: \(E |X^x(t) |^2 \leq ce^{- \beta t} |x|^2+M\)) are considered for the mild solutions of stochastic semilinear evolution equations \(dX=(AX+F(X)) dt+ B(X) dW(t)\) in a real Hilbert space. The authors give a necessary and sufficient condition of the EUB in terms of the existence of a Lyapunov function for the linear case and use the first order approximation to study the nonlinear case. For the exponential stability in the MSS, a Lyapunov function is also constructed as a necessary and sufficient condition and this bounded below Lyapunov function is used to study the problem of the stability in probability.