In this work we study the asymptotic behaviour of the solutions of neutral type stochastic functional-differential equations of the form d[u(t) + g(ut)] = [Au + f(ut)]dt + σ(ut)dW(t) for t > 0; (1) u(t) = φ(t), t ∈ [−h, 0), h > 0. Here A is an inifinitesimal generator of a strong continuous semigroup {S(t), t ≥ 0} of bounded linear operators in real separable Hilbert space H. The noiseW(t) is a Q-Wiener process on a separable Hilbert space K. For any h > 0 denote Ch := C([−h, 0],H) to be a space of continuous H-valued functions φ : [−h, 0] → H, equipped with the norm ∥φ∥Ch := sup t∈[−h,0] ∥φ(t)∥H, where ∥ · ∥H stands for the norm in H. The functionals f and g map Ch to H, and σ : Ch →L02 , where L02 = L(Q1/2K,H) is the space of Hilbert-Schmidt operators from Q1/2K to H. Finally, φ : [−h, 0] ×Ω → H is the initial condition, where (Ω,F,P) is the probability space. We study two questions: the existence and uniqueness of the solution to the initial problem and establish the existence of invariant measures in the shift spaces for such equations. Our approach is based on Krylov-Bogoliubov theorem on the tightness of the family of measures. We present sufficient conditions for the existence of invariant measures. These conditions are expressed in terms of the coefficients of the equations.