The purpose of this paper is to study the stabilizability problem for control stochastic nonlinear systems driven by a Wiener process. Sufficient conditions for the existence of stabilizing feedback laws that are smooth, except possibly at the equilibrium point of the system, are provided by means of stochastic Lyapunov-like techniques. The notion of dynamic asymptotic stability in probability of control stochastic differential systems is introduced and the stabilization by means of dynamic controllers is studied.