The purpose of this paper is to state sufficient conditions for the stabilizability of stochastic differential systems when both the drift and diffusion terms are a ne in the control. This result extends to stochastic differential systems the well-known theorem of Jurdjevic-Quinn [ J. Differential Equations, 28 ( 1978), pp. 381 389] and incorporates earlier stabilization results proved in [ P. Florchinger, Stochastic Anal. Appl., 12 ( 1994), pp. 473 480] and [ R. Chabour and M. Oumoun, Stochastic Anal. Appl., 16 ( 1998), pp. 43 50].