We regard the stochastic functional differential equation with infinite delay dx(t) = f (x(t))dt +g(x(t))dw(t) as the result of the effects of stochastic perturbation to the deterministic functional differential equation (x) over dot (t) = f (x(t)), where x(t) = X-t (theta) is an element of C((-infinity, 0]; R-n) is defined by x(t) (theta) = x(t + theta), theta is an element of (-infinity, 0]. We assume that the deterministic system with infinite delay is exponentially stable. In this paper, we shall characterize how much the stochastic perturbation can bear such that the corresponding stochastic functional differential system still remains exponentially stable. (C) 2009 Elsevier Ltd. All rights reserved.