  We study stochastic perturbations of linear systems of the form $$
dv(t)+Av(t)dt = \epsilon P(v(t))dt+\sqrt{\epsilon}B(v(t)) dW (t),
v\in\mathbb{R}^{D}, (*) $$ where $A$ is a linear operator with non-zero
imaginary spectrum. It is assumed that the vector field $P(v)$ and the
matrix-function $B(v)$ are locally Lipschitz with at most a polynomial growth
at infinity, that the equation is well posed and first few moments of norms of
solutions $v(t)$ are bounded uniformly in $\epsilon$. We use the Khasminski
approach to stochastic averaging to show that as $\epsilon\to0$, a solution
$v(t)$, written in the interaction representation in terms of operator $A$, for
$0\le t \le Const\,\epsilon^{-1}$ converges in distribution to a solution of an
effective equation. The latter is obtained from (*) by means of certain
averaging. Assuming that eq.(*) and/or the effective equation are mixing, we
examine this convergence further.
