  We consider the averaging principle for stochastic reaction-diffusion
equations. Under some assumptions providing existence of a unique invariant
measure of the fast motion with the frozen slow component, we calculate
limiting slow motion. The study of solvability of Kolmogorov equations in
Hilbert spaces and the analysis of regularity properties of solutions, allow to
generalize the classical approach to finite-dimensional problems of this type
in the case of SPDE's.
