  The article is devoted to the generalization of the second Bogolyubov's
theorem to non-almost periodic dynamical systems. We prove the analog of the
second Bogolyubov's theorem for recurrent or pseudo recurrent dynamical systems
in Banach spaces. Namely, we obtain the relation between a recurrent dynamical
system and its averaged dynamical system. We also study existence of recurrent
and pseudo recurrent motions (including special cases of periodic,
quasi-periodic and almost periodic motions) in related nonautonomous systems.
