  For two linear evolution differential equations systems - a normal ordinary
differential equations system and a partial differential equations system with
Stokes operator in a main part - with rapidly oscillating by time coefficients
in a case of an averaged stationary operator multiple degeneracy time-periodic
solutions problem was considered. The results about their existence and
uniqueness were proved and their asymptotic expansions were constructed and
proved. Moreover, for normal ordinary differential equations system the
convergence of the asymptotic expansion was proved in the ordinary meaning and
Lyapunov's stability questions were investigated.
