  An averaging principle is derived for the abstract nonlinear evolution
equation where the almost periodic right hand-side is a continuous perturbation
of the time-dependent family of linear operators determining a linear evolution
system. It generalizes classical Henry's results for perturbations of sectorial
operators on fractional spaces. It is also proved that the main hypothesis of
the nonlinear averaging principle is satisfied for general hyperbolic evolution
equations introduced by Kato.
