  Motivated by recent problems in mathematical cosmology, in which temporal
averaging methods are applied in order to analyze the future asymptotics of
models which exhibit oscillatory behavior, we provide a theorem concerning the
large-time behavior for solutions of a general class of systems. We thus
propose our result to be applicable to a wide range of problems in spatially
homogenous cosmology with oscillatory behavior. Mathematically the theorem
builds upon the standard theory of averaging in non-linear dynamical systems.
