In this paper, we are interested in the asymptotical behavior
of the error between the solution of a differential equation
perturbed by a flow (or by a transformation) and the solution
of the associated averaged differential equation.
The main part of this redaction is devoted to the ascertainment
of results of convergence in distribution analogous to those
obtained in [10] and [11]. As in [11], we shall use a representation
by a suspension flow over a dynamical system. Here, we make an
assumption of multiple decorrelation in terms of this dynamical
system. We show how this property can be verified for ergodic
algebraic toral automorphisms and point out the fact that, for
two-dimensional dispersive billiards, it is a consequence of
the method developed in [18]. Moreover, the singular case of
a degenerated limit distribution is also considered.