  We consider a system of N classical particles, interacting via a smooth,
short- range potential, in a weak-coupling regime. This means that N tends to
infinity when the interaction is suitably rescaled. The j-particle marginals,
which obey to the usual BBGKY hierarchy, are decomposed into two contributions:
one small but strongly oscillating, the other hopefully smooth. Eliminating the
first, we arrive to establish the dynamical problem in term of a new hierarchy
(for the smooth part) involving a memory term. We show that the first order
correction to the free flow converges, as N \rightarrow \infty, to the
corresponding term associated to the Landau equation. We also show the related
propagation of chaos.
