The work of the previous paper is applied to the study of weakly interacting systems. Either by quasilinear techniques or by analyzing the perturbation series for the smoothed probability density, it is possible to derive a master equation equivalent to that of Brout and Prigogine without requiring the size of the system to become infinite. The properties of this equation are discussed. The equation is self-consistent provided the interactions are weak enough; however, examination of higher terms in the perturbation series shows that their effect might make the master equation invalid for times longer than that taken by a typical particle to cross the containing vessel. In many physical cases, the relaxation time will be shorter than this; also, further studies may show the higher terms to be less important than they seem.