The polyhedral structure of various versions of the single item lot-sizing problem have been studies previously. These include the uncapacitated and capacitated versions of the problem, with and without changeover costs. However, the polyhedral structure of the multi item problem has not been studied in detail. In this paper we describe several classes of inequalities and facets for the multi item capacitated lot-sizing problem with changeover costs. Some of these facets are valid for the uncapacitated problem as well. We also solve the separation problem for some inequalities.