  In this paper we prove a generalized version of Hall's theorem for
hypergraphs. More precisely, let H be a k-uniform k- partite hypergraph with
some ordering on parts as V1, V2,..., Vk. such that the subhypergraph generated
on union of V1, V2,..., Vk-1 has a unique perfect matching. In this case, we
give a necessary and sufficient condition for having a matching of size t =
|V1| in H. Some relevant results and counterexamples are given as well.
