  A perfect matching in a hypergraph is a set of edges that partition the set
of vertices. We study the complexity of deciding the existence of a perfect
matching in orderable and separable hypergraphs. We show that the class of
orderable hypergraphs is strictly contained in the class of separable
hypergraphs. Accordingly, we show that for each fixed $k$, deciding perfect
matching for orderable $k$-hypergraphs is polynomial time doable, but for each
fixed $k\geq 3$, it is NP-complete for separable hypergraphs.
