If G is any graph, the prism graph of G , denoted P ( G ) , is the cartesian product of G with a single edge, or equivalently, the graph obtained by taking two copies of G , say G 1 and G 2 , with the same vertex labelings and joining each vertex of G 1 to the vertex of G 2 having the same label by an edge. A connected graph G has property E ( m , n ) (or more briefly “ G is E ( m , n ) ”) if for every pair of disjoint matchings M and N in G with | M | = m and | N | = n respectively, there is a perfect matching F in G such that M ⊆ F and N ∩ F = ∅ . A graph which has the E ( m , 0 ) property is also said to be m -extendable. In this paper, we begin the study of the E ( m , n ) properties of the prism graph P ( G ) when G is an arbitrary graph as well as the more special situations when, in addition, G is bipartite or bicritical.