Let G be a graph with a perfect matching and let n be an integer, 1⩽n<|V(G)|⧸2. Graph G is n-extendable if every matching of size n in G is a subset of a perfect matching. Graph G is bicritical if G—u—v has a perfect matching for every pair of points u and v in V(G). It is proved that every 3-connected claw-free graph is bicritical and for n⩾2, every (2n+1)-connected claw-free graph is n-extendable. Matching extension in planar and toroidal claw-free graphs is then considered.
