  Suppose M is a noncompact connected PL 2-manifold and let H(M)_0 denote the
identity component of the homeomorphism group of M with the compact-open
topology. In this paper we classify the homotopy type of H(M)_0 by showing that
{\cal H}(M)_0 has the homotopy type of the circle if M is the plane, an open or
half open annulus, or the punctured projective plane. In all other cases we
show that H(M)_0 is homotopically trivial.
