  We exploit the techniques developed in [Le] to study N-expansive
homeomorphisms on surfaces. We prove that when f is a 2-expansive homeomorphism
defined on a compact boundaryless surface M without wandering points then f is
expansive. This condition on the wandering set cannot be relaxed: we present an
example of a 2-expansive homeomorphisms on the bitorus with wandering points
that is not expansive.
