  In this paper we continue the study of the geometrical features of a
functional approach to classical mechanics proposed some time ago. In
particular we try to shed some light on a N=2 "universal" supersymmetry which
seems to have an interesting interplay with the concept of ergodicity of the
system. To study the geometry better we make this susy local and clarify
pedagogically several issues present in the literature. Secondly, in order to
prepare the ground for a better understanding of its relation to ergodicity, we
study the system on constant energy surfaces. We find that the procedure of
constraining the system on these surfaces injects in it some local grassmannian
invariances and reduces the N=2 global susy to an N=1.
