  We show how to formulate $2$-dimensional supersymmetric $N=1,2$ theories,
both massive and conformal, within a manifestly supersymmetric hamiltonian
framework, via the introduction of a (super)-Poisson brackets structure defined
on superfields. In this approach, as distinct from the previously known
superfield hamiltonian formulations, the dynamics is not separated into two
unrelated $2D$ light-cone superspaces, but is recovered by specifying boundary
conditions at a given ``super-time" coordinate. So the approach proposed
provides a natural generalization of canonical hamiltonian formalism. One of
its interesting features is that the physical and auxiliary fields equations
appear on equal footing as the Hamilton ones.
