  We give the formulation in extended superspace of an $N=2$ supersymmetric KP
hierarchy using chirality preserving pseudo-differential operators. We obtain
two quadratic hamiltonian structures, which lead to different reductions of the
KP hierarchy. In particular we find two different hierarchies with the $N=2$
classical super-${\cal W}_n$ algebra as a hamiltonian structure. The relation
with the formulation in $N=1$ superspace is carried out.
