  We consider the even parity superLax operator for the supersymmetric KP
hierarchy of the form $L~=~D^2 + \sum_{i=0}^\infty u_{i-2} D^{-i+1}$ and obtain
the two Hamiltonian structures following the standard method of Gelfand and
Dikii. We observe that the first Hamiltonian structure is local and linear
whereas the second Hamiltonian structure is non-local and nonlinear among the
superfields appearing in the Lax operator. We discuss briefly on their
connections with the super $w_{\infty}$ algebra.
