  We consider the Hamiltonian theory for the multi-component KP hierarchy. We
show that the second Hamiltonian structures constructed by Sidorenko and
Strampp[J. Math. Phys. {\bf 34}, 1429(1993)] are not Hamiltonian. A candidate
for the second Hamiltonian Structures is proposed and is proved to lead to
hereditary operators.

High Energy Physics - Theory