  For each partition p of an integer N \geq 2, consisting of r parts, an
integrable hierarchy of Lax type Hamiltonian PDE has been constructed recently
by some of us. In the present paper we show that any tau-function of the
p-reduced r-component KP hierarchy produces a solution of this integrable
hierarchy. Along the way we provide an algorithm for the explicit construction
of the generators of the corresponding classical W-algebra W(gl_N,p), and write
down explicit formulas for evolution of these generators along the Hamiltonian
flows.
