  We consider solutions of the KP hierarchy which are elliptic functions of
$x=t_1$. It is known that their poles as functions of $t_2$ move as particles
of the elliptic Calogero-Moser model. We extend this correspondence to the
level of hierarchies and find the Hamiltonian $H_k$ of the elliptic
Calogero-Moser model which governs the dynamics of poles with respect to the
$k$-th hierarchical time. The Hamiltonians $H_k$ are obtained as coefficients
of the expansion of the spectral curve near the marked point in which the
Baker-Akhiezer function has essential singularity.
