  We consider solutions of the 2D Toda lattice hierarchy which are elliptic
functions of the zeroth time t_0=x. It is known that their poles as functions
of t_1 move as particles of the elliptic Ruijsenaars-Schneider model. The goal
of this paper is to extend this correspondence to the level of hierarchies. We
show that the Hamiltonians which govern the dynamics of poles with respect to
the m-th hierarchical times t_m and \bar t_m of the 2D Toda lattice hierarchy
are obtained from expansion of the spectral curve for the Lax matrix of the
Ruijsenaars-Schneider model at the marked points.
