  We consider solutions of the 2D Toda lattice hierarchy which are
trigonometric functions of the ``zeroth'' time $t_0=x$. It is known that their
poles move as particles of the trigonometric Ruijsenaars-Schneider model. We
extend this correspondence to the level of hierarchies: the dynamics of poles
with respect to the $m$-th hierarchical time $t_m$ (respectively, $\bar t_m$)
of the 2D Toda lattice hierarchy is shown to be governed by the Hamiltonian
which is proportional to the $m$-th Hamiltonian $\mbox{tr}\, L^m$
(respectively, $\mbox{tr}\, L^{-m}$) of the Ruijsenaars-Schneider model, where
$L$ is the Lax matrix.
