  Action-angle type variables for spin generalizations of the elliptic
Ruijsenaars-Schneider system are constructed. The equations of motion of these
systems are solved in terms of Riemann theta-functions. It is proved that these
systems are isomorphic to special elliptic solutions of the non-abelian 2D Toda
chain. A connection between the finite gap solutions of solitonic equations and
representations of the Sklyanin algebra is revealed and discrete analogs of the
Lame operators are introduced. A simple way to construct representations of the
Sklyanin algebra by difference operators is suggested.
