  We give the construction of quantum Lax equations for IRF models and
difference versions of Calogero-Moser-Sutherland models introduced by
Ruijsenaars. We solve the equations using factorization properties of the
underlying face Hopf algebras/elliptic quantum groups. This construction is in
the spirit of the Adler-Kostant-Symes method and generalizes our previous work
to the case of face Hopf algebras/elliptic quantum groups with dynamical
R-matrices.
