  The rational and hyperbolic Ruijsenaars-Schneider models and their
non-relativistic limits are maximally superintegrable since they admit action
variables with globally well-defined canonical conjugates. In the case of the
rational Ruijsenaars-Schneider model we present an alternative proof of the
superintegrability by explicitly exhibiting extra conserved quantities relying
on a generalization of the construction of Wojciechowski for the rational
Calogero model.
