  The Ruijsenaars-Schneider models are conventionally regarded as relativistic
generalizations of the Calogero integrable systems. Surprisingly enough, their
supersymmetric generalizations escaped attention. In this work, N=2
supersymmetric extensions of the rational and hyperbolic Ruijsenaars-Schneider
three-body models are constructed within the framework of the Hamiltonian
formalism. It is also known that the rational model can be described by the
geodesic equations associated with a metric connection. We demonstrate that the
hyperbolic systems are linked to non-metric connections.
