  The Ruijsenaars-Schneider systems are `discrete' version of the
Calogero-Moser (C-M) systems in the sense that the momentum operator p appears
in the Hamiltonians as a polynomial in e^{\pm\beta' p} (\beta' is a deformation
parameter) instead of an ordinary polynomial in p in the hierarchies of C-M
systems. We determine the polynomials describing the equilibrium positions of
the rational and trigonometric Ruijsenaars-Schneider systems based on classical
root systems. These are deformation of the classical orthogonal polynomials,
the Hermite, Laguerre and Jacobi polynomials which describe the equilibrium
positions of the corresponding Calogero and Sutherland systems. The
orthogonality of the original polynomials is inherited by the deformed ones
which satisfy three-term recurrence and certain functional equations. The
latter reduce to the celebrated second order differential equations satisfied
by the classical orthogonal polynomials.
