  We present explicit generators of an algebra of commuting difference
operators with trigonometric coefficients. The operators are simultaneously
diagonalized by recently discovered q-polynomials (viz. Koornwinder's
multivariable generalization of the Askey-Wilson polynomials). From the
viewpoint of physics the algebra can be interpreted as consisting of the
quantum integrals of a novel difference-type integrable sytem. This system
generalizes the Calogero-Moser systems associated with non-exceptional root
systems.
