  Oscillator and Coulomb systems on N-dimensional spaces of constant curvature
can be generalized by replacing their angular degrees of freedom with a compact
integrable (N-1)-dimensional system. We present the action-angle formulation of
such models in terms of theradial degree of freedom and the action-angle
variables of the angular subsystem. As an example, we construct the spherical
and pseudospherical generalization of the two-dimensional superintegrable
models introduced by Tremblay, Turbiner and Winternitz and by Post and
Winternitz. We demonstrate the superintegrability of these systems and give
their hidden constant of motion.
