  We suggest to use the action-angle variables for the study of properties of
(quasi)particles in quantum rings. For this purpose we present the action-angle
variables for three two-dimensional singular oscillator systems. The first one
is the usual (Euclidean) singular oscillator, which plays the role of the
confinement potential for the quantum ring. We also propose two singular
spherical oscillator models for the role of the confinement system for the
spherical ring. The first one is based on the standard Higgs oscillator
potential. We show that, in spite of the presence of a hidden symmetry, it is
not convenient for the study of the system's behaviour in a magnetic field. The
second model is based on the so-called CP(1) oscillator potential and respects
the inclusion of a constant magnetic field.
