  We study the motion of test particles around a center of attraction
represented by a monopole (with and without spheroidal deformation) surrounded
by a ring, given as a superposition of Morgan & Morgan discs. We deal with two
kinds of bounded orbits: (i) Equatorial circular orbits and (ii) general
three-dimensional orbits. The first case provides a method to perform a linear
stability analysis of these structures by studying the behavior of vertical and
epicyclic frequencies as functions of the mass ratio, the size of the ring
and/or the quadrupolar deformation. In the second case, we study the influence
of these parameters in the regularity or chaoticity of motion. We find that
there is a close connection between linear stability (or unstability) of
equatorial circular orbits and regularity (or chaoticity) of the
three-dimensional motion.
