  We present results of extensive numerical studies of the stability of
non-interacting particles in the planetary systems of stars Upsilon Andromedae,
GJ 876, 47 UMa, and 55 Cancri. We discuss the possibility of the existence of
islands of stability and/or instability at different regions in these
multi-body systems, and their probable correspondence to certain mean-motion
resonances. The results of our study may be applied to questions concerning the
stability of terrestrial planets in these systems and also the trapping of
particles in resonances with the planets.
