Near a black hole or an ultracompact star, motion of particles is governed by strong gravitational field. Electrically charged particles feel also electromagnetic force arising due to currents inside the star or plasma circling around. We study a possibility that the interplay between gravitational and electromagnetic action may allow for stable, energetically bound off-equatorial motion of charged particles. This would represent well-known generalized Störmer´s ?halo orbits?, which have been discussedin connection with the motion of dust grains in planetary magnetospheres. We demonstrate that such orbits exist and can be astrophysically relevant when a compact star or a black hole is endowed with a dipole-type magnetic field.