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In the magnetosphere of neutron stars represented by a dipole field in the Schwarzschild spacetime charged test particles influenced by the Lorentz force can follow circular orbits "in" and "off" the equatorial plane coinciding with the symmetry plane of the dipole field. Chaotic motion in belts concentrated around the off-equatorial orbits is possible for particles under strong magnetic attraction. In close vicinity of the circular orbits of both types, the epicyclic motion of harmonic character is possible. Frequencies of the epicyclic and orbital motion can be related to those of the high-frequency quasiperiodic oscillations observed in systems containing a neutron star. Influence of the additional back-reaction force related to the radiation of the particles, appropriately described by the Landau-Lifshitz equation, can cause in dependence on the character of the magnetic force the succesive fall of the orbiting particle onto the neutron star surface, or unexpected widening of the particle orbit.