  We investigate the existence of repulsive gravitational acceleration near
naked singularities. The investigation is carried out by means of the
acceleration tensor, which is a coordinate invariant object. We find that the
gravitational acceleration is repulsive in the vicinity of the origin in the
Reissner-Nordstr{\o}m and in the Kerr space-times, and attractive at large
distances in the expected Newtonian way. We further address the space-time of a
point massive particle, which also exhibits repulsive effects near the origin.
