Аннотация:Some genuine gravitational phenomena, associated with the conical structure of space-time, which can be attributed to the Aharonov-Bohm gravitational interaction are discussed. It is shown that cosmic string produces specific kinematical anomalies in the relative motion of gravitating bodies. Conical space topology leads to the modification of their Newtonian interaction potential and produces tidal force acting upon a single point particle. This tidal force is attractive and opens the possibility of gravitationally bound states of a body and a straight cosmic string. Tidal interaction also produces gravitational friction force upon the string meeting some system of massive bodies. In contrast, there is no tidal interaction between two parallel straight strings at rest. Gravitational radiation emitted by a test particle moving near the cosmic string, is shown to increase as the third power of the associated Lorentz-factor. Finally, it is shown that quantum gravitational fluctuations around a cosmic string dominate over vacuum polarization of lower spin fields.