Abstract
We propose an explanation for the origin of hyperfast neutron stars (e.g. PSR B1508+55, PSR B2224+65, RX J0822-4300) based on the hypothesis that they could be the remnants of a symmetric supernova explosion of a high-velocity massive star (or its helium core) which attained its peculiar velocity (similar to that of the neutron star) in the course of a strong three- or four-body dynamical encounter in the core of a young massive star cluster. This hypothesis implies that the dense cores of star clusters (located either in the Galactic disk or near the Galactic centre) could also produce the so-called hypervelocity stars -- the ordinary stars moving with a speed of ~1000 km/s.