We apply a population synthesis technique to study the formation and evolut
ion of low-mass X-ray binaries with black holes, observed as X-ray novae, f
rom hierarchical triple systems. A scenario is suggested in which an inner
close binary system evolves into an X-ray system with a large mass ratio. T
he high rate of accretion onto the neutron star leads to a common envelope
stage, which may result in the formation of a Thorne-Zytkow (TZ) object. Du
ring its evolution, the envelope of the TZ object expands, encompassing the
third star. The recurrent common-envelope stage decreases the size of the
orbit of the third star, leading to the formation of a low-mass X-ray nova
with a black hole. The dynamical stability of triple systems automatically
ensures that only low-mass X-ray novae form. We also consider the possible
formation of an X-ray nova from a binary in the case of asymmetrical core c
ollapse during a supernova explosion. (C) 2001 MAIK "Nauka/Interperiodica".