The thermalization of a low-density gas of excitons in Cu2O is analyze
d within the phonon-assisted Boltzmann kinetics in the presence of a w
eak interaction with the light field. For optically quadrupole-allowed
orthoexcitons, the thermalization kinetics is formulated in terms of
the polariton picture. A ''bottleneck'' relaxation along the lower pol
ariton branch strongly dominates over the accumulation of orthoexciton
s in the energy minimum of the upper polariton dispersion branch. For
paraexcitons, which are strictly forbidden in resonant optical transit
ions, a rather slow nonexponential occupation kinetics of the ground-s
tate mode at temperature T less than or equal to T-c (T-c is the conde
nsation critical temperature) prevents the development of a steady-sta
te Bose-Einstein condensate within the optical-phonon-assisted radiati
ve lifetime of paraexcitons. While at T less than or equal to T-c the
high-energy orthoexcitons or paraexcitons quasiequilibrate into the Pl
anck distribution (the effective chemical potential is equal to zero),
the low-energy excitons in a narrow spectral band (<100 mu eV) are st
ill far from equilibrium. This provides us with an alternative interpr
etation of the recent reports on the observation of quasi-steady-state
Bose-Einstein condensation of excitons in Cu2O. [S0163-1829(98)03816-
8].