  We have considered scenarios for the evolution of close binaries resulting in
the formation of semi-detached systems in which a white dwarf can accumulate
Chandrasekhar mass by accretion from a main-sequence or subgiant companion with
$M\sim 2 M_\odot$. These white dwarfs, probably, explode as type Ia supernovae
or collapse with formation of neutron stars. We have carried out a population
synthesis study for these systems and have estimated the occurrence rate of
such events in the Galaxy, depending on the parameter of common envelopes,
mass-exchange rate in the binary, reaction of the main-sequence component on
accretion of helium in the intervening phase of evolution. We have found that
the model occurrence rate of SNe Ia in semi-detached systems is $\simeq 0.2
\times 10^{-3}$ yr$^{-1}$, i. e., it does not exceed $\sim 10%$ of the
observational estimate of the Galactic occurrence rate of SNe Ia.
