  We analyze temporal evolution of the number of accreting white dwarfs with
shell hydrogen burning in semidetached and detached binaries. We consider a
stellar system in which star formation lasts for 10 Gyr with a constant rate,
as well as a system in which the same amount of stars is formed in a single
burst lasting for 1 Gyr. Evolution of the number of white dwarfs is confronted
to the evolution of occurrence rate of events that usually are identified with
SN Ia or accretion-induced collapses, i.e. with accumulation of Chandrasekhar
mass by a white dwarf or a merger of a pair of CO white dwarfs with total mass
not lower than the Chandrasekhar one. In the systems with a burst of star
formation, at $t=$10 Gyr observed supersoft X-ray sources, most probably, are
not precursors of SN Ia. The same is true for an overwhelming majority of the
sources in the systems with constant star formation rate. In the systems of
both kinds mergers of white dwarfs is the dominant SN Ia scenario. In symbiotic
binaries, accreting CO-dwarfs do not accumulate enough mass for SN Ia
explosion, while ONeMg-dwarfs finish their evolution by an accretion-induced
collapse with formation of a neutron star.
