We present a scenario model of the population of close binaries in whi
ch the brighter component is a helium or a carbon-oxygen white dwarf.
The other, dimmer component can be a helium white dwarf, a carbon-oxyg
en white dwarf, or a low-mass (less than or equal to 0.3 M.) main-sequ
ence star. The model takes into account the effects of observational s
election related to the cooling of white dwarfs and the relative brigh
tness of components. The total birthrate of such binaries in our Galax
y is estimated to be similar to 0.17 yr(-1). In the model, in 63% of a
ll cases, the dimmer component is also a white dwarf. In 82% of the sy
stems that consist of two close white dwarfs, the brighter component i
s a helium white dwarf. This explains why, in at least seven out of th
e eight white dwarf pairs found in recent years, the primary is compos
ed of helium. We estimate that close white dwarf pairs may constitute
1/9 of the total sample of observed white dwarfs. Systems that have a
total mass exceeding 1.4 M. and in which the components are close enou
gh to merge in a Hubble time may constitute similar to 1/40 of all clo
se white dwarf pairs. This means that the sample of observed white dwa
rf pairs must be at least quadrupled before one may hope to find a hyp
othetical Type Ia supernova (SN Ia) precursor. The total number of SN
Ia precursors is estimated to exceed the observable number by a factor
of about 20. The merger frequency of close binary helium white dwarfs
in the Galaxy is estimated to be similar to 0.02 yr(-1). This number
is consistent with the fact that, in the total sample of known white d
warf pairs, there are three in which the components are close enough t
o merge in a Hubble time. In one system (WD 1101 + 364), the merger ma
y result in the formation of a helium subdwarf (nondegenerate helium s
tar), and in two others (WD 2331 + 290 and WD 0957 - 666), probably in
the formation of a hydrogen-deficient subgiant and possibly later of
an R CrB star. The predicted merger frequency is also consistent with
the fact that two out of seven white dwarfs selected for their low mas
s are apparently single, while five are in close binaries.