  We study two models for AM CVn stars: white dwarfs accreting (i) from a
helium white dwarf companion and (ii) from a helium-star donor. We show that in
the first model possibly no accretion disk forms at the onset of mass transfer.
The stability and the rate of mass transfer then depend on the tidal coupling
between the accretor and the orbital motion. In the second model the formation
of AM CVn stars may be prevented by detonation of the CO white dwarf accretor
and the disruption of the system. With the most favourable conditions for the
formation of AM CVn stars we find a current Galactic birth rate of 6.8 10^{-3}
yr^{-1}. Unfavourable conditions give 1.1 10^{-3} yr^{-1}. The expected total
number of the systems in the Galaxy is 9.4 10^{7} and 1.6 10^{7}, respectively.
We model very simple selection effects to get some idea about the currently
expected observable population and discuss the (quite good) agreement with the
observed systems.
