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 \times 10 ^ { -3 } { yr ^ { -1 } } .
Unfavourable conditions give 1.1 \times 10 ^ { -3 } { yr ^ { -1 } } .
The expected total number of the systems in the Galaxy is 9.4 \times 10 ^ { 7 } and 1.6 \times 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 .