  Most close double helium white dwarfs will merge within a Hubble time due to
orbital decay by gravitational-wave radiation. However, a significant fraction
with low mass ratios will survive for a long time as a consequence of stable
mass transfer. Such stable mass transfer between two helium white dwarfs (HeWD)
provides one channel for the production of AM\,CVn binary stars. In previous
calculations of double HeWD progenitors, the accreting HeWD was treated as a
point mass. We have computed the evolution of 16 double HeWD models in order to
investigate the consequences of treating the detailed evolution of both
components. We find that the boundary between binaries having stable and
unstable mass transfer is slightly modified by this approach. By comparing with
observed periods and mass ratios, we redetermine masses of eight known AM\,CVn
stars by our double HeWDs channel, i.e. HM\,Cnc, AM CVn, V406\,Hya, J0926,
J1240, GP\,Com, Gaia14aae and V396\,Hya. We propose that central spikes in the
triple-peaked emission spectra of J1240, GP\,Com and V396\,Hya and the surface
abundance ratios of N/C/O in GP\,Com can be explained by the stable double HeWD
channel. The mass estimates derived from our calculations are used to discuss
the predicted gravitational wave signal in the context of the Laser
Interferometer Space Antenna (LISA).
