Аннотация:Context. Ultracompact cataclysmic variables (CVs) of the AM CVn type are deemed to be important verification sources for thefuture space gravitational wave detectors such as the Laser Interferometer Space Antenna (LISA).Aims. We model the present-day Galactic population of AM CVn stars with He-star donors. Such a population has long expected toexist, though only a couple of candidates are known.Methods. We applied the hybrid method of binary population synthesis (BPS) which combines a simulation of the population ofimmediate precursors of AM CVn stars by a fast BPS code with subsequent tracking of their evolution by a full evolutionary code.Results. The model predicts that the present birthrate of He-donor AM CVn stars in the Galaxy is 4.6×10−4 yr−1and the Galaxy mayharbour '112 000 objects of this class which have orbital periods P . 42−43 min. The foreground confusion limit and instrumentalnoise of LISA prevent the discovery of longer periods systems in gravitational waves. We find that about 500 He-star AM CVns maybe detected by LISA with signal-to-noise ratio (S/N) > 5 during a 4 yr mission. Within 1 Kpc from the Sun, there may exist up to130 He-star AM CVns with the periods in the same range, which may serve as verification binaries, if detected in the electromagneticspectrum. In the Milky Way, there are also '14 800 immediate precursors of AM CVn stars. They are detached systems with a strippedlow-mass He-star and a white dwarf companion, out of which about 75 may potentially be observed by LISA during its mission.