  We study the formation of neon-enriched donor stars in ultracompact X-ray
binaries (orbital periods P<80 min) and show that their progenitors have to be
low-mass (0.3 - 0.4 solar mass) ``hybrid'' white dwarfs (with CO cores and
thick helium mantles). Stable mass transfer is possible if in the initial
stages of mass exchange mass is lost from the system, taking away the specific
orbital angular momentum of the accretor (``isotropic re-emission''). The
excess of neon in the transferred matter is due to chemical fractionation of
the white dwarf which has to occur prior to the Roche lobe overflow by the
donor. The estimated lower limit of the orbital periods of the systems with
neon-enriched donors is close to 10 min. We show that the X-ray pulsar 4U
1626-67, which likely also has a neon-enriched companion, may have been formed
via accretion induced collapse of an oxygen-neon white dwarf accretor if the
donor was a hybrid white dwarf.
