  To improve the understanding of the pulsational instabilities of some of the
PG1159-type pre-white dwarfs we performed detailed stability analyses on helium
star evolutionary models. With the canonical chemical compositions, pulsational
instabilities were encountered for all stellar masses considered (0.57, 0.63,
0.7 M_sol). The blue boundary agrees satisfactorily with observations. The red
edge, on the other hand, is found to extend lower temperatures than presently
admitted by observers. The dependence of the pulsational instabilities on
helium or even hydrogen abundance in the stellar envelopes is less stringent
than emphasized hitherto. In particular, we found pulsationally unstable
g-modes for model stellar envelopes which are representative for HS2324+3944, a
newly discovered PG1159-star with a hydrogen abundance X of approximately 0.2
and being pulsating.
