  We explore the adiabatic pulsational properties of massive white dwarf stars
with hydrogen-rich envelopes and oxygen/neon and carbon/oxygen cores. To this
end, we compute the cooling of massive white dwarf models for both core
compositions taking into account the evolutionary history of the progenitor
stars and the chemical evolution caused by time-dependent element diffusion. In
particular, for the oxygen/neon models, we adopt the chemical profile resulting
from repeated carbon-burning shell flashes expected in very massive white dwarf
progenitors. For carbon/oxygen white dwarfs we consider the chemical profiles
resulting from phase separation upon crystallization. For both compositions we
also take into account the effects of crystallization on the oscillation
eigenmodes. We find that the pulsational properties of oxygen/neon white dwarfs
are notably different from those made of carbon/oxygen, thus making
asteroseismological techniques a promising way to distinguish between both
types of stars and, hence, to obtain valuable information about their
progenitors.
