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 noticeably different from those made of carbon/oxygen, thus making asteroseismological techniques a promising way to distinguish between the two types of stars and, hence, to obtain valuable information about their progenitors.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plata