Recent observations of very cool white dwarfs suggest that the low-lum
inosity portion of the white dwarf luminosity function is indeed domin
ated by the contribution of massive objects. These objects should pred
ominantly be made of oxygen, neon and other trace isotopes. In this pa
per we compute cooling sequences for massive oxygen-neon (ONe) white d
warfs and we examine the question of whether massive ONe white dwarfs
could represent a significant contribution to the white dwarf luminosi
ty function at very low luminosities. We fmd that massive ONe white dw
arfs cool much faster than carbon-oxygen (CO) white dwarfs and that, c
onsequently, their population effectively detaches from the bulk of CO
white dwarfs leading to the formation of a tail in the low-luminosity
portion of the white dwarf luminosity function. Nevertheless, the pos
ition of the reported cut-off in the white dwarf luminosity function i
s not affected and, therefore, the age estimates of the solar neighbou
rhood inferred from the position of the drop-off of the white dwarf lu
minosity function remain unaffected.