  The interpretation of microlensing results towards the Large
  Magellanic Cloud (LMC) still remains controversial. White dwarfs have been
proposed to explain these results and, hence, to contribute significantly to
the mass budget of our Galaxy. However, several constraints on the role played
by regular carbon-oxygen white dwarfs exist. Massivewhite dwarfs are thought to
be made of a mixture of oxygen and neon. Correspondingly, their cooling rate is
larger than those of typical carbon-oxygen white dwarfs and they fade to
invisibility in short timescales. Consequently, they constitute a good
candidate for explaining the microlensing results. Here, we examine in detail
this hypothesis by using the most recent and up-to-date cooling tracks for
massive white dwarfs and a Monte Carlo simulator which takes into account the
most relevant Galactic inputs. We find that oxygen-neon white dwarfs cannot
account for a substantial fraction of the microlensing depth towards the LMC,
independently of the adopted initial mass function, although some microlensing
events could be due to oxygen--neon white dwarfs. The white dwarf population
contributes at most a 5% to the mass of the Galactic halo.
