  The nature of the several microlensing events observed by the MACHO team
towards the Large Magellanic Cloud (LMC) is still a subject of debate. Low-mass
substellar objects and stars with masses larger than ~M_{sun} have been ruled
out as major components of a Massive Astrophysical Compact Halo Object (MACHO)
Galactic halo, while stars of half a solar mass seem to be viable candidates.
Main sequence stars have been already discarded, and there are tight
restrictions on the role played by white dwarfs with hydrogen-dominated
atmospheres. In this paper we evaluate the contribution to the dark matter
content of the Galaxy of white dwarfs with hydrogen-deficient atmospheres. For
this purpose we use a Monte Carlo simulator which incorporates up-to-date
evolutionary sequences of white dwarfs with hydrogen-rich and
hydrogen-deficient atmospheres. We also take into account detailed descriptions
of the thick disk and the halo of our Galaxy as well as of a reliable model of
the LMC. We find that the contribution of white dwarfs with hydrogen-deficient
atmospheres moderately increases the theoretical estimate of the optical depth
with respect to the value obtained when only hydrogen-rich white dwarfs are
considered. We also find that the contribuiton of the thick disk population of
white dwarfs is comparable to the halo contribution. However, the contributions
of both the halo and the thick disk white-dwarf populations are still
insufficient to explain the number of events observed by the MACHO team.
Finally, we find that the contribution to the halo dark matter of the entire
population under study is less than 10% at the 95% conficence level.
