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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.