Received??/??/1999, accepted Abstract. In this article, we have investigated the possibility to distinguish between different galactic models through the microlensing parallax studies. We show that a systematic search for parallax effects can be done using the currently running alert systems and complementary photometric telescopes, to distinguish between different lens distance distributions. We have considered two galactic dark compact objects distributions, with total optical depths corresponding to the EROS current upper limits. These models correspond to two extreme hypothesis on a three component galactic structure made of a thin disk, a thick disk, and a spherically symmetric halo. Our study shows that for sub-solar mass lenses, an exposure of 8 ×10 7 star×yr toward LMC should allow to distinguish between these two extreme models. In addition the self-lensing hypothesis (lensing by LMC objects) can efficiently be tested through the method proposed here
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