  The nature and the location of the lenses discovered in the microlensing
surveys done so far towards the LMC remain unclear. Motivated by these
questions we computed the optical depth for the different intervening
populations and the number of expected events for self-lensing, using a
recently drawn coherent picture of the geometrical structure and dynamics of
the LMC. By comparing the theoretical quantities with the values of the
observed events it is possible to put some constraints on the location and the
nature of the MACHOs. Clearly, given the large uncertainties and the few events
at disposal it is not yet possible to draw sharp conclusions, nevertheless we
find that up to 3-4 MACHO events might be due to lenses in LMC, which are most
probably low mass stars, but that hardly all events can be due to self-lensing.
The most plausible solution is that the events observed so far are due to
lenses belonging to different intervening populations: low mass stars in the
LMC, in the thick disk, in the spheroid and some true MACHOs in the halo of the
Milky Way and the LMC itself. We report also on recent results of the
SLOTT-AGAPE and POINT-AGAPE collaborations on a search for microlensing events
in direction of the Andromeda galaxy, by using the pixel method. The detection
of 4 microlensing events, some likely to be due to self--lensing, is discussed.
One microlensing light curve is shown to be compatible with a binary lens. The
present analysis still does not allow us to draw conclusions on the MACHO
content of the M31 galaxy.
