Microlensing towards LMC and M31

(Short version) The nature and the location of the lenses discovered in the microlensing surveys done so far towards the LMC remain unclear. This contribution is comprised of two distinct parts. In the first part, motivated by these questions, we compute the optical depth for the different intervening populations an the number of expected events for self-lensing, using a recently drawn coherent picture of the geometrical structure and dynamics of the LMC disk. In the second part (section 5), a preliminary account of the final results from the EROS-2 programme is presented. Based on the analysis of 33 million LMC and SMC stars followed during 6.7 years, strict limits on the macho content of the galactic halo are presented; they cover the range of macho masses between 0.0001 and 100 solar mass. The limits are better than 20% (resp. 5%) of the standard halo for masses between 0.0002 and 10 (resp. 0.001 to 0.1) solar mass. This is presently the data set with the largest sensitivity to halo machos.