It has been shown by Paczynski that gravitational microlensing is a us
eful method to detect brown dwarfs in the dark halo of our galaxy. At
present several experiments are carried out to monitor several million
stars in the Large Magellanic Cloud with the aim to find such microle
nsing events. Here I discuss the possibility to use as targets stars i
n the Andromeda galaxy. Such an experiment would be sensitive to both
the brown dwarfs in our halo and in the one of M31. The optical depth
tau to gravitational microlensing due to brown dwarfs in the halo of M
31 turns out to be approximately 10(-6), which is comparable to the va
lue Of tau for our own halo. I also compute the microlensing rate and
the average lensing duration and consider moreover the dependence of t
au on the shape of the halo.