  We present the analysis of the first two years of the OGLE search for
gravitational lenses towards the Galactic bulge. We detected 9 microlensing
events in an algorithmic search of $ \sim 10^8 $ measurements of $ \sim 10^6 $
stars. The characteristic time scales are in the range $ 8.6 < t_0 < 62 $ days,
where $ t_0 = R_E / V $. The distribution of amplitudes is consistent with
theoretical expectation. The stars seem to be drawn at random from the overall
distribution of the observed bulge stars. We find that the optical depth to
microlensing is larger than $ ( 3.3 \pm 1.2 ) \times 10^{-6}$, in excess of
current theoretical estimates.
