  We present new evidence of X-ray absorption variability on time scales from a
few hours to a few days for several nearby bright AGNs. The observed N_H
variations imply that the X-ray absorber is made of clouds eclipsing the X-ray
source with velocities in excess of 10^3 km/s, and densities, sizes and
distances from the central black hole typical of BLR clouds. We conclude that
the variable X-ray absorption is due to the same clouds emitting the broad
emission lines in the optical/UV. We then concentrate on the two highest
signal-to-noise spectra of eclipses, discovered in two long observations of NGC
1365 and Mrk 766, and we show that the obscuring clouds have a cometary shape,
with a high density head followed by a tail with decreasing N_H. Our results
show that X-ray time resolved spectroscopy can be a powerful way to directly
measure the physical and geometrical properties of BLR clouds.
