  We investigate the accuracy of astrometric measurements with the VLT/FORS1
camera and consider potential applications. The study is based on two-epoch
(2000 and 2002/2003) frame series of observations of a selected Galactic Bulge
sky region that were obtained with FORS1 during four consecutive nights each.
Reductions were carried out with a novel technique that eliminates atmospheric
image motion and does not require a distinction between targets and reference
objects. The positional astrometric precision was found to be limited only by
the accuracy of the determination of the star photocentre, which is typically
200-300 microarcsec per single measurement for bright unsaturated stars
B=18-19. Several statistical tests have shown that at time-scales of 1-4 nights
the residual noise in measured positions is essentially a white noise with no
systematic instrumental signature and no significant deviation from a Gaussian
distribution. Some evidence of a good astrometric quality of the VLT for frames
separated by two years has also been found. Our data show that the VLT with
FORS1/2 cameras can be effectively used for astrometric observations of
planetary microlensing events and other applications where a high accuracy is
required, that is expected to reach 30-40 microarcsec for a series of 50 frames
(one hours with R filter).

Astrophysics