  We search for faint X-ray bursts with duration 10--300 seconds in the ROSAT
PSPC pointed observations with a total exposure of 1.6e7 seconds. We do not
detect any events shorter than ~100s, i.e. those that could be related to the
classic gamma-ray bursts. At the same time, we detect a number of long flares
with durations of several hundred seconds. Most, but not all, of the long
flares are associated with stars. If even a small number of those long flares,
that cannot identified with stars, are X-ray afterglows of GRB, the number of
X-ray afterglows greatly exceeds the number of BATSE GRB. This would imply that
the beaming factor of gamma-rays from the burst should be >100. The
non-detection of any short bursts in our data constrains the GRB counts at the
fluences 1--2.5 orders of magnitude below the BATSE limit. The constrained
burst counts are consistent with the extrapolation of the BATSE log N - log S
relation. Finally, our results do not confirm a reality of short X-ray flashes
found in the Einstein IPC data by Gotthelf, Hamilton and Helfand.
