  We present a systematic search for variability among the ROSAT All-Sky Survey
(RASS) X-ray sources. We generated lightcurves for about 30000 X-ray point
sources detected sufficiently high above background. For our variability study
different search algorithms were developed in order to recognize flares,
periods and trends, respectively. The variable X-ray sources were optically
identified with counterparts in the SIMBAD, the USNO-A2.0 and NED data bases,
but a significant part of the X-ray sources remains without cataloged optical
counterparts. Out of the 1207 sources classified as variable 767 (63.5 %) were
identified with stars, 118 (9.8 %) are of extragalactic origin, 10 (0.8 %) are
identified with other sources and 312 (25.8 %) could not uniquely be identified
with entries in optical catalogs. We give a statistical analysis of the
variable X-ray population and present some outstanding examples of X-ray
variability detected in the ROSAT all-sky survey. Most prominent among these
sources are white dwarfs, apparently single, yet nevertheless showing periodic
variability. Many flares from hitherto unrecognised flare stars have been
detected as well as long term variability in the BL Lac 1E1757.7+7034.
