  We report on a powerful and variable off-nuclear X-ray source in the nearby
spiral galaxy NGC 4945. Two ROSAT PSPC observations show the source to brighten
in 0.5--2.0 keV flux by a factor of about 9 on a time-scale of 11 months or
less. It is seen by ASCA about one month after the second PSPC pointing, and is
seen to have dimmed by a factor of > 7 in a ROSAT HRI pointing about one year
after the second PSPC pointing. Its maximum observed 0.8--2.5 keV luminosity is
about 8E38 erg/s, making it brighter than any known persistent X-ray binary in
the Milky Way. Its total X-ray luminosity is probably larger than 1.2E39 erg/s.
The observed variability argues against a superbubble interpretation, and the
off-nuclear position argues against a low-luminosity active galactic nucleus.
The source is therefore probably either an ultra-powerful X-ray binary or an
ultra-powerful supernova remnant. Optical monitoring has not identified any
supernovae in NGC 4945 during the time of the X-ray observations, and any
supernova would have had to have been either very highly absorbed or
intrinsically optically faint.
