  The X-ray luminosity function (XLF) of galaxies is dominated by AGN
(classified by their optical spectra) above
  Lx=10**42 erg/s, below this value by normal galaxies. The X-ray flux of AGN
at low X-ray luminosity therefore contains contributions from stellar processes
(winds, supernova explosions etc.). Until now it is not clear which fraction of
the observed X-ray flux has to be associated to the underlying stellar
emission. We started to investigate a complete luminosity-limited sample of AGN
and galaxies with log Lx < 42.5 to discriminate between the nuclear and galaxy
flux. Using the ROSAT HRI data we calculated the radial wobble-corrected
profiles of the sources which were compared to a new HRI point spread function
(PSF) template derived from 21 X-ray bright stars. The majority of the
low-luminosiy AGN shows evidence for a significant fraction of extended X-ray
emission.
