  We cross-correlated the Chandra XASSIST and XMM-Newton Serendipitous Source
Catalogues with the 2 degree Field Galaxy Redshift Survey (2dfGRS) database.
Our aim was to identify the most X-ray luminous (L_X > 10^42 erg s^-1) examples
of galaxies in the local Universe whose X-ray emission is dominated by stellar
processes rather than AGN activity ('normal' galaxies) as well as to test the
empirical criterion log(f_X/f_O) < -2 for separating AGN from NGs. With
XMM-Newton (Chandra) we covered an area of ~8.2 (~5.8)deg^2 down to a flux
limit of ~10^-15 (~1.6 x 10^-15) erg cm^-2 s^-1 and found 18 (20) 2dfGRS
galaxies. Using emission-line intensity ratios, we classified 6 2dfGRS spectra
as star-forming, H II nuclei, and 2 spectra as possible H II nuclei. The rest
of the objects are absorption-line galaxies and AGN, including 3 possible
LINERs. No luminous 'normal' galaxies have been found but out of 19 'normal'
galaxies in this sample 5 H II and 3 absorption-line galaxies have log(f_X/f_O)
> -2. We performed a similar search in two nearby-galaxy samples from the
literature. All 44 galaxies in the Zezas (2001) sample have log(f_X/f_O) < -2
and L_X < 10^42 erg s^-1. In the Fabbiano et al. (1992) sample, out of a total
of 170 'normal' galaxies, we found 16 galaxies with log(f_X/f_O) >-2, the
majority of which are massive ellipticals. Three of these have L_X > 10^42 erg
s^-1 .
