  (abridged) A detailed comparison is performed of the LFs compiled at
infrared, radio and optical wavelengths and converted into XLFs using available
relations with the XLF directly estimated in the 0.5--2 keV energy band from
X-ray surveys (Norman et al). We find that the XLF from the local sample of
IRAS galaxies (Takeuchi et al) provides a good representation of all available
data samples; pure luminosity evolution of the form (1+z)^\eta, with \eta< ~3,
is favoured over pure density. The local X-ray luminosity density is also well
defined. We discuss different estimates of the galaxies LogN-LogS, selected
from the Chandra Deep Fields with different selection criteria: these have
similar slopes, but normalisations scattered within a factor ~2, of the same
order of the Poissonian error on the counts. We compare the observed LogN-LogS
with the counts predicted by integrating our reference z=0 XLF. By using number
counts alone, it is not possible to discriminate between density and luminosity
evolution; however, the evolution of galaxies must be stopped in both cases at
z~1-2. The contribution of galaxies to the X-ray background is found to be in
the range 6%--12%. Making use of cosmic star formation models, we find that the
X-ray LogN-LogS might be not compatible with very large star formation rates at
z ~ 3 as suggested by sub-mm observations in Blain et al. 1999. As to the
content of current and, possibly, future X-ray surveys, we determine the
fraction of galaxies around the current flux limit: (30+-12 %). At fainter
fluxes the fraction of galaxies will probably rise, and overcome the counts
from AGN at fluxes < ~10^{-17} erg/s/cm^2.

Astrophysics