  We have carried out a fluctuation analysis in four bands (R4, R5, R6 and R7
corresponding to 0.44-1.01 keV, 0.56-1.21 keV, 0.73-1.56 keV and to 1.05-2.04
keV respectively) of two very deep ROSAT PSPC observations in directions where
the galactic H{\small I} column is minimal. This has enabled us to study the
average spectrum of the sources contributing to 0.5-2 keV fluxes $\sim 10^{-15}
\rm \ergpcmsqps$. The best fit spectral energy index for the average faint
source spectrum, $\alpha=0.95^{+0.10}_{-0.15}$, is still steeper than the one
measured for the extragalactic XRB at these energies $\alpha\sim 0.4-0.7$, but
flatter than the typical AGN spectral index $\alpha\sim 1-1.5$. This result has
allowed us to constrain the existence of a population of sources harder than
the AGNs contributing to the source counts at these fluxes. We find that a
population of X-ray sources with energy spectral index $\alpha\sim 0.4-0.6$
would contribute $(30\pm 20)$ per cent to the source counts at these fluxes if
the rest of them are AGNs with energy spectral index $\alpha\sim 1.2$.
