  A complete sample of 60 serendipitous hard X-ray sources with flux in the
range $\sim 1 \times 10^{-13}$ \ecs to $\sim 4 \times 10^{-12}$ \ecs (2 - 10
keV), detected in 87 ASCA GIS2 images, was recently presented in literature.
Using this sample it was possible to extend the description of the 2-10 keV
LogN(>S)-LogS down to a flux limit of $\sim 6\times 10^{-14}$ \ecs (the
faintest detectable flux), resolving about a quarter of the Cosmic X-ray
Background. In this paper we have combined the ASCA GIS2 and GIS3 data of these
sources to investigate their X-ray spectral properties using the "hardness"
ratios and the "stacked" spectra method. Because of the sample statistical
representativeness, the results presented here, that refer to the faintest hard
X-ray sources that can be studied with the current instrumentation, are
relevant to the understanding of the CXB and of the AGN unification scheme.
