  We compute the synthetic 2-100 keV spectrum of an actively star forming
galaxy. To this aim we use a luminosity function of point sources appropriate
for starbursts (based on Chandra data), as well as the types of stellar sources
and their corresponding spectra. Our estimates indicate that a Compton spectral
component - resulting from scattering of SN-accelerated electrons by ambient
FIR and CMB photons - could possibly be detected, in deep INTEGRAL observations
of nearby starburst galaxies, only if there is a break in the spectra of the
brightest (L > 2x10^{38} erg/s) point sources.
