  We present a study of the hard X-ray properties of a sample that includes all
the Luminous Infrared Galaxies (LIGs, L_IR > 10^11 L_sun) observed in the 2-10
keV energy band (new and archival data). We find that a significant fraction of
the sources optically classified as AGNs do not show any indication of nuclear
activity in the X rays, thus suggesting heavy absorption along our line of
sight. The absence of strong emission in the 20-200 keV band in a subsample of
LIGs observed with BeppoSAX suggests that in many cases these sources are
completely Compton thick (N_H > 10^25 cm^(-2)). From a comparison between the
infrared and the X-ray emission we deduce that the mid-IR emission is absorbed
by a lower column density than the X-ray emission or, alternatively, that the
dust-to-gas ratio is lower than Galactic. We describe a simple model that
reproduces the IR-X correlation by means of mixed AGN and starburst
contributions and we compare the predictions of this model with the
observational data at X-ray and optical wavelengths. Finally, we discuss the
biases that affect the currently available samples of LIGs and briefly analyze
a small unbiased sample, finding that at least 50% of the sources host a (weak)
AGN.

Astrophysics