We present a study of the hard X-ray properties of a sample that includes a
ll the Luminous Infrared Galaxies (LIGs, L-IR > 10(11) L-circle dot) observ
ed in the 2-10 keV energy band (new and archival data). We find that a sign
ificant fraction of the sources optically classified as AGNs do not show an
y indication of nuclear activity in the X rays, thus suggesting heavy absor
ption 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 ma
ny cases these sources are completely Compton thick (NH > 10(25) cm(-2)). F
rom a com parison between the infrared and the X-ray emission we deduce tha
t 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 Galacti
c. 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. F
inally, we discuss the biases that affect the currently available samples o
f LIGs and briefly analyze a small unbiased sample, finding that at least 5
0% of the sources host a (weak) AGN.