We present a study of the HI, CO and FIR emission properties of galaxies in dense groups and compare with those of the reference sample of extremely isolated galaxies defined in the AMIGA project. We have previously proposed an evolutionary scenario in which the amount of HI decreases with the secular evolutionary state of a group. A key question involves the fate of the HI in stripped galaxies, and how it affects the other ISM components. In order to investigate the process leading to HI deficiency, we imaged HI in a redshift limited sample of compact groups using the VLA. Surprisingly, some of these groups show little HI emission down to a column density as low as 1019 cm-2. We find a trend for the most HI deficient groups to be also deficient in CO and FIR emission, and we propose that when HI is removed from the galaxies the molecular gas is not replenished, inhibiting future star formation activity.