We study the atomic (H i) and molecular hydrogen (H2) contents of early-type galaxies (ETGs) and their gas sources using the galform model of galaxy formation. This model uses a self-consistent calculation of the star formation rate, which depends on the H2 content of galaxies. We first present a new analysis of H i Parkes All-Sky Survey and ATLAS3D surveys, with special emphasis on ETGs. The model predicts H i and H2 contents of ETGs in agreement with the observations from these surveys only if partial ram pressure stripping of the hot gas is included, showing that observations of neutral gas in ‘quenched’ galaxies place stringent constraints on the treatment of the hot gas in satellites. We find that ≈90 per cent of ETGs at z = 0 have neu...