We review the results of nuclear magnetic resonance studies of the molecular dynamics of the quantum gases HD and CH 4 adsorbed in the cages of microporous structures. Measurements of the variation of the nuclear spinlattice and nuclear spin-spin relaxation times with temperature provide detailed information about the translational and rotational dynamics of the adsorbed molecules over a wide temperature range. PACS: 76.60.-k Nuclear magnetic resonance and relaxation.