Detailed knowledge of the dynamics and interaction of adsorbate molecules in the cavities of zeolites is crucial for a better understanding of the catalytic propertes of these materials. The dynamics of molecular hydrogen adsorbed in the cavities of partially exchanged type A zeolite (Co4.1Na3.8-A) has been investigated in the energy range 0-40 mev by incoherent inelastic neutron scattering. Both rotational and vibrational excitations are identified in the spectra. The rotational tunnel splitting of the librational ground state of the adsorbed molecular hydrogen is observed at 3.8 mev. Analysis of the data in terms of a 2-fold cosine potential with two degrees of rotational freedom best accounts for the observed spectral features among several models tested. A barrier height of about 1.4 kcal/mol is calculated. A mode at 15.3 mev is accordingly assigned as a vibration of the bound hydrogen. Evidence for the torsional mode of Al(OH)4 complexes, formed in the β-cages during ion exchange, is found in the vibrational spectra at 21 mev.