The quantum dynamics of dihydrogen molecules entrapped inside fullerene cages has been investigated using inelastic neutron scattering (INS). For the endofullerene H 2 @C 60 the low-lying energy levels of the manifold of coupled translational and rotational states have been accurately determined by studying INS spectra recorded in the temperature range 1.5 T 240 K. The majority of transitions observed in the INS spectra interconvert the nuclear spin isomers orthohydrogen and parahydrogen. The cage potential has icosahedral symmetry and splittings observed in the INS spectra reveal the coupling of translational and rotational angular momentum of the H 2 molecules. The effects of nuclear spin symmetry, isotope mass effects, and cage anisotropy have been further investigated by studying HD@C 60 and H 2 inside an open cage endofullerene. The momentum transfer κ arising from the neutron scattering event has also been investigated. The κ-dependence spectra reflect the physical dimensions of the dihydrogen molecule and its confinement in its cage. We show how this may be used as a tool for assigning the INS transitions.