H-2 in D2O ice clathrate has been studied by hydrogen NMR. In a previous report, the H-2 line shape was shown to be due to incompletely averaged intramolecular dipolar interactions. Here the relaxation times T-1, T-1 rho, and T-2 are reported. T-1 passes through a minimum at 10 K, indicating that the rotational transition rate Gamma between the three sublevels of J = I passes through the resonance frequency at this temperature. On the cold side, T-1 varies as T-(2.6); on the hot side, the rate T-1(-1) varies as T-2 plus a constant (due to paramagnetic impurities). These indicate a two-phonon process drives the rotational transitions Gamma. The spin-echo T-2 is nearly independent of temperature and in reasonable agreement with the Van Vleck intermolecular H-2-H-2 second moment. T-1 rho deviates from the expected T-1 rho = T1 behavior above 85 K, revealing an additional slow-motion source of relaxation. The deviation is driven by the hopping of H-2 between large cages. Ortho-para conversion is measured to be much slower in the clathrate than in the bulk solid, reflecting the greater distances between the H-2, Molecules.