The theory of deuteron spin-lattice relaxation for free D 2 quantum rotors is developed.Relaxafion rates are calculated for ortho-D z and p a r a -D 2. The spin-rotational interaction as well as quadrupole and dipole-dipole interactions under interference condition are taken into account. Relaxation rates, to be compared with experiment, are derived as weighted sums of cont¡ from different rotational states according to their Boltzmann populations. The theory is applied to explain relaxation rates measured in a wide temperature range for D 2 molecules in NaY zeolite cages. At high temperatures (above 110 K), a scattering of molecules on the cage walls provides the relaxation mechanism. At low temperatures, molecules stay close to the surface and undergo reorientations in a potential introduced by the adsorption centers.