Relaxation of the nuclear dipolar energy is considered. The static part of HD sets up an energy reservoir, and its dynamic part is taken as the predominant cause for the spinlattice relaxation. This situation may be realized in nature in such pure solids in which molecular reorientations are frequent. Relaxation steps in which the total nuclear spin quantum number does not change are treated in detail. They are found to involve always three nuclear spins. The theory is applied to solid benzene in which the molecules are assumed to reorient about their 6fold symmetry axis. Both intra- and intermolecular interactions need to be taken into account. The theoretical results obtained are in close agreement with recent measurements of van Steenwinkel.