Deuterium (H-2) NMR relaxation plays a major role in the study of lipid reorientational dynamics, with the angular dependence of the relaxation rates providing a novel and critical test of proposed motional models. Spin-lattice relaxation rates (R(1Z)) were measured for macroscopically oriented bilayers of 1,2-diperdeuteriolauroyl-sn-glycero-3-phosphocholine (DLPC-d(46)) in the liquid-crystalline (L(alpha)) phase. The results for different positions along the chain (index i) were dependent on the angle theta between the macroscopic bilayer normal and the static external magnetic field, and allowed the anisotropy of R(1Z)((i)) to be determined for nine resolved quadrupolar resonances. Angular-dependent relaxation data were evaluated using simple models of anisotropic rotational diffusion within an odd or even potential of mean torque as a framework for describing (i) segmental reorientations of the chains, or alternatively (ii) noncollective molecular motions within the bilayer. Moreover, (iii) a simple quasi-hydrodynamic formulation involving collective fluctuations of a local director axis was considered (continuum model).