This work presents the anisotropic pseudorotation (APR) model, which is a new dynamic model for the interpretation of experimental nuclear spin-lattice relaxation times in paramagnetic (S=1) complexes of low symmetry. It comprises two dynamic processes active in modulating the zero-field splitting interaction (ZFS). Reorientation of the complex modulates a static zero-field splitting, defined as a measure of the asymmetry in the equilibrium geometry at the paramagnetic site. Local motions of the ligands surrounding the paramagnetic site further contribute a rapidly fluctuating (transient) zero-field splitting interaction. This dynamic model is evaluated within a general theoretical framework capable of dealing with the electron-spin system in the low- and high-magnetic field limits for both Redfield and slow-motion cases, i.e., where the motions : inducing electron-spin relaxation and the electron-spin relaxation itself are characterized by the same time scale. The dynamic model is characterized and discussed by calculating results for a large number of parameter sets. The obtained results are compared with the traditional theory, the Solomon-Bloembergen-Morgan equations (SBM), by least-squares fitting the SBM equations to the APR model. Results show that in most cases the SBM model can fit the nuclear magnetic relaxation dispersion (NMRD) profiles from the APR model at the expense of using a different parameter set. For both models, a restricted fit to-experimental NMRD data, from bis(2,2,6,6-tetramethyl-3,5-heptanedionato)Ni(II)(aniline-d(5))(2) (abbreviated Ni(dpm)(2)(aniline-d(5))(2) or simply NIDPM) in solution, has been performed. The parameters obtained suggest that NIDPM is a slow-motion case comprising a static contribution to its zero-field splitting, so that the SBM model is inapplicable.