Often the paramagnetic defects have important impact on the nuclear relaxation even in the "nominally" pure samples. These effects show themselves either by the nearest neighbors only or by the dipolar long-range interaction. The former are addressed in this paper in which we built a model for calculation of T-1, T-1Q, T-2, T-1 rho when there is-o- not a residual quadrupolar interaction. This model shows that the maxima of R-2 = 1/T-2 and R-1 rho = 1/T-1 rho are shifted toward the low frequencies (low temperatures with regards to the one of R-1 = 1/T-1), the maximum of R-1 rho is shifted toward the low frequencies with regards to the one of R2, and this model is general and can be applied to any system which relaxes by transferred hyperfine interaction. This model was applied to Li.1.3Al0.3Ti1.7(PO4)(3). It accounts for all the experimental results of T-1 (Li-6), T-1 (Li-7), T-1Q, (Li-7), T-2 (Li-7), and T-1 rho (Li-7) which were used to highlight local dynamic properties of the lithium versus temperature. The analysis of these results allows us to conclude that inside the natrium superionic conductor (NASICON) framework the lithium undergoes an anisotropic motion, evidenced both with the residual quadrupolar interaction and the measures of the relaxation times, and the relaxation of the lithium is mainly due to the hyperfine transferred fluctuations. Thus, the motion drives the lithium ions in the neighborhood of the oxygens, and these dynamical results allow confirming structural aspects concerning the conducting pathways.