The validity of the analytical expressions to the problem of NMR relaxation of spin- 3 2 nuclei, based on the second-order perturbation theory, is examined by comparison to numerical solution of the Lionville equation. It is shown that for a slowly rotating site, although relaxation may be well fitted to biexponential decay, second-order perturbation theory does not give the correct values for the decay rates unless κ ≤ 1, with κ = ( χ ω0)26ω0τR, in which X and TR are the quadrupole interaction and the reorientation time, respectively. The above criterion is also examined for relaxation of spins that exchange between slow and fast rotating sites. Relaxation processes with reorientation times longer than the exchange times are also considered. Analytical expressions are given for the longitudinal relaxation of a system with exchanging sites at any concentration ratio.