We present ferrimagnetic-resonance linewidth measurements at 9.3 Gc/sec and 16.9 Gc/sec between 1.5 and 250°K in the principal crystallographic directions for a single crystal of yttrium iron garnet (YIG) doped with 0.82% Nd. These results are compared with the linewidth predicted by the longitudinal (so-called "slow relaxing ion") mechanism of relaxation for a single Kramers doublet. We find that the temperature and frequency dependences of the linewidths are in good agreement with the predictions, but that the anisotropic exchange splitting of the ground-state Kramers doublet is not accurately described by a tensor G, according to (G12i2+G22j2+G32k2)12, probably through the admixture of higher states into the ground doublet. However, the tensor G1~40 cm-1; G2~20 cm-1; G3~80 cm-1 describes the basic topology of the splitting. We also deduce τ, the relaxation time of the Nd3+ ion in the YIG environment. The results are somewhat limited except in the  direction, where they suggest that for T<40°K a direct process dominates, and is given by (1τ)D=(1τ0)D(δ1112kT) with (1τ0)D~4×1010 sec-1 for the average splitting in the  direction δ111 equal to 61.3 cm-1. We cannot say whether this observed direct process is predominantly spinmagnon or spin-lattice, for a rough estimate shows that both processes could conceivably be of the observed order of magnitude. At higher temperatures, the temperature dependence of the observed relaxation time follows that expected for the Orbach or resonance process, as described by (1τ)O=B[exp(∆kT)-1] with B=9×1011 sec-1 for a value of ∆ of 85 cm-1, as is indicated by the Orbach-process relaxation-time results reported for Nd3+ in yttrium gallium garnet, for which the value of B is about an order of magnitude smaller than the value reported here.