We report careful measurements of the relaxation times T-1 and T-2 of the phosphorus nucleus on the (CH3P+ ions in varying concentrations of .ON (SO3)(2)(2)- anion free radicals in D2O solutions at 25 degrees C for an NMR frequency v(1) = 81 MHz. The hyperfine scalar coupling between the P-31 nuclei and the free radicals is determined from the frequency shifts of the resonance lines with respect to their position in the diamagnetic solution, It is shown that this interaction has a negligible effect on the longitudinal relaxation time T-1, which is governed by the magnetic dipolar intermolecular coupling, but significantly contributes to the transverse relaxation time T-2, leading to a ratio, T-1/T-2 congruent to 1.5, in excellent agreement with experiment.