We investigate the NMR relaxation of solvent nuclei in non viscous paramagnetic solutions, in the case where the electronic spin of the paramagnetic species is submitted to an internal hyperfine field H-hyp. General expressions of the intermolecular longitudinal relaxation rates 1/T-1 are provided, and three distinct regimes corresponding to an applied external field lower, larger and much larger than H-hyp appear, with three distinct linear laws for the relaxation rate 1/T-1 vs v(1)(1/2) ,, where vl is the nuclear resonance frequency. From each of these laws and mainly the third one, it is possible to derive the relative diffusion constant of the paramagnetic and solvent molecules without any model assumption for solutions with a rather high radical concentration of 10(-1) mol L-1. This is illustrated for a triglyme solution with new stable (NTMIOD)-N-15 free radicals at various concentrations. For this solution, T-1 measurements were performed at v(1) = 244 MHz, then at low and intermediate frequencies by the field cycling technique and finally in the Earth＇s magnetic field. From these results and from measurements of the solvent molecule diffusion constant by the pulsed magnetic field gradient technique, a determination of the diffusion constant of the free radicals is obtained which is compared with that obtained from a direct ESR measurement at low concentration. These data are used for the interpretation of the frequency and temperature dependence of the relaxation rates in this solution.