The characteristic features of ionic mobility in polymer gel electrolytes are closely related to those shown by the incorporated liquid electrolytes and as such much research is concentrated on the liquid electrolytes in the absence of the polymer host. In this paper, longitudinal relaxation (T-1) measurements of H-1, Li-7, and F-19 nuclei in tetraglyme/LiCF3SO3 and N,N-dimethylformamide/LiCF3SO3 liquid electrolytes are reported. From comparisons with measurements of self-diffusion coefficients and solution viscosity it is concluded that in general there are contributions to T1 from both translational and rotational motions.