F-19 and Li-7 pulsed field gradient (PFG) NMR measurements have been undertaken to determine anion and cation diffusion coefficients of tetraethylene glycol dimethyl ether/LiCF3SO3 and N,N dimethyl formamide/LiCF3SO3 solutions over a range of temperatures and concentration. The diffusion of the solvent molecules has also been determined by H-1 PFG NMR measurements. In addition, viscosity and ionic conductivity measurements have been undertaken. The ionic diffusion and ionic conductivity data are discussed in terms of the Nernst-Einstein equation and the relationship between ionic diffusion and viscosity are considered in terms of the Stokes-Einstein equation. Finally, NMR T-1 data are considered in terms of diffusion and rotation of solvent molecules.