The NMR pulsed field gradient spin echo technique has been used to measure the self-diffusion coefficients of Li-7, F-19 and protons in two polymer gel electrolytes, based on polyvinylidene fluoride (PVDF) and LiCF3SO3 with tetraglyme (TG) or N,N-dimethylformamide (DMF). Predicted values for the ionic conductivity were obtained from the NMR diffusivities using the Nernst-Einstein equation and compared with those from direct a.c. conductivity measurements to provide estimates of the degree of ionic association as a function of temperature and salt concentration. The results for the gel electrolytes are compared with those for the corresponding liquid electrolytes and are found to be very similar. There are, however, some small but significant differences between the behaviours of the gel electrolytes and the liquid electrolytes and these are discussed. The picture that emerges is of a two-phase material with regions of liquid electrolyte existing within a polymer gel rich matrix. This is consistent with measurements of the transverse relaxation time T-2 on these systems. The combination of high ionic conductivity with good mechanical properties of these polymer gel electrolytes is confirmed by their excellent performance in prototype battery systems.