Two solvent-free cross-linked polymer electrolytes, a random ethyleneoxide and propyleneoxide copolymer, poly(EO-PO) and a random ethyleneoxide and 2-[2-(2-methoxyethoxy)ethoxy]ethylglycidylether copolymer, poly(EO-GE) doped with LiN(SO2CF3)(2) in the ratio 10:1 (polymer oxygen:lithium) were studied using ionic conductivity and H-1,F-19 and Li-7 NMR measurements in the temperature range of similar to 303-353 K. Correlation times for the polymer segmental and the lithium hopping motions of the order of 10(-10)-10(-8) s were determined from the minima in the temperature dependence of the spin-lattice relaxation of the polymers (H-1) and lithium (Li-7). At the same temperature such motions are faster in the poly(EO-PO) than in the poly(EO-GE) systems and the temperature dependencies of these motions are larger in the poly(EO-PO) system. Since the relaxation behaviors of the anion (19F) were consistent with a single component, the self-diffusion coefficients of the anion were measured using the pulsed-gradient spin-echo (PGSE) NMR method. Although the diffusion data were consistent with a single isotropically diffusing species at each temperature, the measured diffusion coefficients were dependent on Delta (the timescale of the diffusion measurement) but became constant at long Delta values. We surmise that at long Delta the anion has sufficient time to diffuse amongst enough microdomains of the polymer electrolyte system to complete a 'true average'. During shorter times, the anion appears to diffuse faster. The activation energies obtained from the apparent diffusion coefficients at longer Delta values agreed with those obtained from ionic conductivity measurements for the two polymer electrolytes. The anion diffusion in poly(EO-PO) is faster than in poly(EO-GE) at every temperature.