The diffusional mobility of water, Cs, and Li counterions in oriented DNA fibers have been investigated by means of NMR self-diffusion measurements as a function of varying water content and salt concentration. in addition, H-1 relaxation times T-1 of water in the;systems have been measured. To interpret these data and gain insight into the dynamics and structure of the DNA samples, molecular dynamics (MD) computer simulations have been carried out for corresponding systems at high water content. Data from MD simulations have been used to calculate the anisotropic self-diffusion coefficients and orientational distribution functions to reveal the most probable coordination sites for the counterions. The mutual agreement between the simulated and experimental self-diffusion coefficients is very good. In both the experiments and the simulations, it is found that Li ion diffusion is considerably slower than the Cs ion diffusion. This is found to be due to loss of water of hydration for Li+, giving strong and long-lived interactions with the negatively charged DNA phosphate groups.