The anisotropic self-diffusion coefficient of Li-7(+) (I = 3/2) counterions has been studied in hydrated, macroscopically oriented Li-(B)DNA fibers at relatively high water contents, corresponding to approximate DNA-DNA helix axis distances of 22-35 Angstrom, using the pulsed field gradient nmr spin-echo method. Self-diffusion coefficients parallel (D-parallel to) and perpendicular (D-perpendicular to) to the DNA helix axis increase with increasing salt content and with increasing DNA-DNA helix axis distance. The observed anisotropy D-parallel to/D-perpendicular to, decreases from 1.6 to 1.2 with the DNA-DNA separation increasing from 22 to 35 Angstrom in the salt-free sample. This result can be understood by the obstruction effect caused by the DNA molecules themselves. The values of the Li+ self-diffusion coefficients in the most water-rich system with no added salt (corresponding to an approximate distance of 35 Angstrom between the DNA helix axes) were D-parallel to similar to 1.15 X 10(-10) m(2) s(-1) and D-perpendicular to similar to 0.98 X 10(-10) m(2) s(-1), compared to 9.14 X 10(-10) m(2) s(-1) for the diffusion of Li+ in an aqueous solution of LiCl (similar to 2.1M). The possible occurrence of restriction effects in the DNA fibers have also been studied by determining the self-diffusion coefficient at different effective diffusion times. The self-diffusion coefficient of Li+ in the sample with the largest DNA-DNA helix axis distance seems to be independent of the effective diffusion time, which indicates that the lithium ions are not trapped within impermeable barriers. The possibility of diffusion through permeable barriers has also been investigated, and is discussed. (C) 1994 John Wiley & Sons, Inc.