The quadrupolar NMR relaxation of Na-23(+) counterions has been studied in a solid sample of macroscopically oriented DNA fibers which was equilibrated at relative humidities of 95 and 98%. The equilibrations resulted in a sample of relatively high water contents, corresponding to approximate distances between the DNA surfaces of 1.1 and 1.3 nm, respectively. Using a combination of relaxation experiments, including two-dimensional spin echo and two-dimensional double quantum quadrupolar echo techniques, the spectral densities J(0)(0), J(1)(omega(0)), and J(2)(2 omega(0)) have been determined at different orientations of the sample with respect to the external magnetic field. The high-frequency spectral densities, J(1)(omega(0)) and J(2)(2 omega(0)) were also determined at two and four different magnetic field strengths, respectively. It was found that they are largely determined by fluctuations of the quadrupolar interaction that occur on a time scale of nanoseconds. The results indicate that the main contribution to J(1)(omega(0)) and J(2)(2 omega(0)) originates from local motions in the vicinity of the DNA molecule. Assuming that this contribution can be divided into two contributions, one fast (assumed to be a constant frequency-independent term) and one slow (assumed to be governed by a Lorentzian function), the experimental frequency dependence could be fitted. The effective correlation time for the slow local motion is in the range of 2-3 ns, depending on water content. It is suggested that this slow local motion is due to the relative motion of the sodium counterion in the vicinity of a charged phosphate group, caused by local diffusion of the sodium counterion and/or motion of the phosphate group itself.