The displacement of water molecules associated with the flow of water inside a nonconsolidated packing of 800 &mgr;m OD glass spheres has been measured by a pulsed gradient NMR technique. Using a stimulated spin‐echo sequence, mean displacements of up to 300 &mgr;m corresponding to measurement times of up to 200 ms can be analyzed. The measurement can be quantitatively calibrated using the pure molecular self‐diffusion of water at zero flow conditions. For molecular displacements much smaller than the pore size, the distribution of the flow velocity component along the mean flow direction is determined at Reynolds numbers high enough so that longitudinal molecular diffusion is negligible. An exponential decay of the probability distribution of the displacements is observed at large distances. The results are very similar to those obtained by numerical solution of the Stokes equation in random sphere packings. At longer displacement distances, a secondary peak of the displacement distribution is observed: It is interpreted as the first step toward the transition toward classical dispersion at displacements much larger than the pore size. The influence of molecular diffusion and of the heterogeneities of the magnetic permeability also are discussed. ©1996 American Institute of Physics.