Dispersion at short times is studied using a PFG-NMR (pulsed field gradient NMR) technique inside a fixed bed of nonconsolidated spherical beads saturated with water flowing at a constant velocity. This allows measurement of the probability distribution of the displacement of water molecules along the magnetic field gradient during a preset measurement time&Dgr;: the mean displacement of the water molecules is varied between 0.1 and 7.3 times the bead diameter by varying&Dgr;between 20 and 100 ms and the bead diameter between 800 and 81&mgr;m. At short times, the displacement of the molecules is small enough so that the local displacement is proportional to the local velocity component along the magnetic field gradient. At mean displacements larger than 5 bead diameters, the displacement distribution is Gaussian and centered about the mean displacement; the width of the distribution corresponds to the macroscopic dispersion coefficient as measured by other techniques. At intermediate displacements, this distribution displays two peaks corresponding to a combination of the two processes. The main features of this transition can be reproduced by a simple Monte-Carlo simulation modeling the porous medium as a set of finite length tubes with random orientations. ©1997 American Institute of Physics.