The nonlocal dispersion tensor D NL provides a fundamental description of velocity correlations and displacement information in a dispersive system. It is shown that pulsed gradient spin echo nuclear magnetic resonance can be used to measure this tensor, and we present here the first measurement of D NL in a complex flow by this or any other methods. These measurements are complemented by simulations based on a lattice-Boltzmann calculation of the fluid flow. For dispersive flow in a random bead pack of monosized spheres, six nonzero, independent components remain. These components have been measured at three times less than v , the time to flow one bead diameter. It is shown here that the various elements of D NL provide insights regarding the dispersive flow, which are extremely sensitive to the details of local correlations.