By using dynamic NMR microscopy with 40 mum spatial resolution we have demonstrated the existence of specific wall effects in electroosmotic and pressure-driven flows through a fixed bed at low column-to-particle diameter ratio. While the geometrical wall effect encountered in pressure-driven flow through the packed capillary is due to the radial distribution of interstitial porosity, with increasing void space closer to the wall, the electrokinetic wall effect is caused by different values of the zeta-potential associated with the inner surface of the capillary and those of the particles. It is shown that these wall effects are very systematic along the column axis for both types of fluid flow. They can cause a persistent (i.e., tong-time) disequilibrium in the axial dispersion behavior, and associated correlation lengths of the flow field may cover the total radius of the packed capillary needing trans-column equilibration. The characteristic times of these macroscopic flow heterogeneities in electroosmotic and pressure-driven flows exceed by far those of the stagnant mobile phase mass transfer in the bed as we show by complementary pulsed field gradient NMR measurements.