Numerical simulation of water flow in a two-dimensional, macroscopically homogeneous, Miller-similar medium showed the existence of a network of flow channels with two complementary states separated by a critical point <Roth, 1995>. The consequences of this for solute transport are explored by numerical simulations using particle tracking. It is found that many experimentally observed features of transport through soil are reproduced qualitatively by these simulations. Analyzing the results reveals that in the corresponding effective medium the travel distance for the transition to convection-dispersion and the effective dispersivity depend on the water flux. In particular, the effective longitudinal dispersivity, which is often assumed to be a material constant of the porous structure, is found to vary by more than an order of magnitude with a minimum near the critical point. The simulations further demonstrate that the local structure of the velocity field and the subscale hydrodynamic dispersion are of minor importance for the field-averaged transport process. ¿ American Geophysical Union 1996