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The effect of local heterogeneities in a porous medium, which are randomly distributed, upon longitudinal spreading in groundwater transport problems is described and related to the permeability ratio between the heterogeneities and the surrounding porous medium. Numerous experimental runs using simplified model aquifers provide a large data base. The measured breakthrough curves indicate the transport behavior of the system. They are compared with the solution of the classical Fickian advection-dispersion equation for the given boundary conditions as well as with a numerical approach of a modified transport formulation following the dual porosity concept of Coats and Smith. A significant difference in the transport behavior depending on the permeability of the heterogeneities is observed: while mass transport in the model aquifers with local heterogeneities of higher relative permeability remained Fickian, local heterogeneities of lower relative permeability caused a marked tailing and a significant spreading of the tracer. In the dual porosity formulation of transport the transfer coefficient had to be fitted, while the remaining transport parameter could be determined directly.