The relation between the heterogeneity of hydraulic properties and effective asymptotic transport is studied for microscopically heterogeneous but macroscopically homogeneous unsaturated media with steady flow. Heterogeneity is described by the scaling of the hydraulic functions &thgr;(&psgr;m) and K(&thgr;). The study is based on an analytical approximation of asymptotic dispersivity under the assumption that matric potential is spatially constant. For the special case of a water-saturated medium the result of the stochastic continuum theory is recovered. When applied to several published numerical simulations, the approximated asymptotic dispersivities are found to agree well with the numerical values. By exploring the heterogeneous media for various hydraulic states, the approximation resolves some apparent inconsistencies found in the simulations. The cases considered span the entire range from perfect to zero correlation between scaling factors of matric potential and hydraulic conductivity. It is demonstrated that this correlation is crucial for the behavior of asymptotic dispersivity with changing flow rate. Since weak to moderate correlations are often found in soils, this result has significant implications for solute transport through heterogeneous soils. ¿ 1998 American Geophysical Union