The influence of microscopic heterogeneity on flow through a macroscopically homogeneous, variably saturated medium is studied by numerical simulations in a two-dimensional, Miller-similar medium. As a consequence of the local heterogeneity there appears a complex network of flow channels with interspersed islands of low-flux domains. This hydraulic structure of the medium is characterized by two states which are separated by a critical point at which the hydraulic structure practically disappears. Transitions between the states are governed by the degree of saturation. The flow channels of the two states are complementary in that high-flux regions of one state become low-flux regions of the other one, and vice versa. This variable hydraulic structure clearly has far-reaching practical and theoretical consequences for the transport of dissolved chemicals. The simulations further indicate that the autocovariance model of the microscopic heterogeneity is of minor importance for the global structure of the flow field. ¿ American Geophysical Union 1995