A pore network model is used to describe constitutive relationships between saturation, capillary pressure, relative permeabilities, and interfacial areas over the full range of saturations. We focus on residual nonwetting-phase saturations, that is, the saturation range between main drainage and primary drainage. Interphase mass transfer and dynamic miscible transport are modeled to generate the range of saturations over which the extended constitutive relationships are calculated. To accommodate all saturations in a consistent way, we define capillary pressure as the areal average of local capillary pressures associated with each fluid-fluid interface. The extended constitutive relationships provide input for continuum-scale models covering the entire saturation range and indicate that special care is needed in the general formulation of continuum-scale equations. ¿ 2001 American Geophysical Union