Large-scale capillary pressure <$overline {P}c {left(overline {S}w right)}$> and effective permeability-saturation <knw${left(overline {S}w right)}$> constitutive relationships for an incompressible, two-phase system have been developed for a two-dimensional, nonorthogonal fracture network utilizing numerical simulation. The simulations account for capillary, viscous, and gravity effects consistent with the Darcian approach adopted for this study, and were performed within the scale of the REV of the system which was consistent for both single and multiphase flow behavior. The large-scale $overline {P}c {left(overline {S}w right)}$ relationship for steady state flow conditions was found to be sensitive to the mean and the variance of the underlying aperture distribution as well as the nonwetting phase density. The overall effects of varying the aperture statistics on the relationships were found to be analogous to porous media, with an increased mean aperture leading to lower capillary pressures and an increased aperture variance leading to steeper curves. The large-scale knw${left(overline {S}w right)}$ curves representative of flow in the vertical direction followed the general form of the underlying local-scale Brooks-Corey constitutive relationship and were relatively insensitive to a change in variance of the aperture distribution. The large-scale knw${left(overline {S}w right)}$ curves representing flow in the horizontal direction due to an imposed gradient in the vertical direction, however, are significantly different than the underlying local-scale relationships, showing maximum values at intermediate saturations. The ratio of vertical to horizontal effective permeability is saturation dependent.