A comparative experimental study of ＇steady-state＇ two-phase flow in two types of model porous media is made to determine the effects of nonplanarity on the flow mechanisms and the mesoscopic flow behavior. The two model porous media have virtually the same pore geometry, but one has a planar network skeleton, whereas the other has a nonplanar (two-layer) skeleton. The latter is a new type of model porous medium that permits detailed visual observation and quantitative measurements without sacrificing the 3D character of the pore network topology. The capillary number and the flowrate ratio are changed systematically, whereas the viscosity ratio and the wettability (contact angle) are kept constant. Conventional relative permeabilities are determined and correlated with the porescale flow phenomena. In the range of parameter values investigated, the flow mechanism observed was ganglion dynamics (intrinsically unsteady, but giving a time-averaged steady-state). The nonplanarity is shown to have small qualitative but significant quantitative effects. In the nonplanar porous medium, the ganglion size distribution is wider, the mean ganglion size larger, and the stranded ganglia are fewer than those in the planar one, under the same flow conditions.