We study the effects of rock wettability on the flow of oil, water, and gas in hydrocarbon reservoirs. We describe the three-phase fluid configurations and displacement processes in a pore of polygonal cross section. Initially water-filled, water-wet pores are invaded by oil, representing primary oil migration. Where oil directly contacts the solid surface, the surface will change its wettability. We then consider water injection followed by gas injection for any possible combination of oil/water, gas/water, and gas/oil contact angles. We find the capillary pressures for the different displacement processes and determine the circumstances under which the various fluid configurations are stable. Using empirical expressions for the phase conductances, we find three-phase relative permeabilites for a bundle of pores of different sizes with constant triangular cross sections. For gas injection, we show that the oil remains connected in wetting layers down to low oil saturation with a characteristic layer drainage regime, which gives very high ultimate oil recoveries. The only exceptions are nonspreading oils in water-wet media and large gas/oil contact angles. The relative permeability of the phase of intermediate wettability depends on two saturations, while the relative permeabilities of the other phases are functions of their own saturation only. In water-wet media, oil is the intermediate-wet phase. In weakly oil-wet media, water is intermediate-wet. In strongly oil-wet media, gas is intermediate-wet. This finding contradicts the assumptions made in many empirical models that gas is always the most nonwetting phase and that its relative permeability depends only on the gas saturation. This work indicates appropriate functional dependencies for three-phase relative permeabilities,and represents a necessary first step toward the development of a predictive pore-scale model that accounts for the effects of wettability in three-phase flow.