This paper investigates oil-water two-phase flows in microchannels of 793 and 667 mu m hydraulic diameters made of quartz and glass, respectively. By injecting one fluid at a constant flow rate and the second at variable flow rate, different flow patterns were identified and mapped and the corresponding two-phase pressure drops were measured. Measurements of the pressure drops were interpreted using the homogeneous and Lockhart-Martinelli models developed for two-phase flows in pipes. The results show similarity to both liquid-liquid flow in pipes and to gas-liquid flow in microchannels. We find a strong dependence of pressure drop on flow rates, microchannel material, and the first fluid injected into the microchannel.