Gas-liquid-liquid slug flow in a capillary reactor is a promising new concept that allows one to incorporate gas-liquid reaction, liquid-liquid extraction, and facile catalyst separation in a single unit. In order to assess the performance of a gas-liquid-liquid slug flow reactor, it is necessary to predict the slug velocity and pressure drop to ascertain residence times and reaction rates. New empirical models for velocity and pressure drop were developed based on existing models for two-phase gas-liquid and liquid-liquid slug flows, and these were validated experimentally.