The article presents a mathematical model to simulate three-phase (liquid/liquid/gas) stratified and slug flows. The approach is based on the one-dimensional transient two-fluid model in which the two-phases consist of the gas and the mixture of the two liquids, with the motion of the liquid phases relative to each other being modelled via a drift flux model. In order to close the model, a scalar transport equation for the conservation of mass for one of the liquid phases is introduced. Other closure models incorporated relate to the liquid-liquid flow pattern (stratified or fully dispersed), the phase inversion point (when the continuous liquid phase becomes dispersed in the other and vice-versa), the slip between the liquid phases and the mixture viscosity (which changes abruptly when phase inversion occurs). The equations are solved numerically using a previously developed finite volume methodology that had been applied to the prediction of two-phase slug flow and by which liquid slugs are automatically captured as an outcome of the numerical integration. The new method is applied to the study of the flow of oil, water and air in horizontal pipes. The method is shown to be able to predict locally whether the two liquids form a dispersion (of either oil droplets in water continuous flow (O/W) or water droplets in oil continuous flow (W/O)) or flow in stratified layers. It is demonstrated that the developed model is capable of correctly predicting slugging, and is moreover able to reproduce successfully observed experimental trends for the major slug properties, such as pressure gradient, slug frequency, and total liquid hold-up. The study revealed that the slip between the two liquid phases plays a major role in determining the slug characteristics in three-phase flow. (C) 2003 Elsevier Ltd. All rights reserved.