A two-fluid model for transient flow of two immiscible liquids in a pipeline was formulated based on two transient continuity equations and a combined momentum equation in a quasi-steady form. It can be used for simulating both stratified and dispersed flow. Numerical simulations were performed to investigate the behavior of oil-water flow during transients caused by an increase or decrease in the water volume fraction at the entrance to the pipeline. An increase in the water flow rate within the stratified flow regime may result in the formation of a shock (an abrupt change in the water holdup). In transients produced by a decrease in the input water volume fraction, the smoothening of the water holdup wavefront occurs. This behavior is explained by a strong dependence of the speed of the holdup wave propagation in stratified flow on the water holdup. The results obtained for inclined pipelines show that the slope of the pipe affects the flow behavior significantly. The liquid-liquid flow model was used to simulate the transport of corrosion inhibitor in a pipeline conveying an oil-water mixture.