Abstract In this work we challenge the assumption that the capillary entry pressures for displacements in three-phase flow are the same as those in two-phase flow. Using an energy balance, as derived by Mayer and Stowe (1965) and Princen (1969a,b, 1970) for two-phase flow, we derive a general formula for determination of the capillary entry pressures for piston-like displacement of two bulk phases in a pore where a third phase may also be present.