This article deals with the development of a non-equilibrium model for solving problems with three liquid phases. The model consists of the material balance equations, the interface material balance equations, the transfer-rate equations and the interface equilibrium equations. First the two liquid phase non-equilibrium solution is obtained. Then rigorous stability analysis in the form of the tangent plane criterion is used on two liquid phase solutions to detect the presence of the third liquid phase. The model equations are then solved to obtain the three liquid phase non-equilibrium solution.