Two of the most significant contributions in the last two decades to separation process are the numerical implementation of the tangent-plane criterion to check the stability of any given mixture and the use of mass-transfer models to solve separation;process problems. This work combines the use of the tangent-plane analysis with mass-transfer models to solve problems with multiple liquid phases. As in equilibrium-stage problems, the tangent-plane analysis works effectively with nonequilibrium-stage separation-process problems. An example is presented where the nonequilibrium model, when used in conjunction with the tangent-plane criterion, predicts the correct number of phases, while the equilibrium model predicts the incorrect number of phases.