A nonequilibrium (NEQ) model for a complete three-phase distillation in tray columns is described. The model consists of a set of mass and energy balances for each of the three possible phases present. Mass and heat transfer between these phases is modeled using the Maxwell-Stefan equations. Equilibrium is only assumed at the phase boundary between two phases. The equilibrium stage model is a special case of the general model. The method of solving the NEQ model equations described here consists of first solving the equilibrium two phase model, using this solution to obtain a converged solution for the equilibrium three-phase problem by means of a differential arc length continuation method, and subsequently using this as a starting guess for the nonequilibrium three-phase model with Newton's method. Incorporated into the algorithm model is a liquid phase stability check and phase split calculation to evaluate the thermodynamic stability of all liquid phases present in the distillation column each iteration. We have found that the component Murphree efficiencies tend to be lower and more highly variable in the two-liquid phase region than they are in the single liquid region. There may be a jump discontinuity in component efficiencies as we move from homogeneous to heterogeneous liquid phase regions of composition space. EQ models modified by efficiency factors should not, in general, be used for the simulation of three-phase distillation processes. NEQ models should be preferred in general. (C) 2004 Published by Elsevier Ltd.