A rigorous mathematical model of dynamical behaviour of a distillation column with a possible occurrence of several (e.g. three) liquid phases on individual trays is described. The generalized model is based on the concept of the equilibrium tray. By solving the algebraic part of DAE system, the phase situation is tested and the system is changing adaptively in the course of the integration. Examples of a distillation of mixtures with possible existence of two and three liquid phases are presented.