Distillation is the most important separation technique even for nonideal and azeotropic mixtures. A hybrid approach for the design and optimization of such distillation processes using thermodynamics and mathematical programming is presented. In a first step, a superstructure is derived from a knowledge of the feed composition and the phase equilibrium The basic idea is to establish a superstructure that consists of a sequence of preferred separations, i.e. distillations with minimum energy input. Thus, an upper bound on the number of columns is determined. The column interconnections allow for direct heat integration and recycling of intermediate fractions. This ensures that even complex column structures are included. In a second step the rigorous stage-model of the superstructure is optimized by means of mixed-integer nonlinear programming (MINLP). The objective of the mixed-integer optimization is a function based on a detailed description of both the capital and the utility costs. Optimizing the whole set of variables with respect to total annualized costs leads to an economic optimal process design. The methodology is applicable to zeotropic as well as to homogeneous azeotropic mixtures. Superstructures for ternary and quaternary azeotropic mixtures and examples for the optimization of such a superstructure are given. (C) 1998 Elsevier Science Ltd. All rights reserved.