This paper addresses the synthesis of distillation column configurations to separate nonazeotropic multicomponent mixtures containing N components. It is shown that, for sharp separations of an N-component mixture, it is possible to develop a superstructure that takes into account all of the possibilities, from thermally linked systems with only one reboiler and one condenser to sequences with only conventional columns [2(N - 1) condensers and reboilers]. Al of the partially thermally linked superstructures are included. The superstructure is systematically generated using the state task network (STN) formalism, in which only the tasks that can be performed are specified, but not equipment. A set of logical relationships between tasks is proposed that allows only feasible configurations that use the minimum number of column sections and that takes into account the fact that; the minimum number of column sections and the number of heat exchangers are not independent. The superstructure is modeled using generalized disjunctive programming independent of the equations that represent each of the tasks (shortcut, aggregated, or rigorous models). In this paper, the procedure is illustrated using a modified version of Underwood's equations proposed by Carlberg and Westerburg (Carlberg, N. A.; Westerberg, A. Temperature Heat Diagrams for Complex Columns. 2. Underwood's Method for Side Stripers and Enrichers. Ind. Eng. Chem. Res. 1989, 28, 1379-1386. Carlberg, N. A.; Westerberg, A. Temperature Heal; Diagrams for Complex Columns. 3. Underwood's Method for the Petlyuk Configuration. Ind. Eng. Chem. Res. 1989, 28, 1386-1397). A modified version of the logic-based outer approximation algorithm is used to solve the resulting model.