The distillation-based separation of ideal liquid mixtures has been comprehensively studied. The optimization of the different separation structures has allowed the development of general heuristic rules to aid the designers in finding good solutions quickly for the type of problem at hand. The separation of nonideal mixtures is also an exhaustively studied area, but because of the complexity of the vapor-liquid-liquid behavior of such mixtures, it is more difficult to suggest guidelines for synthesis in separation sequences. On the other hand, recently several special so-called hybrid separation tools have also been involved in that kind of synthesis task, complicating further the synthesis problem. To obtain some general conclusions for the separation structure synthesis of such mixtures, in this study the separation of two nonideal quaternary mixtures containing one nonazeotropic-forming component (most volatile or least volatile) is studied based on optimization of the separation structures. The separation schemes involve the so-called extractive heterogeneous azeotropic distillation, which is a novel hybrid separation process. The economic optimization of the different separation structures results in the conclusion that the heuristic rule for ideal mixtures, that is, "easy separation first should be done and the complicated one should be made last", is valid also for such nonideal mixtures.