The problem of analyzing the stability of chemical process plants is considered. The idea of exchange plants has been extended with more general binary transfer terms and binary equilibrium, resulting in the idea of binary exchange-equilibrium plants. Their structural stability is analyzed using results on conservation matrices. It was found that binary exchange-equilibrium plants with no azeotropes are stable irrespective of the connections of their operating units. The general results are illustrated in examples of practical importance: heat-exchanger networks and binary distillation columns with constant molar flows.