In this paper, we analyze the nonlinear behavior of two-phase reactors under boiling conditions. First we focus on a simple nth-order reaction of the form A --> B, which allows a rigorous analytical treatment. Three necessary conditions for the existence of multiple steady states have been identified: the reactant A has to be the light-boiling component, the difference in boiling point temperatures between the reactant A and the product B has to be sufficiently large, and the order of the reaction has to be less than some physical parameter a. This parameter cc can be interpreted as a measure for the phase-equilibrium-driven self-inhibition of the reaction mechanism. Thus, we have found an elegant explanation for the occurrence of multiplicities. Analytical and therefore general quantitative criteria identifying the regions of multiplicity for the model system are presented. Practical relevance of our results is demonstrated by means of two examples, the Monsanto process for the production of acetic acid and the ethylene glycol reactive distillation system. (C) 2003 Elsevier Science Ltd. All rights reserved.