In this paper, we discuss the behavior of a coupled reactor-separator system. The reactor is modeled as a continuously stirred tank reactor (CSTR) sustaining an elementary first-order reaction and the separator as a single-stage flash unit. The coupling occurs via the recycling of the bottoms stream from the downstream separator to the upstream reactor. The emphasis in this paper is on studying the behavior of the coupled system when the vapor-liquid equilibrium (VLE) of the mixture has an azeotrope. Consequently, the bottoms stream can be reactant-rich or reactant-lean. Different control strategies for the operation of the reactor and separator are discussed. The stability of the steady states is analyzed analytically for each strategy. Physical explanations for the stabilty results are presented. Generally, the recycle of the reactant lean stream is observed to cause instability.