In this paper we analyze the behavior of a coupled reactor-separator system with reactant recycle. The reactor is represented by a continuously stirred tank reactor, and the separator is represented by a flash unit. The reactor is operated isothermally and sustains a first-order reaction A → B. The individual units always possess a unique, stable, and feasible steady state. Surprisingly, even for the simple model system considered here, more complex patterns of behavior-involving infeasibility, multiple steady states, and limit cycles-can be observed when the recycle is closed. It is shown that the behavior crucially depends on the flow and the flash control strategy. Stability criteria are derived for different flow and flash control strategies. They depend on the operating conditions and on the basic physicochemical properties of the mixture. Potential sources for instability are systematically identified and illustrated.