The operation of a continuous stirred tank reactor (CSTR) in the steep domain of its nonlinear process characteristic is studied, using catalyzed hydrogen peroxide decomposition as a model process because of its transparent nonlinear dynamics. Unstable equilibrium states and corresponding limit cycles exist in the steep domain, the latter representing dynamically stable modes of operation where safer control is expected due to the lower educt concentration in the reactor. For CSTR control in the steep domain, a fuzzy approach is applied based on simulations and experimental understanding of the stable and unstable states of the reactor. Simulations are carried out for the set-point control of an unstable equilibrium state, and the tracking control of the corresponding stable limit cycle. The simulation results show that operation in the limit cycle requires much less control energy than that of the corresponding unstable equilibrium state in the case of disturbances, e. g., due to unavoidable modelling errors.