Special kinetic behaviors in isothermal reactions on heterogeneous catalysts composed of two components with different roles are studied with the focus on bistabilities that could occur in stirred-tank flow reactors when control of catalytic sites on one component by mobile (spillover) species produced by the other operates. The comprehensive kinetic model involves : (1) generation of spillover species on the second phase, their transfer to the potentially catalytic phase, and their reaction with this acceptor to generate selective sites; (2) the kinetics of the catalytic reaction. We developed a model for selective catalytic oxidation, where catalyst sites change from nonselective to selective under the influence of the control by spillover oxygen. The model is based on the system of differential equations. By integration and iteration to the steady state for each value of the external control parameter under investigation the oxygen and hydrocarbon reactant consumption, as well as the stare of the catalyst, is calculated. These calculations predict bistable selectivity for certain ranges of concentration in the feed. Data on the boundaries of the hysteresis loops as a function of catalyst composition and oxygen partial pressure are discussed, as well as the variation of these hysteresis boundaries as a function of the internal parameters.