Up to three stable steady states are possible in a simple commensalistic system, taking place in an open‐loop mixed reactor when the growth rates of the two species are inhibited by the substrates they prey on (Self‐inhibition). Two stable states are possible in a system with noncompetitive inhibition of the species by the substrate they are not preying on (cross‐inhibition). A large number of steady states as well as oscillatory states are possible when both self‐ and cross‐inhibition are strong. Multiplicity of steady states is also possible in a reactor with biomas recirculation for these kinetics. Yet, the latter is more stable than the open‐loop reactor in the sense that the domain of steady‐state multiplicity is narrower. The stability of steady states and the dynamics of the systems for each of the investigated kinetics are summarized in a qualitative phase plane. The importance of the analysis for improving the selectively and yield of the system and for predicting the response of the system to changes in the operating conditions, is discussed.