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The origin of bistable solutions in the kinetic equations describing the chemistry of dense interstellar clouds is explained as being due to the autocatalysis and feedback of oxygen nuclei from the oxygen dimer (O2).We identify four autocatalytic processes that can operate in dense molecular clouds, driven respectively by reactions of H+, He+, C+, and S+ with O2. We show that these processes can produce the bistable solutions found in previous studies, as well as the dependence on various model parameters such as the helium ionization rate, the sulfur depletion and the H+3 electron recombination rate. We also show that iongrain neutralizations are unlikely to affect the occurrence of bistability in dense clouds. It is pointed out that many chemical models of astronomical sources should have the potential to show bistable solutions. It is pointed out that many chemical models of astronomical sources should have the potential to show bistable solutions.