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When the entities undergoing a chemical reaction are not available simultaneously, the classical rate equation in the reaction-limited regime, should be extended by including non-Markovian memory effects. We consider the two cases of an external feedback, realized by fixed functions and an internal feedback originated in a self-organized manner by the relevant concentration itself. Whereas in the first case the fixed points are not changed, although the dynamical process is altered, the second case offers a complete new behavior, characterized by the existence of a time persistent solution. As an example we consider a single-species pair annihilation A + A → Ø process combined with a spontaneous creation of particles Ø → A. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]