This paper deals with one-variable nonlinear rate processes occurring in disordered systems. A general stochastic approach is introduced for these processes based on the following assumptions. The total rate coefficient is made up of the additive contributions of a large number of individual reaction channels. These contributions are random functions of time and their stochastic properties are characterized by a functional random point process. Exact analytical expressions for the time dependence of the average concentration are derived by using a characteristic functional technique. These expressions are valid for systems with both dynamic and static disorder and are nonlinear analogs of the general kinetic law derived by Huber [Phys. Rev. B 31, 6070 (1985); Phys. Rev. E 53, 6544 (1996)] for linear rate processes in systems with static disorder. For independent rate processes with static disorder and a self-similar distribution of reaction channels we derive a nonlinear analog of the stretched exponential. A closed analytic expression of the nonlinear stretched exponential is given in terms of Fox’s $H$ functions. As expected, when the reaction order of the process is one, the nonlinear kinetic law reduces to a stretched exponential with a scaling exponent characterizing the self-similar distribution of the individual reaction channels. For nonlinear processes the tail of the averaged kinetic curve is self-similar and obeys a scaling law with a negative power law. Surprisingly, the scaling exponent of the tail depends only on the reaction order of the process and is independent of the scaling exponent that characterizes the self-similar distribution of the individual channels. We examine the possibilities of experimental evaluation of the statistical distribution of the total rate coefficient: The moments of different orders of the rate coefficient can be evaluated from the time derivatives of the survival function.

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