Lumping of the kinetics of mixtures described by a continuous distribution function of concentration is discussed for the case where individual reactions have nonlinear kinetics. The assumption of independent kinetics, which leads to a paradox, is not used. Functional-differential equations govern the kinetic behavior of the mixture. Formal solutions are presented for a class of kinetic behavior that includes Langmuir isotherm catalysis and for the special case of bimolecular reactions. A class is defined for which the kinetic functionals can be expanded in a series of integrals for which the kernels are entirely determined. Finally, a thermodynamic analysis is presented to show that the commonly accepted equilibrium theory implies a kinetic approximation of maximal rank for the kinetics at the equilibrium point.