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Abstract The effect of the association of reactants on the kinetics of reaction in the liquid phase is studied. The mathematical modelling of chemical reactions that are described by nonlinear differential equations is performed. The steady states, the conditions for the emergences of intermediates, and the nature of their concentration oscillations in the reaction system are described. The influence of low-frequency sonolysis on the kinetics of bimolecular reactions was studied with due regard for the association of dimers/trimers of starting reagents. With increasing frequency and amplitude of low-frequency sonic waves (up to some critical value), they observed the disappearance of trimers and concomitant cessation of the reaction. This observation offers an additional tool for controlling reaction rate by the external action of low-frequency vibrations.