A nonlinear dynamical model describing Frumkin-type oscillations and multiplicity of steady states in systems with the electroreduction of anions has been proposed. It is an extension and improvement of previously known models, which have been widely used in a description of oscillation processes during the reduction of anions at the cathode. The model equations are based on the proven and well-known theories of the structure of the electrical double layer (Gouy-Chapman-Stern-Graham's model), electrochemical kinetics and mass transfer. The analysis was performed using the mathematical apparatus of the theory of nonlinear dynamics. The model was studied for the system with the electroreduction of persulfate ions at a copper rotating disk electrode. Good agreement of our theoretical results with experiment is observed for amplitude, frequency, form and range of the oscillations. (C) 2013 Elsevier Ltd. All rights reserved.