The conditions for the appearance of limiting currents in an electrochemical system in the cases of excess and no supporting electrolyte have been studied theoretically. It is shown that the partial currents of parallel reactions are interdependent not only because of their competition for common reactants but also because of the influence of the electric field on the transport processes of the charged reagents and reaction products. The system containing ions of three arbitrary charge numbers has been analyzed in detail for the cases of one, two and three parallel electrochemical reactions. Explicit expressions for partial and total limiting currents have been determined. A geometrical interpretation of the evolution of the system with changing potential difference is given.