In this work, the problem of convective stability of electrochemical system (a horizontal electrode and a solution containing three types of ions) under the non-steady-state mass-transfer conditions is solved. A set of equations involving the Navier-Stokes equation for incompressible viscous liquid to the Boussinesq approximation, the ion-transfer equations that account for diffusion, migration, and convection, and the electroneutrality condition were used as the mathematical model. The problem is solved within the framework of linear theory of stability. The set of amplitude equations obtained for vertical component of hydrodynamic velocity and concentrations was solved numerically by the shooting method. As a result, the critical Rayleigh number, the wave number, and the critical time of onset of natural convection were determined. It is shown that the supporting electrolyte has a strong effect on the convective stability of the system. (c) 2006 Elsevier Ltd. All rights reserved.