The current passage through a binary electrolyte solution contained in a plane-parallel cell is considered, The cell is formed by two identically ideal selective ion-exchange membranes. Nonetheless, the solution of the problem can also be employed for a cell made by two uniformly reversible electrodes, Using the corresponding boundary conditions it is taken into account that the solution can be involved in an electro- and capillary osmotic slipping at the membrane (electrode)/soIution interface provided the tangential gradients of the electrolyte concentration and/or the potential are close to the interface, The analysis of the stability of the well-known one-dimensional solution corresponding to linear concentration distribution in the cell is carried out. The analysis shows that the slipping gives rise to a hydrodynamic instability of the one-dimensional solution when colons have sufficiently low diffusion coefficients in the order of about 10(-6) cm(2) s(-1). Under this condition convective flows with periodical structure : may arise when current approaches the limiting value.