When a two-layer system which consists of a solvent (upper layer) and a solution (lower layer) is heated from a vertical side wall and cooled from the opposing side wall, convection starts in each layer, A Galerkin finite-element method was employed for the numerical analyses of this two-layer convection, Computations were carried out for the Prandtl number Pr = 6, the aspect ratio A = 4, the Rayleigh number Ra = 10(4), the buoyancy ratio N = 2 to 10 and the Lewis number Le = 10 to 100. The concentration in the upper layer increased linearly with time through the transfer of the solute across the interface between the layers. In conclusion, the flux of a solute across the interface was independent of the concentration difference between the layers, but dependent on the diffusion coefficient.