Simultaneous heat and mass transfer between parallel plates are analyzed taking into account the Soret and Dufour effects. Both heat and mass transport are examined considering conduction in the axial and transverse directions plus longitudinal advection. The equations differ from the classical heat and mass transfer ones in considering the effect of the temperature gradient upon the mass flux, and conversely the effect of the concentration gradient upon heat flux, in accordance with the dictates of thermodynamics of irreversible processes. The special problems solved evaluate the effect of an imposed temperature difference between the confining walls upon the solute concentration distribution of a multisolute which diffuses against the concentration gradient forced by the prevailing temperature gradient. Details and numerical results are presented only for binary solutions. The asymptotic concentration difference, for a specified temperature difference, depends on the Soret and Dufour coefficients. The approach to the asymptotes is determined by the complete solution of the governing equations.