A two-dimensional mathematical model based on Darcy’s law with Boussinesq approximation has been used to study double-diffusive natural convection in a rectangular fluid-saturated vertical porous enclosure subject to apposing and horizontal gradients of heat and solute. Results are presented for 50 less than or equal to R(c) less than or equal to 250, 0.01 less than or equal to N less than or equal to 10, 10 less than or equal to Le less than or equal to 40 and 1 less than or equal to A less than or equal to 10, where R(c), N, Le and A correspond to the solutal Rayleigh-Darcy number, inverse of buoyancy ratio, Lewis number and enclosure aspect ratio, respectively. The numerical integration of the full problem reveals that for sufficiently large R(c), Le and A, there is a domain of N in which one obtains oscillating convection. Outside this domain, the solution approaches steady-state convection, for which analytical solutions are developed and presented. The agreement between the analytical and the numerical solutions is shown to be satisfactory.