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International audience; This paper reports a study of the heat and mass transfer in a two-dimensional magnetohydrodynamic free convection boundary layer flow along a vertical semi-infinite flat surface immersed in a thermal and mass stratified Darcy porous medium under the influence of the Soret and Dufour effect. The nonlinear partial differential equations governing the problem under consideration are transformed by a similarity transformation into a system of ordinary differential equations which in turn are solved numerically by an aptly derived finite difference scheme following the Keller box approach. Obtained results, for test cases, are compared with those from the literature and found to be in good agreement. The numerical results are demonstrated graphically for various values of the parameters involved in the problem like magnetic parameter (Mg); buoyancy ratio (B); Lewis (Le), Soret (Sr), and Dufour (Df) numbers; and the presence of thermal (ST) and Mass (SC) stratification. Local and average Nusselt (Nu) number and Sherwood (Sh) number plots are presented in all cases.