The finite-difference method is used to predict numerically the characteristics of hydromagnetic double-diffusive convective flow of a binary gas mixture in a rectangular enclosure with the upper and lower walls being insulated. Constant temperatures and concentrations are imposed along the left and right walls of the enclosure and a uniform magnetic field is applied in the x-direction. Consistent with what is reported by previous investigators, an oscillation in the flow is observed in the absence of the magnetic field for a specific range of buoyancy ratio values where the Prandtl number Pr = 1, the Lewis number Le = 2, the thermal Rayleigh number Ra-T = 10(5), and the aspect ratio 4 = 2 for the enclosure, In the presence of the magnetic field, however, no oscillatory behavior is observed. Numerical results are reported for the effect of the heat generation or absorption coefficient and the Hartmann number on the contours of streamline, temperature, concentration and density. In addition, results for the average Nusselt and Sherwood numbers are presented and discussed for various parametric conditions. In this study, the thermal and compositional buoyancy forces are assumed to be opposite.