The Darcy model with the : Boussinesq approximation is used to study the onset of double-diffusive natural convection in an inclined porous cavity. Transverse gradients of heat and solute are applied on two opposing walls of the cavity, while the other two walls are impermeable and adiabatic. The analysis deals with the particular situation where the buoyancy forces induced by the thermal and solutal effects are opposing and of equal intensity. The objective of this study is to investigate the critical stability of this system in terms of the inclination angle, the aspect ratio of the cavity and the Lewis number. The subsequent behavior of the convective flow is also discussed in terms of the governing parameters of the problem. Numerical procedures based on the Galerkin and finite element methods are carried out to investigate the onset of double-diffusive convection using the linear stability analysis. It is shown that for values of Lewis number around unit, overstability is possible provided that the normalized porosity of the porous medium epsilon is made smaller than unity. For supercritical convection, the occurrence of multiple solutions, for a given range of the governing parameters, is demonstrated. The numerical results also indicate the existence of subcritical convective regimes.