Double-diffusive natural connective flow within a rectangular enclosure has been studied for an anisotropic porous medium using a non-Darcy extension. The principal direction of the permeability tensor has been taken oblique to the gravity vector. The spectral element method has been used to solve the problem numerically. The method has been validated using existing analytical and numerical results. Parametric studies are presented for isotropic and anisotropic cases for different fundamental parameters, e.g., buoyancy ratio, Lewis number, Rayleigh number, Darcy number. The results show that anisotropy causes significant changes in the Nusselt and Sherwood numbers. In particular, the present analysis shows that permeability orientation angle has a significant effect on the flow rate and, consequently, on the heat and mass transfer. © 1998, Taylor & Francis Group, LLC. All rights reserved.