Enclosures of parallelogrammic shape present high potential to be used in heat and/or mass transfer applications, as they can act as heat and/or mass transfer inhibitors or promoters, being usually referred to as heat and/or mass transfer diodes. The heat and/or mass transfer characteristics and performances of such enclosures depend mainly on the imposed boundary conditions and geometrical arrangement. In this work, the double-diffusive natural convection problem in parallelogrammic enclosures filled with fluid-saturated porous media is studied numerically. The pressure-velocity link for the fluid contained within the fluid-saturated porous media is modeled using the Darcy Law, and a discussion is presented about the use of this model. Emphasis is given to the situation when the porous media that fill the enclosure are saturated with moist air. A short set of values of the dimensionless governing parameters for steady two-dimensional parallelogrammic enclosures is taken, and analysis is concentrated over the numerical results obtained for such combinations of governing parameters. The situations of combined or opposite global heat and mass flows are considered. Results clearly show the strong potential of parallelogrammic enclosures filled with fluid-saturated porous media for heat and mass transfer applications. Such single parallelogrammic enclosures can be assembled, thus giving rise to complete, and even complex, efficient heat and/or mass transfer systems. (C) 2004 Elsevier Ltd. All rights reserved.