Steady cavity flows in porous media, driven by a horizontal temperature gradient, are examined in the intermediate limit when the Rayleigh number is comparable with the cavity aspect ratio, L (???? 1). In this regime the flow departs from the single-cell Hadley structure, valid only for very shallow cavities, and separate circulations can develop at each end of the cavity. The existence of these closed cells is consistent with numerical solutions of the full cavity problem. Suitable heat-transfer laws are developed for conducting and for adiabatic horizontal boundaries.