A formulation of the three-dimensional combined free and forced convection boundary-layer flow in a corner is derived and discussed in terms of the corner orientation with respect to the buoyancy force. The corner is imagined to be formed by the abutment of two quarter-infinite wedges along a side edge parallel to an incoming uniform stream, Based on this formulation, similarity-type solutions are derived for different boundary-layer regions corresponding to almost planar horizontal corners, the numerical solutions of which are found to be characterized by their non-uniqueness in the corner-layer with a secondary flow exhibiting varying and sometimes complex flow patterns in function of the flow parameters; the most interesting feature is perhaps the existence of two streamwise symmetrically disposed vortices arising in layers immediately adjacent to the corner-layer.