Steady state two-dimensional mixed convection problem in a vertical two-sided lid-driven differentially heated square cavity is investigated numerically. The left and right moving walls are maintained at different constant temperatures while upper and bottom walls are thermally insulated. Three cases were considered depending on the direction of moving walls. Richardson number, Ri = Gr/Re-2 emerges as a measure of relative importance of natural and forced convection modes on the heat transfer. Governing parameters were 0.01 < Ri < 100 and Pr = 0.7. It is found that both Richardson number and direction of moving walls affect the fluid flow and heat transfer in the cavity. For Ri < I the influence of moving walls on the heat transfer is the same when they move in opposite direction regardless of which side moves upwards and it is reduced when both move upwards. For the case of opposing buoyancy and shear forces and for Ri > 1, the heat transfer is somewhat better due to formation of secondary cells on the walls and a counter rotating cell at the center. (C) 2003 Elsevier Ltd. All rights reserved.