Transient thermosolutal opposing convection of a liquid-water mixture in a square cavity subject to horizontal temperature and concentration gradients is numerically investigated by a third-order upwind finite-difference scheme. Results are particularly presented to illustrate the effects of the Lewis and Grashof numbers on the evolution of flow patterns and the associated heat and mass transfer characteristics for solutally dominant situations. Results for Le = 100 clearly show the double-diffusive nature of the convection. In the initial stage the flow is dominated by the interface velocities at the vertical side walls driven by the concentration gradients there. Later, the flow is governed by the thermal buoyancy. At a much later time, the solutal buoyancy set in inducing new recirculating cells along the side walls. These cells gradually grow and squeeze the thermally driven cell in the core region. Multilayer flow structure is finally formed. The counterrotating cells resulting from the opposing thermal and solutal buoyancies cause significant velocity, temperature and concentration oscillations with time at high Grashof numbers.