The unsteady behaviour of gravity cuirents which arises at relatively high discharges, is analyzed using a two-layer model. A self-similar solution that satisfies boundary conditions and a condition at the front of the gravity current is obtained. At high discharges the gravity current is found to take on the shape of an intruding wedge. The solutions considered substantially extend the theoretical range of discharges that produce a twolayer gravity current. Satisfactory agreement with experimental results reported in the literature is obtained.