A wall structure for a gas turbine combustor arranged to have a general direction of fluid flow therethrough includes inner and outer walls defining a space therebetween. The inner wall is made up of a plurality of tiles having axial edges aligned generally with the direction of fluid flow, a gap being defined between axial edges of adjacent tiles. Orifices are provided within the axial edges to direct leakage air passing through the gaps to give the leakage air a flow component in the general direction of fluid flow through the combustor.