Abstract: In order to facilitate efficient use of high pressure cooling air in a turbine rotor blade its aerofoil has a triple-pass convoluted cooling air duct in its leading edge region, and a triple-pass convoluted cooling air duct in its mid-chord region, both of them being fed from a common high pressure inlet in the root of the blade. The trailing edge region has a single-pass duct fed by low pressure cooling air from an inlet located just under the blade platform. The shroud of the blade also has cooling air passages and these are fed from the ends of respective ones of the ducts. Air from the ducts also exits through rows of film cooling holes to film cool the concave flank of the aerofoil and through a row of holes in its trailing edge to remove heat from the thinner metal section in that area.