An internal fluid cooling system for a gas turbine aerofoil comprises a plurality of multi-pass cooling arrangements each of which consists of a serpentine passage in the interior of the aerofoil. The cooling fluid—in particular air—is supplied to an inlet end of each passage and exhausted through a multiplicity of discharge holes to provide tip, leading edge, trailing edge and surface film cooling. The inlet end of a first serpentine passage is positioned close to the leading edge and flows rearwards while the inlet end of the second serpentine passage is positioned close to the trailing edge and flows forwards. These serpentine passages are disposed side-by-side, one adjacent the pressure surface and the other adjacent the suction surface on opposite sides of a main load carrying member which comprises a major part of the internal structure of the aerofoil.