The invention relates to the design of rotor blades of an axial turbomachine compressor, especially the method of attaching the blades to the rotor. The blades comprise an aerofoil portion and a platform for attaching them to the rotor. The platform comprises, along the main axis of the blade, a first layer forming a surface bounding the fluid stream and skirting the aerodynamic surfaces and a second layer, underneath the first layer with respect to the aerodynamic surfaces, designed to be able to mate with the inner face of a wall of the rotor around an aperture in the rotor for the purpose of attaching it.