An axial flux electrical machine is provided. The machine includes a plurality of rotors, each sandwiched between a respective pair of stator parts. The plurality of rotors, together with their respective stators, are axially-stacked to form a multistage machine. Heat exchangers are provided adjacent each stator to provide cooling. Each rotor disc is a composite rotor disc in which permanent magnets are embedded. The magnets are embedded in apertures through each disc so that surfaces of the magnets are flush with surfaces of the respective rotor disc.