An aircraft gas turbine engine includes a counter-rotatable generator driven by a turbine includes a generator stator and counter-rotatable radially inner pole and outer magnet rotors. A gearbox may be used for counter-rotating the pole and magnet rotors. Counter-rotatable first and second sets of booster stages may be co-rotatable with corresponding ones of the pole and magnet rotors. The generator and the gearbox may be disposed within a booster cavity or a tail cone of the engine. The magnet rotor, the pole rotor, and the stator may be concentric. A particular embodiment of generator includes the magnet rotor encircling the pole rotor, the pole rotor encircling the stator, a rotor air gap between the magnet and pole rotors, and a transformer air gap between the pole rotor and the stator. The counter-rotatable generator may be driven directly by a counter-rotatable turbine.