An electro-mechanical transmission system, driven by a prime mover, includes two epicyclic gearsets (12,14) connected between input (23) and output shafts (43), and two electrical machines having their rotors (52,54) connected to respective elements of the two gearsets (12,14). The torque on the output shaft (43) is boosted by a controller which dumps energy from the system when one of the machines is acting as a generator and the other as a motor.