The invention relates to a device for transmitting mechanical torque between a driving member and a driven member, in particular between a heat engine and an air compressor (2) for supplying power to the engine. Said transmission device includes at least one pulley (10, 11, 12, 13), for transmitting the torque between the driving member and the driven member, and a release means (17) controlling at least one of said pulleys (10, 11, 12, 13) so as to enable the transmission of the torque between the driving member and the driven member when the latter are in an engaged state, or so as to restrict the transmission when the latter are in a disengaged state. The invention also relates to an air-compression system for supplying power to a heat engine, in particular for a motor vehicle, said system including a compressor (2) and a torque-transmitting device (3) enabling torque to be taken up on a belt (9) of the engine and said torque to be transmitted to the compressor, said transmission device (3) being capable of transmitting said torque at a first transmission ratio up to a certain engine speed threshold and of no longer transmitting said torque when said threshold is exceeded, or of transmitting said torque at a lower transmission ratio when the engine speed is above said threshold.