An infinitely variable power bypass transmission with two operating modes for a motor vehicle with a thermal engine, including: at least two power lines parallel-connecting the thermal engine with the vehicle wheels and each including a coupling/decoupling device capable of locking or releasing a transmission shaft according to the operating mode; a line including a continuous speed controller; and a mode switch control device configured to control the coupling/decoupling devices. The transmission includes a single actuator for the two coupling/decoupling devices, which is configured to, when a mode switch occurs, trigger simultaneously the two modes while locking the two transmission shafts.