The device has an electrical traction machine (20) suspended to a body of a hybrid or electric motorization vehicle and providing engine torque (CM) applied to rear wheels (3, 4). A mechanical link is provided between the machine and a deformable crossmember (2) to transmit torque effect (CR) with the engine torque to the crossmember for descending the rear wheels with respect to the body of the vehicle and for creating anti-squat effect during acceleration in electric propulsion of the vehicle. The link is provided with a connection shaft (30) connected to two levers (21, 33).