A control device for an automatic gearbox, coupled to the engine or a motor vehicle, by a torque converter, including a locking device for a fixed connection of the output shaft of the engine to the input shaft of the automatic gearbox, to produce a lock-up and conversely to release the lock-up. The device further includes an engine control unit, for providing an order for the engine, such as a demand for torque, and a control unit for the gearbox for transmitting to the engine control unit an order such as a torque request. The gearbox control unit may transmit to the engine control unit a torque request as a function of slip and the torque value as demanded by the driver of the vehicle such that the speed of the engine may approach the speed of a turbine of the torque converter so that a lock-up or lock-up release can be carried out.