Method for operating a device for starting a combustion engine comprising an alternator-starter, a starter and a computer, characterized in that the method comprises a first activation step and a second activation step that are mutually exclusives: - the first activation step comprising emission of an activation signal, in particular a power supply signal, for the alternator-starter, and - the second activation step comprising emission of an activation signal, in particular a power supply signal, for the starter and in that the method comprises a first operating mode implemented between powering up the starting device, in particular the computer, and the first starting of the engine following this switching on and a second operating mode the rest of the time, i.e. after the first starting of the engine following the switching on and until the disconnection of the device or the computer, characterized in that the first operating mode comprises, for the first starting of the combustion engine: - a step of requesting starting of the combustion engine, then a step of detecting submerged starter and/or leak in a sealing system of the starter that is implemented by means of a submerged starter detector, the implementation of an activation step involving starting the engine with the alternator-starter, if it is determined that the starter is submerged and/or if there is a leak in the sealing system of the starter; - a step of measuring the temperature of the engine that is implemented by means of a temperature sensor, in the case in which it has not been detected that the starter is submerged and no leak has been detected in the sealing system of the starter, the activation step involving starting the engine with the alternator-starter being implemented if the temperature of the combustion engine is above a first threshold (Level 1), and the activation step involving the starting of the engine with the starter being implemented if the temperature of the combustion engine is below a first threshold (Level 1). - the first activation step comprising emission of an activation signal, in particular a power supply signal, for the alternator-starter, and - the second activation step comprising emission of an activation signal, in particular a power supply signal, for the starter and in that the method comprises a first operating mode implemented between powering up the starting device, in particular the computer, and the first starting of the engine following this switching on and a second operating mode the rest of the time, i.e. after the first starting of the engine following the switching on and until the disconnection of the device or the computer, characterized in that the first operating mode comprises, for the first starting of the combustion engine: - a step of requesting starting of the combustion engine, then a step of detecting submerged starter and/or leak in a sealing system of the starter that is implemented by means of a submerged starter detector, the implementation of an activation step involving starting the engine with the alternator-starter, if it is determined that the starter is submerged and/or if there is a leak in the sealing system of the starter; - a step of measuring the temperature of the engine that is implemented by means of a temperature sensor, in the case in which it has not been detected that the starter is submerged and no leak has been detected in the sealing system of the starter, the activation step involving starting the engine with the alternator-starter being implemented if the temperature of the combustion engine is above a first threshold (Level 1), and the activation step involving the starting of the engine with the starter being implemented if the temperature of the combustion engine is below a first threshold (Level 1). - a step of requesting starting of the combustion engine, then a step of detecting submerged starter and/or leak in a sealing system of the starter that is implemented by means of a submerged starter detector, the implementation of an activation step involving starting the engine with the alternator-starter, if it is determined that the starter is submerged and/or if there is a leak in the sealing system of the starter; - a step of measuring the temperature of the engine that is implemented by means of a temperature sensor, in the case in which it has not been detected that the starter is submerged and no leak has been detected in the sealing system of the starter, the activation step involving starting the engine with the alternator-starter being implemented if the temperature of the combustion engine is above a first threshold (Level 1), and the activation step involving the starting of the engine with the starter being implemented if the temperature of the combustion engine is below a first threshold (Level 1).