An internal combustion engine in a motor vehicle is automatically shut off and started by way of a start-stop device, wherein an automatic shut-off process is initiated during a coasting operation phase of the internal combustion engine, and an automatic start process is initiated when at least one activation command occurs. For shutting off the internal combustion engine in the coasting operation phase, a gas exchange in cylinders of the internal combustion engine is at least almost completely suppressed and, at the same time, a torque converter lock-up clutch disposed between the internal combustion engine and the transmission for power transmission purposes is actuated such that the torque converter lock-up clutch remains or is at least almost completely engaged.