A method includes continuously recording, by the autonomous driving safety or driver assistance system, at least one of vehicle-related data and vehicle surroundings-related data, continuously repeatedly deciding, based on the recorded data, whether a driving safety or driver assistance system process is to be autonomously initiated or carried out, and carrying out a checking process, during which sensor data and parameter settings that are necessary for the operation of the driving safety or driver assistance system are checked for the plausibility thereof. The checking process is carried out immediately following a start of travel of the motor vehicle. In a period of time between the start of travel of the motor vehicle and a start of operation of the driving safety or driver assistance system, an auxiliary process for an immediate and safe auxiliary mode of the driving safety or driver assistance system is used during a checking period.