A longitudinally guiding driver assistance system in a motor vehicle has a first detection system for detecting currently applying events or relevant events lying ahead, which require a change of the permissible maximum speed, a second detection system for detecting the course of the route, and a function unit which, when detecting a relevant event while taking into account the location of the relevant event, determines a location-dependent point in time, whose reaching causes the function unit to initiate an automatic adaptation of the currently permissible maximum speed or an output of a prompt information for permitting an automatic adaptation of the currently permissible maximum speed to anew permissible maximum speed. The function unit is designed to take into account available information concerning the course of the route when determining the location-dependent point in time.