An assistance system for motor vehicles has at least one monitoring unit monitoring a space external to a vehicle, in particular in a direction of travel of the motor vehicle, with a warning zone being defined in the monitored external space on each side of a lane. The warning zone is delimited by an earliest warning line and a latest warning line encompassing the respective lane marking or, as the case may be, boundary. An evaluation unit receives the data transmitted by the monitoring unit and generates a warning signal for an acoustic, visual and/or haptic warning and/or a steering intervention if the evaluation unit detects that a defined warning threshold lying within the warning zone is exceeded. The warning signal is issued only as a function of further planned driver-adaptive conditions.