A driver assistance system in a motor vehicle has a detection system for identifying events ahead that, on account of a currently valid speed limit being lifted, allow the current speed to be increased, and a functional unit for ascertaining an at least two-stage acceleration strategy for increasing the speed, wherein the first stage of the acceleration strategy can be implemented at most up to the location of the event ahead and the second stage of the acceleration strategy can be implemented at the earliest starting from the location of the event ahead. The implementation is started at a defined time and/or location before the event ahead is reached if the implementation of the acceleration strategy is permitted. In the first stage of the two-stage acceleration strategy, the acceleration profile to be implemented is ascertained and/or prompted depending on an identified defined acceleration behavior of a relevant target object travelling ahead.