A driver assistance system having a lane-keeping function, having a device for detecting the lanes on a roadway, and a control unit for intervening in the steering system of the vehicle for lane-keeping. Means are provided in the driver assistance system for detecting the position of the vehicle with respect to the lane marking of the lane. Furthermore, means are provided for detecting a travel of the vehicle through a curve. The control unit executes its control function as a function of the position of the vehicle on the lane and as a function of the cornering. The intervention depends on whether the vehicle is located on the inner side of the curve or on the outer side of the curve.