The invention relates to an apparatus for keeping a vehicle (8) in its lane (10), comprising a reference model (13) which receives from a lane identification system (7) geometric data relating to the position of the vehicle (8) in the lane (10), as well as data relating to the lane profile, and uses this to calculate a set variable (δRef) for control of the vehicle position. In order to allow the cutting of turns, the guidance response of the control system (11) is modified during turning, in such a manner that no steering forces, or only minor steering forces, are exerted on the steering (6) when there is a discrepancy between the movement path of the vehicle (8) and the set movement path in the direction of the inside of the turn.