A method for an overtaking assistant for a vehicle is provided. The vehicle is equipped with environment sensing systems for detecting objects in the own and an adjacent lane on the sides and at the rear of the vehicle. The space in front of the vehicle is preferably detected by environmental sensors as well. Autonomous cutting into an adjacent lane is only initiated if a first vehicle is detected in the adjacent lane. The first vehicle is taken as a reference for a speed of vehicles in the passing lane. It is also assumed that a second vehicle that approaches the first vehicle fast in the same lane has detected the first vehicle and will adjust its speed to the speed of the first vehicle.