The opening of vehicle doors often leads to collisions with stationary obstacles that are not visible to the occupants or with moving obstacles that approach the vehicle without being noticed. Thus to avoid collisions when vehicle doors are opened, the aim of the invention is to take any modifications to the environmental situation of the vehicle as a result of a movement of the vehicle and the detected objects into consideration. This allows a collision of the vehicle doors with the objects to be reliably avoided. To achieve this, in a first step the probable trajectory of a vehicle is determined. In an additional step, the objects in the vicinity of the vehicle are detected and probable trajectories of said detected objects are determined. Respective probability ranges are then defined both for the vehicle and the pivoting zone of the vehicle doors and for the detected objects. The probability ranges of the pivoting zones of the vehicle doors are respectively compared with the individual probability ranges of the objects, in order to determine whether they overlap. If an overlap is identified, a response; signal that indicates the risk of a collision is generated.