The invention relates to a system for preventing collisions of an automobile with obstacles. Sensors mounted in the automobile detect the area surrounding the vehicle. The signals of said sensors are evaluated by a data processing device in order to calculate the available obstacle-free driving space. Other sensors additionally detect the position of all movable vehicle parts (e.g. a trailer) and the dynamic parameters of the current driving situation (e.g. speed, steering angle, etc.). Based on said data, the driving speed required during the following time intervals in order to continue driving is calculated in advance by the data processing device and compared with the actually available obstacle-free driving space that has been detected. Said comparison provides early forecast regarding a possible collision. The driver is warned of a possible collision danger by corresponding warning devices and can consequently react in time. In critical situations (e.g. high driving speed), direct interventions in the control of the vehicle by the data processing device can take place to assist the driver.