A collision and conflict avoidance system for autonomous unmanned air vehicles (UAVs) uses accessible on-board sensors to generate an image of the surrounding airspace. The situation thus established is analyzed for imminent conflicts (collisions, TCAS violations, airspace violations), and, if a probable conflict or collision is detected, a search for avoidance options is started, wherein the avoidance routes as far as possible comply with statutory air traffic regulations. By virtue of the on-board algorithm the system functions independently of a data link. By taking into account the TCAS zones, the remaining air traffic is not disturbed unnecessarily. The system makes it possible both to cover aspects critical for safety and to use more highly developed algorithms in order to take complicated boundary conditions into account when determining the avoidance course.