Method for avoiding collisions between a host vehicle and other vehicles in which the position of the vehicles is determined, the vehicles are equipped with a transmitter/receiver, and in the host vehicle, the possibility of a collision involving the host vehicle is assessed by receiving signals from the transmitter/receivers of each other vehicle, analyzing the received signals to extract positional information about the transmitter/receivers from each signal, and when a received signal contains additional information of interest about a possible collision involving the host vehicle, analyzing the extracted positional information to determine whether any signals contain additional information of interest about a possible collision involving the host vehicle. Additional information is extracted only from such signals and analyzed to ascertain whether a collision between the host vehicle and any other vehicles is likely to occur in order to enable action to be taken to prevent the collision, e.g., evasive action.