With this safety equipment in a multimobile elevator group, collisions between cars (C1 . . . CN) operating in the same shaft (1) can be prevented. For this purpose, each car (C1 . . . CN) is equipped with a safety module (10). In order not to cause any collision in the case of a stop command of a car (C1 . . . CN), the safety module (10) must know the positions and speeds of the other cars (C1 . . . CN) at all times. A decision module (12) integrated into the safety module (10) processes the travel data received by way of the communications system (11) and decides whether a car (C1 . . . CN) may or may not stop. Furthermore, the decision module (12) determines the braking behavior of a car (C1 . . . CN) (normal stop, emergency stop or triggering of the car-catching device).