The method involves moving an elevator unit in a common shaft independent of each other. A collision protective system (20) releases a deceleration for each moving elevator car (A1,A2) by a holding brake, when effective distance between the elevator cars exceeds a critical minimum distance. An emergency stop (21) determines a momentary moving position of the cars by a control system after releaseof the holding brake. The car brake assigned to the cars releases an additional deceleration of one or more elevator cars. An independent claim is also included for an elevator facility with an upperelevator car and a lower elevator car.