In accordance with the present invention concerning operation of an elevator, a traveling mode of the elevator is prevented if it is established that an elevator load exceeds a limit value. During normal operation, the limit value is equal to a first limit value. If it is established that a special situation is present (e.g., an evacuation situation or a peak traffic situation) the system is switched over to a special situation mode. In the special situation mode, the limit value is equal to a second limit value, which is higher than the first limit value.