An elevator installation has at least one shaft door and a monitoring device for monitoring movements for opening the shaft door, the monitoring device has a first, energy-autonomous counting device for counting the movements, which independently of an intact power supply increments a first count value in the case of one of these movements, and a second counting device for counting the movements, which when the power supply is intact increments a second count value in the case of one of these movements, and a comparison circuit which calls up and compares the first and second count values and can generate a signal based on the comparison of the count values.