An elevator sheave wear monitoring device, comprising at least one detector (32, 72, 82) situated to detect a position of elevator roping that is indicative of a condition of a sheave that the roping at least partially wraps around, the at least one detector (32, 72, 82) providing an output corresponding to the detected position of the elevator roping and indicating an amount of wear of the sheave that exceeds at least one threshold; and further comprising a processor configured to: determine when the detected position of the elevator roping indicated by the at least one detector (32, 72, 82) indicates an amount of wear of the sheave that exceeds at least one threshold, and provide an indication that the amount of wear exceeds the at least one threshold; characterized in that the processor is further configured to determine an amount of time that the detected position of the elevator roping indicates the amount of wear of the sheave that exceeds the at least one threshold, and provide the indication only if the determined amount of time exceeds a predetermined minimum, and further characterized in that: the at least one threshold comprises a first threshold and a second threshold, and the processor is configured to determine whether the detected position of the elevator roping indicated by the at least one detector indicates an amount of wear of the sheave exceeds the first threshold; determine whether the detected position of the elevator roping indicated by the at least one detector indicates an amount of wear of the sheave that exceeds the second threshold; and provide the indication by providing a first indication when the amount of wear exceeds the first threshold but not the second threshold, and providing a second indication when the amount of wear exceeds the second threshold. further comprising a processor configured to: determine when the detected position of the elevator roping indicated by the at least one detector (32, 72, 82) indicates an amount of wear of the sheave that exceeds at least one threshold, and provide an indication that the amount of wear exceeds the at least one threshold; determine when the detected position of the elevator roping indicated by the at least one detector (32, 72, 82) indicates an amount of wear of the sheave that exceeds at least one threshold, and provide an indication that the amount of wear exceeds the at least one threshold; characterized in that the processor is further configured to determine an amount of time that the detected position of the elevator roping indicates the amount of wear of the sheave that exceeds the at least one threshold, and provide the indication only if the determined amount of time exceeds a predetermined minimum, and further characterized in that: the at least one threshold comprises a first threshold and a second threshold, and the processor is configured to determine whether the detected position of the elevator roping indicated by the at least one detector indicates an amount of wear of the sheave exceeds the first threshold; determine whether the detected position of the elevator roping indicated by the at least one detector indicates an amount of wear of the sheave that exceeds the second threshold; and provide the indication by providing a first indication when the amount of wear exceeds the first threshold but not the second threshold, and providing a second indication when the amount of wear exceeds the second threshold. the at least one threshold comprises a first threshold and a second threshold, and the processor is configured to determine whether the detected position of the elevator roping indicated by the at least one detector indicates an amount of wear of the sheave exceeds the first threshold; determine whether the detected position of the elevator roping indicated by the at least one detector indicates an amount of wear of the sheave that exceeds the second threshold; and provide the indication by providing a first indication when the amount of wear exceeds the first threshold but not the second threshold, and providing a second indication when the amount of wear exceeds the second threshold. determine whether the detected position of the elevator roping indicated by the at least one detector indicates an amount of wear of the sheave exceeds the first threshold; determine whether the detected position of the elevator roping indicated by the at least one detector indicates an amount of wear of the sheave that exceeds the second threshold; and provide the indication by providing a first indication when the amount of wear exceeds the first threshold but not the second threshold, and providing a second indication when the amount of wear exceeds the second threshold. providing a first indication when the amount of wear exceeds the first threshold but not the second threshold, and providing a second indication when the amount of wear exceeds the second threshold.