A method and system for supervising the safety of an elevator having a car driven by a drive within a hoistway wherein a travel parameter (XABS,X″Acc,X′IGB) of the car is sensed and continually compared with a similarly sensed travel parameter (X′IG) of the drive. If the comparison shows a large deviation between the two parameters, an emergency stop is initiated. Otherwise one of the travel parameters (XABS,X″Acc X′IGB; X′IG) is output as a verified signal (X;X′). The verified signal is then compared with predetermined permitted values. If it lies outside the permitted range then an emergency stop is initiated.