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 (X.sub.ABS,X''.sub.Acc,X'.sub.IGB) of the car is sensed and continually compared with a similarly sensed travel parameter (X'.sub.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 (X.sub.ABS,X''.sub.Acc X'.sub.IGB; X'.sub.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.