A method and control device for monitoring travel movements of an elevator car utilize an electronic control device positioned at the car. Travel movements of the elevator car are travels, speeds or accelerations of the car. At least individual travel movements are subject to redundant detection for the purpose of monitoring. Either the travels or the speeds are redundantly detected and the accelerations singularly detected, or alternatively the accelerations are redundantly detected and the travels or the speeds are singularly detected, or preferably the travels or the speeds and the accelerations are redundantly detected. The electronic control device is preferably arranged at the support rollers of the elevator car.