This paper on a Lyapunov-based stability analysis for metro railway lines is from the proceedings of 14th International Conference on Urban Transport and the Environment in the 21st Century, which was held in Malta in 2008. The authors present a direct method to measure the stability of metro system lines, with respect to a previously constructed time schedule. They first model saturation effects using a real time discrete space state representation and then apply a Lyapunov-based stability analysis considering the time delays of trains as disturbances. The result is the definitions of a new set of indices that relate time delays to the validity of the actual time schedule when falling inside a particular ‘stability area’. This data can then be used to predict the need for rescheduling.