A key challenge in Air Traffic Management (ATM) is to provide a schedule with high throughput on the runways, and at the same time meet objectives connected to taxiing times and punctuality while ensuring safe operations within the apron, taxiway, runway, and terminal manoeuvring area. High throughput is achieved through optimised runway sequences. These sequences must frequently be revised, for example due to uncertainty in the available data. Hence, as updated information become available, the flight scheduling process continues throughout the day. Furthermore, since many of the activities and operations at the airport are prioritized and planned due to the previous schedule, it is important that the scheduling process does not create too much deviation from one plan to another. In this thesis we present an approach for rescheduling, where we have modelled stability requirements in the objective function. We present new distance functions for measuring stability, and stability is formulated with respect to time and the runway sequence. We present computational results and analyse the trade-off between stability and optimality. Our experimental results indicate that including stability in the objective function greatly improves the stability without a major decrease in punctuality.