Abstract: In the paper at hand, the simultaneous computation of fuel-minimal approach trajectories for multiple aircraft present in the vicinity of an airport at a certain point in time is treated. The trajectory optimization task includes the determination of the optimal aircraft queuing sequence on the ILS glide path, minimizing the total fuel consumption of all aircraft involved. The trajectory optimization is based on aircraft point-mass simulation models with the aircraft characteristics taken from the BADA database of EUROCONTROL. Specifically tailored path constraints are introduced that define the permitted airspace and that enforce the aircraft to follow the ILS glide path once they have passed the final approach fix. Furthermore, path constraints are implemented that guarantee certain separation distances between the involved aircraft throughout the approach flights. An algorithmic procedure is set up which is aimed at producing a good initial guess for the multi-aircraft trajectory optimization task. The proposed framework is applied to a generic scenario where a fuel-efficient approach scheduling for four civil passenger aircraft has to be determined.