The GEARS software provides automatic detection and resolution of conflicts in simulated air traffic. The GEARS conflict resolution algorithm finds a set of flyable, conflict-free trajectories for an aircraft which must fly through an environment containing obstacle aircraft whose trajectories are known. The algorithm makes systematic use of a manoeuvre generator and a conflict detector. The manoeuvre generator may embody a variety of aircraft behaviour models which might, for example, take into account standard turn behaviour and wind predictions. The conflict detector may embody a variety of definitions of what makes a trajectory unacceptable,and might, for example, take into account growing uncertainty in the future positions of aircraft. Correctness of solution trajectories is demonstrable. The algorithm may be used to construct trajectories which consist of sequences of manoeuvres of a single type, for example, turns only, climbs and descents only or speed changes only, or sequences of manoeuvres of different types. It may be used for prioritized planning of the motion of a number of aircraft.