A computer-implemented method of managing airspace through which a plurality of aircraft are flying, comprising: receiving (101; 102), from the aircraft, user preferred aircraft intent data corresponding to a full description of how the aircraft is to be operated expressed in a formal language, thereby defining unambiguously the user preferred trajectory of each aircraft; calling an initial global conflict detection procedure comprising: calculating the corresponding user preferred trajectories from the user preferred aircraft intent data received from all the aircraft; and comparing the user preferred trajectories so as to identify one or more conflicts between trajectories; using (112; 114) the comparison of the user preferred trajectories to identify conflicted aircraft and characterised by placing (113; 115) the conflicted aircraft into conflict dependent networks such that each conflict dependent network contains a set of all aircraft in conflict with each other, either directly or indirectly, that is pairs of aircraft in direct conflict with each other and pairs of aircraft linked via a chain of conflicts, such that each conflicted aircraft can be a member of one conflict dependent network only; for each conflict dependent network, calling an initial conflict resolution procedure comprising: revising the user preferred aircraft intent data of one or more of the conflicted aircraft of the conflict dependent network to produce revised aircraft intent data corresponding to a full description of how the aircraft is to be operated expressed in a formal language, thereby defining a corresponding revised trajectory in a way that should remove conflicts from within that conflict dependent network; and sending the revised aircraft intent data to the corresponding conflicted aircraft. receiving (101; 102), from the aircraft, user preferred aircraft intent data corresponding to a full description of how the aircraft is to be operated expressed in a formal language, thereby defining unambiguously the user preferred trajectory of each aircraft; calling an initial global conflict detection procedure comprising: calculating the corresponding user preferred trajectories from the user preferred aircraft intent data received from all the aircraft; and comparing the user preferred trajectories so as to identify one or more conflicts between trajectories; using (112; 114) the comparison of the user preferred trajectories to identify conflicted aircraft and characterised by placing (113; 115) the conflicted aircraft into conflict dependent networks such that each conflict dependent network contains a set of all aircraft in conflict with each other, either directly or indirectly, that is pairs of aircraft in direct conflict with each other and pairs of aircraft linked via a chain of conflicts, such that each conflicted aircraft can be a member of one conflict dependent network only; for each conflict dependent network, calling an initial conflict resolution procedure comprising: revising the user preferred aircraft intent data of one or more of the conflicted aircraft of the conflict dependent network to produce revised aircraft intent data corresponding to a full description of how the aircraft is to be operated expressed in a formal language, thereby defining a corresponding revised trajectory in a way that should remove conflicts from within that conflict dependent network; and calculating the corresponding user preferred trajectories from the user preferred aircraft intent data received from all the aircraft; and comparing the user preferred trajectories so as to identify one or more conflicts between trajectories; using (112; 114) the comparison of the user preferred trajectories to identify conflicted aircraft and characterised by placing (113; 115) the conflicted aircraft into conflict dependent networks such that each conflict dependent network contains a set of all aircraft in conflict with each other, either directly or indirectly, that is pairs of aircraft in direct conflict with each other and pairs of aircraft linked via a chain of conflicts, such that each conflicted aircraft can be a member of one conflict dependent network only; revising the user preferred aircraft intent data of one or more of the conflicted aircraft of the conflict dependent network to produce revised aircraft intent data corresponding to a full description of how the aircraft is to be operated expressed in a formal language, thereby defining a corresponding revised trajectory in a way that should remove conflicts from within that conflict dependent network; and sending the revised aircraft intent data to the corresponding conflicted aircraft.