In the present ATC system conflicts between aircraft are detected and resolved in a stated-based approach. To meet traffic demand predictions, the global air traffic management (ATM) system needs revolutionary changes. Several visions on future ATM operations exist (e.g. NextGen, SESAR). A common function between the different visions is 4D Trajectory management. This function enables trajectory-based operation as opposed to the state-based approach of the present system. Instead of monitoring the current traffic situation and resolving short term conflicts by vectoring, the 4D trajectory management function de-conflicts all trajectories prior to execution. A key function of 4D trajectory management is the resolution of 4D trajectories. Conflict resolution of 4D trajectories is applied to conflict scenarios using constraints. A characteristic of a constraint is that it does not limit the aircraft to a particular solution but provides the aircraft the room to generate a trajectory within the actual solution space. Conflicting trajectories are resolved using constraints where the constraints provides an approximation of the solution space. This concept of trajectory de-confliction through the use of constraints is the topic of this thesis work.