Europe and the USA are developing plans (‘SESAR’ and ‘NextGen’) to transform the processes of Air Traffic Management (ATM). These will improve safety and efficiency, and match predicted increases in air transportation demand. Aircraft would fly on Four Dimensional-Trajectories (4D-Trajectories), incorporating altitude, position, time, and other aircraft positions and vectors. This vision would involve extremely large investments from the airline industry and ATM service providers. Thus, development priorities need to be based on sound business cases. But will these necessarily lead to the strategic vision of a 4D-Trajectory system? Will the changes in practice be limited to a series of short and medium term operational improvements rather than strategic improvements? Killer App(lication)s is jargon for innovations so valuable that they prove the core value of some larger technology. So, are there ‘Killer Apps’ for 4D-Trajectory ATM? Killer Apps generate high degrees of stakeholder technical and financial cooperation. Ironically, most past ATM Killer Apps have improved safety. The analysis here attempts to identify and then size potential 4D-Trajectory ATM Killer Apps. The evidence for Killer Apps has to pass key tests. Killer Apps obviously have to offer enormous benefits to stakeholders in the context of the potential costs. The bulk of these benefits must not be obtainable through technologically ‘cut down’ non−4D-Trajectory versions. Part 1 of this paper sets out the framework for investigating these questions; Part 2 will be published subsequently and will examine potential Killer Apps derived from improvements in Fuel Efficiency, Capacity and Cost. An abbreviated version of this paper was first presented at the European Navigation Conference (ENC 2011), London in November 2011.