It is to be expected that the task of an air traffic controller will change with the introduction of four-dimensional (space and time) trajectories for aircraft, as can be seen in ongoing developments in ATM systems in Europe (SESAR) and the US (NextGen). It is clear that higher levels of automation will need to be developed to support the management of four-dimensional trajectories, but a definite concept on a distribution of the roles of automation and human users has not yet been well defined. This paper presents one approach to the design of a shared representation for 4D trajectory management. The design is based on the Cognitive Systems Engineering framework and by using a formative approach in the analysis of the work domain, a step-wise refinement in the planning and execution of 4D trajectories is proposed. The design is described in three Abstraction Hierarchies, one for each phase in the refinement. The ultimate goal is to design a shared representation that underlies both the design of the human-machine interface and the rationale that guides the automation. It is foreseen that such a shared representation will greatly benefit the shared cognition in ATM and allows shifting back and forth across various levels of automation. A preliminary version of a joint cognitive system for 4D trajectory management has been developed and will be introduced in this paper. Further work will focus on the refinement of the shared representation by means of human-in-the-loop experiments.