An aircraft cockpit display device for information concerning surrounding traffic includes devices to receive information coming from outside the aircraft, to know the flight parameters of the aircraft, to calculate projected trajectories of the aircraft and of a detected aircraft in the immediate vicinity, and to display a representation of the surrounding traffic through symbols and potential messages based on instructions received. A display command device is connected to an on-board calculator to know the flight phase of the aircraft. The display command device has a filtering device to define for each flight phase and/or crew task the nature and the level of information to be displayed.