Two of the proposed airborne collision-avoidance devices at present under discussion are the A.T.A. time-frequency system and a later proposal termed SECANT. The present paper attempts to discuss the geometry of the escape manœuvres associated with the use of one or other of these devices; the electronic problems involved in these ingenious but intricate devices will here be largely ignored, and discussion will be confined to the problems facing two conventional aircraft in an encounter at an appreciable altitude.