In the paper, mathematical relationships which are used to describe kinematic variables of the aircraft-obstacles configuration and motion of the aircraft are presented. These define the base for the set of conditions enabling determination of the possibility and threat of collision. The second important aim of such a definition is creation of prerequisites for selection of an appropriate anti-collision manoeuvre, computation of reference signals and inequalities used as limitations on these signals in the automatic flight control process. Theoretical analysis is illustrated by an example of computer simulation of the flight of aircraft. Two anti-collision manoeuvres are studied in this experiment. The first one, performed in a vertical plane, consists in emergency climbing. The second one, performed in the horizontal plane, is shaped by three turns, each one of small radius, to go around the obstacle and then return to the previously realised flight path.