As the result of the globalization we can experience the increaseing traffic on the roads, on the water and also in the air. The increasing traffic causes greater chances of accidents than previously, so we have to deal with the prevention of accidents. It’s an interdisciplinary area of sciences, which is handled also by controll theory. In the paper we are investigating one of the most important strategical problems in the air traffic management (ATM). This makes the free flying possible, wich enables that the aircrafts to fly without pilots during their route. Most of the cases we can consider the aircrafts as a multi-agent system, so we can apply the tools for avoiding collision, which are developed to multi-agent system controll. In our modelling we consider two aircraft and we have an assumption, that the aircrafts fly at fixed altitude, and can influence their dynamics by angular and linear velocity controll. This movement can be easily modelled with Lie-groups and Lie-algebras, so we apply this kind of differential geometric tools to deduce the aircraft’s differentialequation-system. We use the denomination conflict for the situation, when two aircrafts move on too close to each other, and our goal is to prevent these situations. First we have to calculate the provinces, where one aircraft can cause conflict by searching a saddle point of a functional. After that we are presenting conflict avoiding strategies such as hybrid autamations and make the safety verication of this hybrid automations. In the result of this safety verification we get the provinces, from which the conflict avoidance strategies can move out and be succesfull. The results concern to aircrafts, but we can generalize this in the case of other type multi-agent systems for example mobile-robots without any difficulty.