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Over the last two decades, an interesting area of Brazilian military and civil sectors is the Unmanned Aircraft Vehicle (UAV) development. This article tackles the modeling of conflicts resolution of Unmanned Aircraft System (UAS) using a lightweight Duration Calculus (DC) to verify if the temporal specification and design of the system is correct and to ensure formally that the system implementation meets all its requirements. Moreover, the article proposes a formal modeling (using DC) of a conflicts resolutions set of rules, adapted from Free Flight concept in Communications, Navigation and Surveillance/Air Traffic Management (CNS/ATM). In the adapted approach to UAS, each UAV is surrounded by an imaginary space of two cylinders, which form, respectively, the protected zone and the alert zone. The major contribution of this article is structuring a new scenario application of the conflicts resolution to UAS through formal modeling, using the DC technique to confirm that the models could be implemented without deadlocks and unreachable states, as well as with satisfaction of temporal restrictions. Furthermore, this work uses the state-of- the-art practices in formal methods, including a model checking tool to ensuring correct real-time requirements specification of a real-time critical system.