This paper focuses on the problem of target hunting in multi-unmanned aerial vehicle systems. The core is to achieve stability or boundedness of position and velocity errors between individual UAVs and the hunting target through a coordination mechanism. Initially, based on the perception relationship characteristics between the multi-UAV system and the target, the hunting problem is categorized into two types: target tracking and pursuit-evasion. When the hunting target cannot perceive the state of the multi-UAV system and only maneuvers along a predetermined trajectory, the hunting problem transforms into a target coordinated tracking problem. This paper investigates the coordinated tracking method of the multi-UAV system for dynamic unknown targets in the scenario where there is no delay in target state information. When the target can perceive the state of the multi-UAV system and adopts an avoidance strategy, the hunting problem evolves into a pursuit-evasion problem. To address this, this paper, based on a non-zero-sum differential game model under a distributed structure, designs a reasonable evaluation function to ensure that the control strategy of the multi-UAV system still satisfies the Nash equilibrium condition when relying solely on local information. Finally, simulation experiments verify the effectiveness of the proposed method in multi-UAV target hunting.