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This paper studies the consensus problem of hybrid multi-agent systems, where the multiple discrete-time and continuous-time dynamic individuals constitute a hybrid multi-agent group. Firstly, a hybrid event-triggered method is proposed. Under this method, the hybrid consensus can be achieved asymptotically. Besides, the Zeno-behavior of the hybrid multi-agent system will not make an appearance due to the special design of the hybrid event-triggered conditions. Then, a self-triggered algorithm is further proposed to avoid the continuous monitoring of event-triggered conditions. Finally, several simulation examples are presented which are comparative and show the effectiveness of the two method. Moreover, the impact of the parameters in the main results is analyzed. [ABSTRACT FROM AUTHOR]