This paper studies the consensus of leader-following multiagent systems with nonlinear dynamics. Consider that control protocols for the consensus work under an intermittent framework due to inevitable factors; meanwhile, the event-triggered mechanism is introduced, so as to reduce the update frequency of the control protocols. In particular, threshold parameters in the event-triggered conditions are supposed to be dynamically changed, and the minimum event-triggered intervals are set to be positive in advance. Furthermore, according to whether event-triggered conditions depend on combined measurements or a single measurement, two forms of event-triggered schemes are designed; then, the corresponding distributed control protocols are demonstrated. Based on the graph theory and Lyapunov function method, sufficient conditions and a concrete algorithm for the consensus of multiagent systems are presented. It is shown that the intermittent dynamic event-triggered protocols given in this paper can effectively reduce the update frequency of control and exclude Zeno behavior. Finally, detailed numerical examples are supplied to illustrate the proposed results.