The fully distributed adaptive event-triggered average tracking protocol for general linear multiagent systems (MASs) with a positive minimum interevent time (PMIET) is established in an asynchronous way. First, a fully distributed event-triggered detector and controller for each agent that includes internal variables and adaptive gains are designed to track the average of multiple time-varying references signals asymptotically via intermittent communication without the requirement of global information. Then, activable dynamic event-triggering mechanisms are designed for the detector and the controller, respectively, which can only be activated after certain specific instants; that is, the triggering condition needs to be monitored only after the event-triggering mechanism has been activated. The time interval between the event-triggered instant and a specific activation instant ensures that the event-triggering mechanisms for the detectors and the agents have PMIETs. Finally, the application of spacecraft formation tracking in low Earth orbit illustrates the availability of the theoretical results.