<p>This article investigates the problem of event-triggered adaptive fault-tolerant consensus control (FTCC) for nonlinear multi-agent systems (MAS) with actuator faults and asymmetric error consensus constraint. Firstly, a log-type transformation function is designed for all the tracking errors of the leader and followers, so that all the tracking errors can be constrained to unified asymmetric constrained boundary function. Then, a generalized relative threshold event triggering mechanism is constructed, which reduces the communication burden of the MAS and avoids Zeno behavior. In the process of controller design, the coupling problem of parameters is successfully solved by introducing fault and trigger parameters into the structured parameter vector, and the designed controller can entirely offset the influence of trigger parameters and multi-actuator faults on the MAS. Finally, the MAS including one leader and three followers is used to explain the availability of presented method.</p>