This article investigates the event-triggered adaptive control problem for a class of leaderless multi-agent systems with output constraints and unknown dead-zones. The adaptive updating laws are designed to eliminate the effects of unknown dead-zones by employing adaptive backstepping technique. The barrier Lyapunov function (BLF) is introduced to guarantee that the output constraints are not violated. Then, a generalized relative threshold is proposed by utilizing the neighboring controller errors to alleviate the computation burden dramatically. It is further shown that all the closed-loop signals are uniformly bounded and that the consensus tracking errors asymptotically tend to zero. A simulation example verifies the validation of the developed control strategy.