This paper addresses the output synchronization problem for heterogeneous nonlinear multi-agent systems with distributed event-based controllers. Employing the two-step synchronization process, we first outline the distributed event-triggered consensus controllers for linear reference models under a directed communication topology. It is further shown that the subsequent triggering instants are based on intermittent communication. Secondly, by using certain input-to-state stability (ISS) property, we design an event-triggered perturbed output regulation controller for each nonlinear multi-agent. The ISS technique used in this paper is based on the milder condition that each agent has a certain ISS property from input (actuator) disturbance to state rather than measurement (sensor) disturbance to state. With the two-step design, the objective of output synchronization is successfully achieved with Zeno behavior avoided.