This paper addresses the distributed event-triggered consensus problem for a class of nonlinear multiagent systems subject to actuator saturation. A new distributed event-based dynamic output feedback controller is put forward via the relative output measurements of neighboring agents. It removes the impractical assumptions that the controllers for agents have to update continuously and the observers embedded in agents have to share information with their neighbors, thus the energy consumptions of agents are significantly reduced. Two event-triggered strategies for the cases with and without continuous communication among neighboring agents are established. Sufficient conditions are derived in terms of matrix inequalities to guarantee the exponential leader-following consensus. The problem of designing a distributed event-triggered control law such that the domain of attraction for consensus errors is enlarged, formulated, and solved as an optimization problem with matrix inequality constraints. Simulation results are given to verify the effectiveness of the theoretical results.