Under a fixed directed graph, the leader-following output consensus problem is investigated for a class of nonlinear time delay multiagent systems with the less conservative condition on nonlinear functions. It is the first time that the output feedback consensus algorithms are proposed for nonlinear multiagent systems with time delays on the state. Moreover, the proposed algorithms have a simple design procedure and can be used to address the consensus problem of nonidentical multiagent systems. A novel dynamic compensator is designed for each follower and the distributed memoryless controller is constructed based on the compensator. The controller is independent of time delays, which depends only on the follower output and the relative output information of its neighbor agents, and it can render that all outputs of the agents achieve a consensus. Furthermore, it is proved that the resulting closed-loop system is stable in the sense of semi-global (global) boundedness. Finally, the effectiveness of the output feedback distributed consensus algorithms is demonstrated by a simulation example. (C) 2019 Published by Elsevier Ltd.