<p>The leader-following consensus problem of second-order unmatched nonlinear multi-agent systems under nonuniform time-varying delays and switching topology is studied in this paper. For the considered unmatched nonlinear system, it is supposed that the nonlinearities exist in the dynamics of all system state. To deal with the unmatched system nonlinearities, adaptive neural network method integrating with backstepping approach is introduced for the controller design. Furthermore, to reproduce the leader’s states information under time-varying communication delay and switching topology, a novel dynamic compensator is designed for each agent, and then a distributed consensus controller is developed. Compared with existing results, a feature of this paper is that the considered unmatched nonlinear multi-agent system can be used to formulate more actual systems in practical application scenarios. Finally, numerical simulations are presented to demonstrate the theoretical results.</p>