An adaptive consensus algorithm is proposed for a class of nonlinear multiagent systems with completely unknown agent dynamics. Due to uncertainties in the agent's dynamics, previous consensus approaches usually yield uniformly ultimately bounded consensus error. Our main contribution includes a novel robust consensus algorithm which can guarantee that the consensus error converges to zero asymptotically. In order to address the unknown dynamics, a two-layer neural network (NN) is utilized to learn the unknown dynamics in an online manner, and a robust continuous term is introduced to alleviate effects of the NN residual reconstruction error and external disturbances. The continuousness of the control signal is guaranteed to remove the actuator bandwidth requirement and avoid the caused chattering phenomenon. The proposed consensus algorithm is distributed in the sense that each agent only exchanges information with its neighbor agents. The asymptotic consensus result is achieved via Lyapunov synthesis. Furthermore, the proposed algorithm can also be extended to the case where the agents are required to form a prescribed formation. Finally, simulation studies on a nonlinear multiagent system are provided to demonstrate the performance of the scheme.