This paper investigates the distributed consensus for a class of second-order nonlinear multiagent systems, where agents communicate with each other on switching networks. By the adaptive control and the back-stepping design techniques, a novel protocol is proposed under the restriction that global information, including the number of agents and the topology information, is unavailable. Using the Lyapunov functional method, it is proven that the underlying multiagent systems can reach complete consensus via the developed protocol without the topology dwell time constraint. Then, the proposed results are extended to the consensus problem of multiagent systems with external disturbances. By skillfully integrating the adaptive control and non-smooth control strategies, the external disturbance is well suppressed and the asymptotical consensus can be reached. Finally, we provide numerical examples to illustrate the effectiveness of the given protocols.