This paper investigates the consensus problem for multi-agent systems and presents a class of nonlinear consensus protocols. First, we reveal some structure property of the corresponding Laplacian matrix by decomposing the interaction graph into strongly connected components. Then, by means of the input-to-state stability and algebraic graph theory, we propose a framework to prove consensus for multi-agent systems with nonlinear protocols. In particular, we prove that consensus can be always reached in systems of single-integrator agents with a directed communication topology containing a spanning tree, provided the nonlinear protocol is an odd and increasing function. The nonlinear consensus protocols proposed in this paper include the classical linear consensus protocol as a special case, and may have a wide range of applications, including consensus with faster convergence rates and with bounded control inputs. Copyright © 2012 John Wiley & Sons, Ltd.