Nonlinearities are present in all real applications. Two types of general nonlinear consensus protocols are considered in this paper, namely, the systems with nonlinear communication and actuator constraints. The solutions of the systems are understood in the sense of Filippov to handle the possible discontinuity of the controllers. For each case, we prove the asymptotic stability of the systems with minimal assumptions on the nonlinearity, for both directed and undirected graphs. These results extend the literature to more general nonlinear dynamics and topologies. As applications of established theorems, we interpret the results on quantized consensus protocols.