This paper analyzes a class of nonlinear consensus algorithms where the input of an agent can be decoupled into a product of a gain function of the agents own state, and a sum of interaction functions of the relative states of its neighbors. We prove the stability of the protocol for both single and double integrator dynamics using novel Lyapunov functions, and provide explicit formulas for the consensus points. The results are demonstrated through simulations of a realistic example within the framework of our proposed consensus algorithm.