This paper investigates the global bounded consensus problem of networked multiagent systems consisting of nonlinear nonidentical node dynamics with the communication time-delay topology. We derive globally bounded controlled consensus conditions for both delay-independent and delay-dependent conditions based on the Lyapunov-Krasovskii functional method. The proposed consensus criteria ensure that all agents eventually move along the desired trajectory in the sense of boundedness. Meanwhile, the bounded consensus criteria can be viewed as an extension of the case of identical agent dynamics to the case of nonidentical agent dynamics. We finally demonstrate the effectiveness of the theoretical results by means of a numerical simulation.