In this paper, a time-domain Green's function technique is presented for the analysis of linear and nonlinear guided-wave and radiated-wave effects in highly dispersive metamaterial structures. In addition, several examples are included to demonstrate the practicality of the proposed technique. The main advantages of this approach are: i) unconditional stability and fast computation due to the continuous treatment of time, ii) insight into the physical phenomena provided by the Green's function, and iii) straightforward extensibility for the analysis of arbitrary complex dispersive linear and nonlinear guidance and radiation phenomena, iv) full compatibility with the efficient integral equation technique.