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A novel method for transient analysis of electromagnetic systems with multiple lumped nonlinear loads is presented. The uniqueness of this approach is that we develop time-domain Green's functions for the multiport linear part of the electromagnetic system by suitably terminating the ports. This ensures a short duration of Green's functions. Hence the amount of frequency-domain data necessary to obtain the time-domain Green's functions is modest. The application of this technique to an arbitrary excitation is just a straightforward convolution. With this technique one can analyze responses of systems with arbitrary nonlinear loads (even with memory) as we have at any time instant Thevenin's equivalent of the linear portion of the electromagnetic system. Examples are presented to illustrate the application of this technique to multiport nonlinearly loaded antennas.