This thesis presents computational techniques applicable to the modeling of the interaction between transient electromagnetic fields and nonlinear circuits. The herein investigated problems consist of electromagnetically large structures, meaning that wave effects have to be considered in order to obtain accurate models. Connected to the structures are lumped, nonlinear circuit elements, which interact with voltages and currents induced by either external excitations, in the form of plane waves, or internal excitations, in the form of transient voltage sources. The herein adopted modeling approach is of hybrid nature and exploits that the compound system can be decomposed into a linear part, capturing the wave effects, and a nonlinear part, describing the nonlinear properties of the lumped elements. Using an iterative solver based on Waveform Relaxation, the voltages and currents are computed at the interfaces of the subsystems, making use of numerically efficient formulations of both the linear macromodels and the nonlinear circuit elements. Investigations are carried out for different terminations, excitations and levels of complexity for structures loaded with up to 100 ports.