<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A fast and comprehensive time-domain method for analyzing electromagnetic compatibility (EMC) and electromagnetic interference (EMI) phenomena on complex structures that involve electrically large platforms (e.g., vehicle shells) along with cable-interconnected antennas, shielding enclosures, and printed circuit boards is proposed. To efficiently simulate field interactions with such structures, three different solvers are hybridized: 1) a time-domain integral-equation (TDIE)-based field solver that computes fields on the exterior structure comprising platforms, antennas, enclosures, boards, and cable shields (external fields); 2) a modified nodal-analysis (MNA)-based circuit solver that computes currents and voltages on lumped circuits approximating cable connectors/loads; and 3) a TDIE-based transmission line solver that computes transmission line voltages and currents at cable terminations (guided fields). These three solvers are rigorously interfaced at the cable connectors/loads and along the cable shields; the resulting <emphasis emphasistype="italic">coupled</emphasis> system of equations is solved <emphasis emphasistype="italic">simultaneously</emphasis> at each time step. Computation of the external and guided fields, which constitutes the computational bottleneck of this approach, is accelerated using fast Fourier transform-based algorithms. Further acceleration is achieved by parallelizing the computation of external fields. The resulting hybrid solver permits the analysis of electrically large and geometrically intricate structures loaded with coaxial cables. The accuracy, efficiency, and versatility of the proposed solver are demonstrated by analyzing several EMC/EMI problems including interference between a log-periodic monopole array trailing an aircraft's wing and a monopole antenna mounted on its fuselage, coupling into coaxial cables connecting shielded printed circuit boards located inside a cockpit, and coupling into coaxial cables from a cell phone antenna located inside a fuselage. </para>