[en] Transmission lines in modern pulsed-power machines such as PBFA-II operate at ten or more megavolts with multi-megampere currents. They often have series (voltage) or parallel (current) power addition. In these transmission lines the cathodes emit electrons freely. In addition, perturbations such as plasma opening switches cause additional electrons to be launched into the flow. The large magnetic field due to the transmission line current prevents these electrons from crossing the transmission line to the anode directly, but in most situations electron current flows to the anode after travelling a long distance down the transmission line. Usually these losses occur just before the load or at adder points. Reliable modelling of these lines is important both for design purposes and for use in analyzing data. This paper presents models that can be used for this purposes. The models are primarily based upon known symmetries plus measurable parameters. Comparisons to data, particularly data taken on PBFA-II, are made