Expressions relating far electromagnetic fields and return stroke channel base currents have been derived in the literature for various lightning return stroke models. The use of such relations permits the estimation of channel base currents of return strokes, testing of the individual models using sets of simultaneous current and field measurements, and also the determination of nondirectly measurable parameters of the models. In this paper we derive a relation between the far electromagnetic field and the channelbase current for the Diendorfer-Uman (DU) and the modified Diendorfer-Uman (MDU) models. Additionally, the current-field relations for all models for which such an analytical relation can be derived are summarized. Finally, a numerical solution technique is proposed to solve the equations relating the far field and channel base current of the DU and the traveling current source (TCS) models. ¿ American Geophysical Union 1993