We compare five lightning return stroke current models that exhibit a simple relationship between the current at the return stroke channel-base and the current along the return stroke channel, namely the Bruce-Golde (BG) model, the transmission line (TL) model, the Master, Uman, Lin, and Standler (MULS) model, the Traveling Current Source (TCS) model, and the Modified Transmission Line (MTL) model, by assuming a common current wave shape at the channel base and then calculating the channel currents and charges and the resultant electric and magnetic fields. There are basically two characteristics that distinguish the models, namely, (1) the treatment of the return stroke wave front and (2) the spatial and temporal distribution of charge removed from the leader channel. The simpler BG model can be used as an excellent approximation to the TCS model. The latter reduces to the former when the current injected downward by the traveling current source has an infinite speed. The MULS model is equivalent to the MTL model when the MULS uniform current is assumed to be zero. The BG and TCS models produce sharper initial field peaks than do the TL, MTL, and MULS models. The ratio of the peak field derivative to the peak current derivative is near the ratio of the peak field to the peak current for the MULS and MTL models and is equal for the TL model, whereas for the BG and TCS models the ratio of the peak derivatives is about twice the ratio of the peak field to peak current. The TL model is unrealistic for long-time field calculations due to the fact that no net charge is removed from the channel. The other four models produce overall fields which are reasonable approximations to measured fields from natural lightning even though, for the assumed channel-base current, the BG and TCS models not not reproduce the observed distant-field zero crossing and the MTL and MULS models do not reproduce the magnetic ''hump'' observed after the initial field peak at close range. None of the models can reproduce the fine structure observed in the measured fields. ¿ American Geophysical Union 1990