Estimating parameters of a lightning return stroke model and the current at the base of the lightning channel from measurements of remote electromagnetic fields is an important practical problem. In the present paper we apply a genetic algorithm (a global optimization technique) to the above problem. Firstly, we use the genetic algorithm to reconstruct the return stroke model parameters using the channel-base current and the remote electromagnetic field measured simultaneously. The channel-base current is used to calculate the electric field at the measurement point. The difference between the calculated and the measured fields is minimized using the genetic algorithm, which finds the optimal solution for the return stroke parameters. The transmission line and Diendorfer-Uman return stroke models are used in the illustrations. Secondly, we develop a method to reconstruct the return stroke model parameters and channel-base current from electric or magnetic fields measured at two different distances, one of which is a far-field and the other is a near field. The Diendorfer-Uman model is used in the reconstruction. Thirdly, we develop a method to reconstruct the return stroke model parameters and channel-base current from two magnetic fields at two different distances, one of which is an intermediate field and the other is a near field. For doing the above with the Diendorfer-Uman model we derive an explicit inversion formula using both the induction and the radiation terms of the magnetic field. ¿ 2000 American Geophysical Union