In this paper, an analysis of electric and magnetic fields radiated by lightning first and subsequent return strokes to tall towers is presented. The contributions of the various components of the fields, namely, static, induction, and radiation for the electric field, and induction and radiation for the magnetic field are illustrated and discussed. It is shown in particular that the presence of a tower tends, in general, to increase substantially the electric and magnetic field peaks and their derivatives. This increase is mainly caused by the presence of two oppositely propagating current wavefronts originating from the tower top and by the very high-propagation velocity of current pulses within the tower (practically at the speed or light), and depends essentially on the wavefront steepness of the channel-base current. Because of the last factor, the increase of the field magnitudes is found to be significantly higher for subsequent return strokes, which are characterized by much faster risetimes compared to first return strokes. Furthermore, the presented results are shown to be consistent with recent experimental observations of current in lightning strokes to the Toronto CN Tower and of the associated electric and magnetic fields measured 2 km away. These findings partially explain the fact that subsequent return strokes characterized by lower current peaks but higher front steepnesses and return stroke speeds may result in higher field peaks. The results obtained in this study haste important implications in electromagnetic compatibility. It is found that lightning strikes to tall metallic objects (towers, rods, etc.) lead to increased electromagnetic field disturbances. Also, subsequent return strokes are to be considered an even more important source of electromagnetic interferences than first return strokes. Indeed, electromagnetic fields from subsequent strokes are characterized by faster fronts and additionally, they may reach greater peaks than first strokes. Lastly, findings of this study emphasize the difficulty of extracting reliable lightning return stroke current information from remote electromagnetic field measurements using oversimplified formulae.