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The source region of a nuclear detonation is the region of space in which electric currents induced by the radiation output of the weapon are present. Outside this region, which typically has a radius of up to a few kilometers, the electromagnetic field created by these currents propagates essentially in a free-space environment. Interest in the source-region environment produced by a surface or near-surface detonation has been strong in the nuclear-weapons community for many years, principally because of the necessity of hardening missile silos and, more recently, the horizontal shelters of the MX system against the electromagnetic effects of a nearby burst. The fact that the nuclear source-region environment is as complicated as it is presents an extremely large set of problems and challenges to the electromagnetic theorist and the numerical analyst. In the remainder of this article the author discusses the nuclear source-region environment itself, electromagnetic interactions in the source region, the capabilities and limitations of some of our present computer codes, and areas in which further work will be useful. The hope is to make the readers of this article aware of some of the problems which are currently faced bythose responsible for studying the electromagnetic effects of nuclear weapons, and perhaps to excite their interest in this most challenging area of electromagnetics.