A general analysis of the fluorescent process is described which emphasizes the differing roles of escape probabilities in one-component and two-component gases, and the existence of discrete fluorescent saturation regimes. Explicit formulae are obtained and discussed for astrophysical Bowen fluorescence, as a concrete example, with applications to planetary nebulae, the solar atmosphere and the X-ray binary Sco X-1. An expression is also provided and evaluated for the profile overlap integral involved in the pumping process. A preliminary conclusion is deduced that densities in the fluorescent line-emitting regions of nebular sources may be higher than those derived from forbidden line ratios. We extend the analysis to a proposed laboratory investigation which would exploit the possibility of controlling the determining factors in the fluorescent process, i.e., O m/He II abundance ratio, optical depth and photoexciting radiation field.