The theory of diffusion-limited bimolecular reaction kinetics is investigated for the case in which the reactants are initially produced in spatially correlated pairs. The intent of the study is to discover to what extent information concerning the initial distribution of pair member separations (generally unknown for such systems) can be deduced from empirically observable quantities. The analysis predicts the form of the dependence of the fractional concentration of recombined pairs on various moments of the distribution function as well as the approximate concentration dependence of very late time correlated reactions. It is expected that the model may be applicable to many systems of radiation-and photo-physics, chemistry, and biology; the specific examples of radical reactions in solution and the annealing of damage produced by electron irradiation of metals and semiconductors are discussed.