Primary free radicals generated under oxidative stress in cells and tissues produce a cascade of reactive secondary radicals, which attack biomolecules with efficiency determined by the reaction rate constants and target concentration. Proteins are prominent targets because they constitute the bulk of the organic content of cells and tissues and react readily with many of the secondary radicals. The reactions commonly lead to the formation of carbon-centered radicals, which generally convert in vivo to peroxyl radicals and finally to semistable hydroperoxides. All of these intermediates can initiate biological damage. This article outlines the advantages of the application of ionizing radiations to studies of radicals, with particular reference to the generation of desired radicals, studies of the kinetics of their reactions and correlating the results with events in biological systems. In one such application, formation of protein hydroperoxides in irradiated cells was inhibited by the intracellular ascorbate and glutathione.