The technique of electron spin resonance spectroscopy was employed primarily to study the effects of ionizing radiation, in the form of x-rays (50Co source), on various organosulphur compounds, selected polyamino acids and proteins, and DNA. The work was carried out exclusively at low temperature ( 240K), powder, frozen aqueous or CD3OD/D2O deoxy glass systems being studied. The underlying principle of the work presented here was "radioprotection". To this end, several known thiol radioprotectors have been studied, along with thiol compounds where previous research has not been so extensive. The aim of this was to try to resolve a long-standing controversy in the literature which has both chemical and biochemical implications. The problem is the fate of radicals generated in the thiol "radioprotector" after it has completed its act of repair in a biochemical system. This is studied, evaluated and discussed in Chapters 2-6 and has direct bearing on the work presented in Chapter 8. The reverse of this radioprotection is discussed in Chapters 7 and 8 that is radiation damage to bio-macromolecules. Chapter 7 is concerned primarily with damage occurring via an electron-loss centre in polyamlno acids and proteins whereas Chapter 8 involves damage to the cells primary target - the DNA molecule itself.