A theoretical model permitting estimation of yields of various DNA damages induced by radiations of varying qualities is described. It is based on the Monte-Carlo track structure simulation and DNA structure, and links physical, physicochemical and chemical stages of radiation action. Direct and indirect effects are not strictly distinguished but treated cooperatively. Good agreement between calculated and measured initial yields of double-strand breaks was observed. Other multiple and single damages of DNA are studied. When radiation quality is changed there are quantitative and qualitative transitions in the damage spectrum. The proportion of multiple damage in the damage spectrum is about 30% for low-LET radiations and increases considerably with increasing ionization density.