Mathematical analytical model of the processes running in individual radical clusters during the chemical phase (under the presence of radiomodifiers) proposed by us earlier has been further developed and improved. It has been applied to the data presented by Blok and Loman characterizing the oxygen effect in SSB and DSB formation (in water solution and at low-LET radiation) also in the region of very small oxygen concentrations, which cannot be studied with the help of experiments done with living cells. In this new analysis the values of all reaction rates and diffusion parameters known from literature have been made use of. The great increase of SSB and DSB at zero oxygen concentration may follow from the fact that at small oxygen concentrations the oxygen absorbs other radicals while at higher concentrations the formation of oxygen radicals prevails. It explains the double oxygen effect found already earlier by Ewing. The model may be easily extended to include also the effects of other radiomodifiers present in medium during irradiation.