To analyse a role of the factor of a genetic fundamentals of cells in formation of radiation-induced genome instability (RIGI) we investigated a condition of DNA pattern, content of superoxide anion-radical O2*- and a sum of reactive oxigen species (ROS) (O2*-, OH*, H2O2), and also catalase activity in bone marrow cells of male and female mice of 101/H strain in the norm and at once after chronic (10 day) exposure to 200 mGy gamma-radiation. Thus we based on conception about a significance of mechanisms of DNA repair and production of reactive oxygen species (ROS) in development of radiation-induced genome instability (RIGI), and also on the data on sex bound differences in efficiency of DNA repair in reply to impact of the genotoxic agents for male and female mice of 101/H strain. Sex connected differences in redox system of bone marrow cells were established. In males lower catalase activity was found in the norm, with considerable increase of the activity and the content of ROS after chronic irradiation with a low dose (200 mGy); at the same time a direct correlation between the ROS content and catalase activity occurred. In female, which have higher DNA repair potential, higher level of catalase activity was found in the norm, with reduction after irradiation and lower, than in male, level of O2*- content; no changes in the general ROS content, or direct correlation between the content of a superoxide anion-radical (O2*-) and the sum of ROS were observed. The detected differences between male and female the studied parameters in the norm and after irradiation indicate a connection of the studied characteristics and their changes with a sex, confirm the literature data about a significance of the factor of a genetic fundamentals of bioobject in formation of radiation-induced genome instability.