The study of families irradiated as a result of the accident at the Chernobyl Nuclear Power Plant revealed significantly increased aberrant genomes frequencies (AGFs) not only in irradiated parents (n=106, p<0.01), but also in their children born after the accident (n=159, p<0.05). This is an indicative of the phenomenon of transgenerational genomic instability. To elucidate this phenomenon, experiments were undertaken to model genomic instability by using single and fractional in vitro gamma-irradiation ((137)Cs) of peripheral blood samples from the children and their parents at doses of 0.1, 0.2 and 0.3 Gy. The spectrum and frequency of chromosome aberrations were studied in the 1st and 2nd cell generations. The average AGF was significantly increased at all doses (except 0.1 Gy) in children of irradiated parents, as compared to children born from non-irradiated parents. Amplification of cells with single-break chromosome aberrations in mitosis 2, as compared to mitosis 1, suggests the replication mechanism of realization of potential damage in DNA and the occurrence of genomic instability in succeeding cell generations.