A complex of cytogenetic and of immunogenetic study of the state of the lymphocyte genomes in the liquidators of the ChNPP accident and their unirradiated children has been carried out for the first time. Increased frequencies of the chromosome aberrations, of gene mutations (TCR mutations) and of predictors of apoptosis (cells with CD95+ immunophenotype) have been revealed in both generations. The analysis of correlations between the parameters under study has demonstrated distinctive features characteristic of induction of genomic instability in the organism of unirradiated children as compared to their fathers--liquidators directly exposed to radiation. Individual variability of genome destabilization were observed by all criteria used and manifested themselves in the diverse spectrum of transgenerational mutational effects and in different levels of their expression. The results obtained demonstrate the necessity of integral evaluation of the state of the genome using several genetic criteria to reveal transgenerational genomic instability in children of a special category--the offsprings of irradiated parents.