Abstract: There are widespread testimonies that the genomic instability induced by ionizing irradiation exits in mammal and its vitro cells. Genomic instability can enhance the frequency of genetic changes among the progeny of the original irradiated cells. In the radiation-leukaemogenesis, there is no significant difference between controls and CBA/H mouses of PPI (preconception patenal irradiation), but the offsprings of the PPI recipients show a different character (shorter latent period and higher incidence) after an extra γ-radiation. The radiation-induced genomic instability may get the genome on the verge of mutation and lead to carcinogenes following mutation of some critical genes. The genomic instability, as the early event of initiation of carcinomas, may be play a specific or u-nique role.