At the initial stages of an adaptive response the transposition of the homologous chromosome loci from the peripheral parts of the nucleus and their approach happens. It is necessary for the repair of DNA double strand breaks in the process of the homologous recombination. Was shown that the chromosome loci transposition and accompanied by the nucleolus activities took place first in the irradiated (X-rays, 10 cGy) G0-lymphocytes, and then in the intact (bystander) cells incubated in the growth medium of irradiated lymphocytes. If there is a bystander effect the quantity of irradiated cells may be three order less than the bystander cells that affirms the great capacity of stress-signalization system. Moreover, the DNA fragments (the factors of stress signaling) were obtained from the growth medium supernatant of the irradiated and of the intact lymphocytes. In other independent experiments they were inoculated into the growth medium of recipient cells. Was demonstrated that there is loci transposition of homologous chromosomes loci and of nucleus activity after introducing the DNA fragments of irradiated cells. After introducing the DNA fragments of non-irradiated cells the both effects were not observed. In the work the characteristics of the obtained factors and the possible ways of stress signaling between the irradiated and the bystander lymphocytes were discussed.