During the development of the adaptive response, the pericentromeric loci of homologous chromosomes appear to move from the perimembrane sites of the cell nucleus and approach each other for a possible repair of double-stranded breaks of DNA in the process of homologous recombination. After exposure to X-ray radiation at an adapting dose of 10 cGy, transposition of the chromosomal pericentromeric loci and the accompanying activation of the chromosomal nucleolus-forming regions (NFRs) were observed in the irradiated lymphocytes, and were seen also in the intact bystander cells incubated in the growth medium of the exposed lymphocytes (the so-called bystander effect). From the culture medium of the irradiated and intact lymphocytes, we isolated DNA fragments that were introduced into the medium of nonirradiated cells in independent experiments. The bystander lymphocytes were found to demonstrate both transposition of the loci of homologous chromosomes and activation of the chromosomal NFRs, whereas after inoculation of the DNA fragments of the unirradiated cells, neither of the above effects was observed. Discussed herein are the characteristics of the factors revealed and possible pathways of stress signaling between the irradiated lymphocytes and the bystander cells.