Transposition and mutual approaching of pericentromeric loci 1q12 of homological chromosomes from the nuclear membrane towards the nuclear centre as well as activation of the chromosomal nucleolus-forming regions (NFR) are observed in human mesenchymal stem cells (hMSCs) as an initial stages of the adaptive response (AR) after exposure to low doses of X-radiation (10 cGy). All these reactions are also induced after addition of cultivation medium from irradiated cells to intact bystander-cells and this phenomenon called bystander effect (BE). Recently the same AR and BE induction results were obtained for human G0-lymphocytes. All these data indicate the existence of universal reaction of homological chromosome loci transposition which was revealed during AR development in differentiated (lymphocytes) and non-differentiated (hMSCs) and also it shows possibility of radiational BE development in suspension and monolayer cell cultures upon addition of stress-signalization factors in incubation medium. We suppose that these factors are extracellular genome DNA fragments apoptotic cells.