The authors present a review of findings pertaining to the transplantation of haematopoietic stem cells of the peripheral blood. They pay particular attention to the theoretical basis of this transplantation, its history and technical procedure. The selection of literature concentrates on important original work. The author divided the problem into three parts. In the present second part they pay attention to the beginnings of the clinical application of stem cell transplantations. The author describes work which revealed that the concentration of peripheral stem cells can be elevated under certain conditions, as well as work dealing with the first transplantations of stem cells in humans.