Experimental biology and medicine work with stem cells more than twenty years. The method discovered for in vitro culture of human embryonal stem cells acquired at abortions or from„surplus” embryos left from in vitro fertilization, evoked immediately ideas on the posibility to aim development and differentiation of these cells at regeneration of damaged tissues. Recently, several surprising observations proved that even tissue-specific (multipotent) stem cells are capable, under suitable conditions of producing a while spectrum of cell types, regardless, whether these tissues are derived from the same germ layer or not. This ability is frequently called stem cell plasticity but other authors also use different names -„non-orthodox differentiation” or„transdifferentiation”. In this paper we wish to raise several important questions and problems related to this theme. Let us remind some of them: Is it possible to force cells of one-type tissue to lool and act as cells of another tissue? Are these changes netural? Could these trans-formations be used to treat diseases? What about the bioethic issue? However, the most serious task “still remains to be soloved - how to detect, harvestand culture stem cells for therapy of certain diseases”.