The article considers a hypothesis suggested some years ago by genetics that supposes the Yamnaya culture migration as a cause of dramatic genetic shifts in Central and Western Europe in the early Bronze Age, of the formation of Corded Ware cultures, as well as of the coming of Indo-European languages in Europe. The author points out to some important and complicated questions that the hypotheses of “Steppe migration” has not answered to the moment. Basing on this, the author suggests to discuss the (proposed by him earlier) alternative scenario which supposes the earlier (in the Mesolithic and early Neolithic) coming of so-called “Steppe ancestry” (or, at least, of the key elements that constitute this “Steppe ancestry”) in Europe. Thus, this scenario presumes that the early Bronze Age was the time of broad “manifesting” of the “Steppe ancestry” in Central and Western Europe, and not of its 'coming' to the region.