The article deals with the main range of problems of Grensk culture in the Final Palaeolithic and Mesolithic in the Upper Dnieper region. At present, the understanding of the ways and mechanisms of the formation and the time of habitation of members of this ancient culture are rather debatable. Interpretations of the sources have resulted in two completely different research approaches in terms of methodology, bringing together supporters of the indigenous (U. Budzko, V. Kapytsin, A. Kalechyts, G. Sinitsyna, etc) or migration (L. Zaliznyak, U. Ksiandzou, A. Sorokin, etc) ways of the emergence and the development of Grensk culture. It is impossible to understand the essence of the ‘Grensk question’ without considering the nature of its origin, the problem looked at in this article.