In this article, an attempt is made to determine the legal status of the human body (organs and tissue) both while a person is alive and after a person dies. The article discusses the points of view of various authors in relation to the possibility of considering the human body, its organs and tissue, after their separation from the body, as objects of a person’s property rights, and also as an object of a person’s non-property rights. The article argues the impossibility of qualifying the human body and the organs that were not separated from it during life as parts – and perhaps critical parts – of the existence of the total human being, as objects of real (property) rights including the rights of the persons themselves. The human body as a single object is a personal non-property benefit. The organs and tissue separated from the body may be considered objects of real rights, but on several conditions: if they were indeed separated from the body and if the person gave permission for this in a will. The specific characteristics of the legal status of the separated organs and tissue of a human being are analyzed as things (possessions) with limited turnover. The specific characteristics of the legal status of the organs and tissue separated from the body as possessions in limited turnover are reviewed as well as the impact of personal non-property rights on this status. The main focus of the article is on the legal status of the human body and the organs separated from it after death in view of the fact that transplantology and postmortem organ donation are becoming more and more widespread. This issue is analyzed in terms of the body as a whole and as it applies to the organs and tissue that are not used for transplantation. The proposal is to base our analysis on the status of the human body after death which as a rule cannot be the object of property rights. The human body is disposed of within the framework of the protection of the personal non-property rights of the deceased, including the right of physical inviolability that covers the organs and tissue separated from the body. The article characterizes the legal nature of living wills when people give instructions as to the procedure of their burial and other means of handling their body, including donation of their bodies to science. The article examines the possibility of the right of ownership to organs and tissue separated from the body after death. This right can exist if a complex legal construct is present, including a direct or assumed living will of the person. The specific characteristics of living acts concerning the possibility of after-death organ and tissue harvesting for further use, including for transplantation purposes, and the differences between such acts and last wills are determined.