A number of provisions, conclusions and proposals has been formulated and substantiated due to the research, in particular: the author has proposed a definition of the concept of donation, as a free (except for the special cases) open process, during which a donor, upon written informed voluntary consent, provides his/her anatomical material during the lifetime or disposes of them in case of his/her death for further use by other persons during transplantation for medical, pharmaceutical or scientific purposes. The definition of the concept of transplantation has been given as a paid special treatment method, which is the final stage of donation and is used if there is the immunological compatibility of the donor and the recipient, and means the transplantation of the anatomical material of a person or other biological organism, implants from a donor to a recipient. The author has presented the arguments for the need to expand the circle of people who can be potential donors by amending provisions of the Law of Ukraine On the Safety and Quality of Donated Blood and Blood Components, stating that the donors can be incapacitated persons, who are the recipient’s close relatives (children, grandchildren, parents, grandfather, grandmother, brother, sister, uncle, aunt, nephew and niece) or his/her family members. It has been proposed to understand the notion of a living donor as an adult individual having dispositive legal capacity or a minor individual who, before reaching the age of 18, received full civil legal capacity, a citizen of another state and a stateless person who are legally staying on the territory of Ukraine, gave voluntary consent to the collection of anatomical material for transplantation, and also a person under 18, whose consent to the collection of the hematopoietic stem cells was given by him/her personally and (or) his/her parents or other legal representatives, as a case specified by the Law of Ukraine On the Application of Transplantation of Anatomical material to a Person. It has been justified according to which the medical institution making the collection of anatomical material shall inform the donor and the recipient about the nature and duration of the medical intervention required for the collection of the anatomical material, about the response mechanisms to possible undesirable effects of the procedures, ensuring the anonymity and confidentiality of personal data of the donor and the recipient and safeguarding access to this information, compensation for harm, which may be caused as a result of medical intervention, about the funding sources of the forthcoming operation on collection of anatomical tissues for their subsequent transplantation. It has been concluded that, in the event of a forensic medical examination, the prosecutor supervising the observance of laws during the pre-trial investigation in the form of procedural supervision of the pre-trial investigation shall immediately decide on the possibility or prohibition of the removal of anatomical material from the deceased donor, the pre-trial investigation into whose death is performed. The specified decision shall be motivated and set out in the form of an order. It has been substantiated that the anatomical material removed from the body of a living or deceased donor should be treated as a special object of civil rights, to which a legal regime of a thing shall extend in cases directly determined by law, the procedure for the collection and subsequent use of which should be guided by the special legislation. An essential feature is that the anatomical material collected from a person have some signs of proprietary rights in cases provided for by law. The conclusion has been made that the posthumous donation agreement which is concluded by a family member of the deceased or his/her authorized representative with a medical institution that will collect the anatomical material after the person’s death can be terminated at the request of the person representing the deceased person only if the medical intervention in the recipient’s body for the subsequent transplantation is not at the stage when it may harm his/her life and health. The conclusion on the advisability of amending of the Law of Ukraine On the Safety and Quality of Donated Blood and Blood Components has been reasoned, including the provision that the compensation for harm caused to the health of the recipient due to the transfusion of the donor’s blood of inadequate quality, as a result of which the disease was transmitted to the recipient, or through the components or preparations made from it, shall be fully paid either by the medical institution that carried out the treatment or by the state. It has been substantiated that the quantitative characteristics of the anatomical material that can be callected from the donor should be viewed as the essential conditions of the posthumous donation agreements.