The article analyzes the peculiarities of legal relations arising in connection with the cryopreservation of human biological material – embryos and reproductive cells, namely: determining the origin of a child born in this way. It is noted that the birth of children is a component of the demographic policy of the state, and the use of assisted reproductive technologies can change the demographic situation in society for the better. Cryopreservation is relevant not only in cases when a couple who wants to have children have difficulties with conception, but also when such problems do not yet exist, but they may arise with a high probability – this applies to such categories of citizens who are undergoing treatment for oncological diseases with a risk of loss reproductive health, as well as citizens who constantly risk their lives and health due to their activities: military personnel, policemen or workers at factories with harmful working conditions.
 The author notes that medical biotechnologies are becoming more and more diverse and effective, scientific achievements are penetrating deeper and deeper into the natural processes of human reproduction, therefore there is a need to resolve legal issues related to cryopreservation. And the realization of the right to cryopreservation requires legal regulation of so-called delayed parenthood.
 From the point of view of family law, these relations are of interest in terms of the emergence of new family law relations. The author considers several models for determining the origin of a child born with the use of assisted reproductive technologies using cryopreserved reproductive cells or embryos. Separate issues of postmortem reproduction are considered.
 The author concludes that there is a need for legislative regulation of gaps in the field of cryopreservation of reproductive cells and embryos, which will allow to ensure proper consolidation of the guarantee of the right to paternity/maternity and an effective mechanism for their implementation in cases of restriction of vital activity or death of a person.
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