Currently all countries form or are in process of forming rules of law regulating turnover of new digital objects of rights that are called differently as digital rights, tokens, digital assets, digital currency, and cryptocurrency. The difference in wording does not allow to develop common international approaches to the cross-border turnover of such new objects of rights. States are only looking for ways to regulate relations in the digital economy. To find optimal solutions, a comparative legal research is needed to evaluate models of regulation and find effective ways and means of response to the modern challenges. Aim of the research is to analyze models of legal regulation of the turnover of digital rights and digital currency and offer model of regulation that allow such objects of rights to be fully included in the Russian civil turnover. The following tasks are being solved: choice of jurisdictions and analysis of legal norms that regulate turnover in the field; formulation of regulative models of the turnover of digital rights and digital currency based on legislation, doctrine and law enforcement; study of measures and means of regulation used in various states; analysis of different points of researchers on regulation of relations in the digital economy in Russia and abroad; proposal to the legislator of measures and means of regulation, based on the chosen regulative model of the turnover of digital rights and digital currency. Such methods as comparative legal, formal legal, legal modeling methods were used to compare experience of various jurisdictions and formulate regulative models in need. Also general methods of synthesis, analysis, induction, deduction, comparison, analogy, etc. were used. The study showed that the approaches used in the legal regulation in the field differ both in terms of legal norms and in creation of institutions and conditions for functioning digital market. Models of the corresponding legal regulation also differ. States use both prohibitive model of turnover regulation (prohibition of their issuance and turnover), partially prohibitive (restrictions on the turnover of digital rights and digital currency), partially permissive (admission of turnover of digital rights and digital currency, subject to conditions — licensing, regulatory sandboxes, etc.) and permissive model (allowing the turnover of digital rights and digital currency to all market participants, subject to minimum requirements). Terms like cryptocurrency, tokens, crypto assets, digital assets are more popular abroad, while in Russia the concepts of digital rights and digital currency are used to refer to similar legal phenomena. It would be necessary to compare categories under consideration for the possibility of their use in supranational regulation, and cross-border relations, in order to be able to speak with representatives of other jurisdictions in the same language. From the foreign experience, attention of legislator should be drawn to the need and possibility of licensing in relation to participants in the digital market, as well as to the success of regulatory sandboxes in this area, for example in Britain. At the same time, when establishing law enforcement practice in Russia in the field, especially with participation of consumers, experience in US, Britain, Australia as well as the legal regulation of the crypto industry in Japan shall be considered.