The global architecture of computer networks poses a security dilemma: while modern information and communication technologies allow adversaries to challenge the exclusive power of states over “his own” cyberspace, following traditional notions of sovereignty, respectively, may limit the ability of states to actively counter challenges and threats in global networks. The aim of the study is to determine the possible scope of application of the traditional territorial concept of sovereignty to the activities of states in cyberspace. The article shows that regarding the activities of states and individuals in cyberspace, the scope of the principle of sovereignty is determined by the practical imperatives of states and depends on the sphere of interstate and cross-border interactions affected. Therefore, for example, for the purposes of warfare, there are three levels at which objects for destruction will be determined: physical network, logical network, network user. Other criteria are important for developers, operators and network analysts, and, according to a number of proposals, a global network can include up to seven levels (physical, data transfer, network, transport, session, data, applications). The article demonstrates that despite the exceptional nature of the powers and jurisdictions of the state in relation to the physical level of cyberspace, its logical and social levels are open to cross-border manifestations of the jurisdiction of other states on the basis of the proximity criterion. That is, for those cases when states can establish a real connection with digital objects or online personalities, and, accordingly, exercise authority.