This article explores the two mainstream directions of debates about the possibility of establishing a kind of international cybersecurity regime. It develops the idea of different governance models based on sovereignty, on the one hand, and multistakeholderism on the other. The application of international relations theory helps to understand the current process and stalemate initiatives regarding state cooperation in this field. In addition, the author pays attention to the applicability of the constructivism framework to the understanding of cybersecurity threats and the elaboration of international norms applicable to cyberspace. Finally, the article concludes with the idea that the multistakeholder approach to norm-making may become a viable solution to the problem of constructing an international cybersecurity regime.