The key research method is the dialectical method of analyzing the processes of the digital environment which is connected with the operation and internal organization of the Internet.
The article considers the main problems connected with searching for digital traces on the Internet, particularly in cloud storages. The author describes such problems as physical distribution of the data, its cross-border character, and legal competence during the investigation. The author also analyzes the issues of interaction with providers and administrators of cloud storages which have a significant impact on the investigation process. The article contains the list of predominant means of acquiring and studying the information from cloud storages. The key research method is the dialectical method of analyzing the processes of the digital environment which is connected with the operation and internal organization of the Internet. The author also uses the comparative-legal and the formal-logical methods. The author defines the disunity and complexity level of transnational interaction between law-enforcement authorities of different countries and describes the modern ways of searching for and analyzing the information in cloud storages related to the act under investigation, and the possibilities of automation of investigation activities.