Legislators and developers of by-laws and regulations, theorists and practitioners consider anti-corruption as one of the priorities of Ukraine's domestic policy. However, the work of law enforcement agencies in detecting and investigating corruption offences is not sufficiently productive. But it is in the legal regulation of operational and technical measures and covert investigative actions that several problems have accumulated, which determines the relevance of this study. The purpose of the work is to outline the range of problems of legal regulation and the practical application of operational and technical measures and relevant covert investigative actions in combating corruption offences related to bribery. The methodological tools are chosen according to the chosen purpose and considering the object and subject of the study. The study is based on the general dialectical method of cognition, which is used to explore social and legal phenomena and processes, and to establish their connections with the work of operational and investigative units of law enforcement agencies, prosecutors and courts. In addition, general scientific and specific methods of legal science were used, including: logical-legal (dogmatic); system-structural; comparative legal and comparative; and sociological. It is substantiated that a necessary condition for increasing the efficiency of the application of operational and technical measures and relevant covert investigative actions in combating corruption offences is the specification and detailing of legislative provisions that establish the content and procedure for conducting some activities. The law should define all operational and technical measures (and relevant covert investigative (search) actions), clearly distinguishing between audio, and video control of: a person; a publicly inaccessible place; a publicly accessible place, and visual surveillance of a publicly accessible place using photography, video recording and special technical means for surveillance. The practical value of the work is conditioned upon the prospects of using the results