Currently there is no special legislative regulation in the Russian Federation that takes into account the specifics of the use of artificial intelligence technologies. There are acute issues of working out the mechanisms of civil liability in the event of harm caused by artificial intelligence systems that have a high degree of autonomy in their decision-making, including in terms of ways to compensate for the harm caused by the actions of such systems. Based on the analysis of foreign experience in the legal regulation of civil liability for harm caused by the activities of artificial intelligence systems, and the experience of forming the legal framework in the field of artificial intelligence in Russia, it is proposed to apply tort liability to activities related to the use of artificial intelligence systems, and compensation for damage caused by such activities to be carried out from the funds of a specially created system of compulsory civil liability insurance for developers and owners of artificial intelligence systems, including a specially introduced entity – a specialized operator of artificial intelligence systems, and provide for an insurance deductible due to the autonomy (unpredictability) of the actions of artificial intelligence systems intellect.