Questions about self-awareness of artificial intelligence (AI) and the perspective of full autonomy of AI systems show how complex issues the legislator will have to cope with to establish a legal framework adequate to advanced AI. Although the development of AI systems has not reached the level mentioned above, we already have to deal with the problem of inadequacy of the existing legislative regime to factual situations in which an AI system has caused damage. This article examines the civil liability of AI systems in EU legislation. The analysis discusses current problems with AI liability, proposals of the European Union legislator on how to solve existing problems and includes de lege ferenda suggestions. Conclusions from the observations made allow to answer whether the legal solutions offered by the Products Liability Directive proposal and the AI Liability Directive proposal are adequate to the identified problems with liability for AI systems.