Abstract As Artificial Intelligence (AI) technology develops and more AI systems are put on the market, concern about the implications of such AI systems on humans is growing. A particular area of concern is the impact of AI systems on intellectual property rights (IPRs) as infringement might occur in relation to the use of AI systems. IPR infringements can be committed by training an AI system, as well as by using or when operating an AI system. This raises the question of liability for such IPR infringements. This research covers situations where IPR infringements are committed by training an AI system, as well as those where infringements are committed by using or operating an AI system. One hypothetical situation of an AI system created solely for the purpose of infringing IPRs is investigated, but also includes situations where otherwise legitimate AI systems are misused in criminal activities as tools for the production and sale of infringing goods. These areas are analysed in relation to the proposed AI Liability Directive and other relevant European Union legislation to identify what rules would be applicable to liability for damage in such cases. The research also considers the recently enacted AI Act. In instances where the damage is caused by AI-enabled products and services, the study shows how the ‘rebuttable presumption of causality’ provided for under the AI Liability Directive could be applied.