With the increased availability of AI tools, universities ask themselves whether the marking of exams may be automated. This paper addresses this question from the legal point of view, examining the marking of written student papers. The results of this analysis show that the main requirements that need to be considered originate from the AI Act, from GDPR and from copyright law. It turns out that fully automating such marking involves serious legal problems making such marking very difficult if not impossible. Using the system to support manual marking of the papers, on the other hand, is feasible (from the legal point of view). To address the remaining issues regarding the need to use student papers for training and/or testing the system, the best solution is to offer contracts to the students, offering them some payment in exchange for their agreement to this use of their papers.