This study compares how the generative AI (GenAI) large language model (LLM) ChatGPT performs in grading university exams compared to human teachers. Aspects investigated include consistency, large discrepancies and length of answer. Implications for higher education, including the role of teachers and ethics, are also discussed. Three Master's-level exams were scored using ChatGPT 3.5, and the results were compared with the teachers' scoring and the grading teachers were interviewed. In total, 463 exam responses were graded. With each response being graded at least three times, a total of 1389 gradings were conducted. For the final exam scores, 70% of ChatGPT's gradings were within 10% of the teachers' gradings and 31% within 5%. ChatGPT tended to give marginally higher scores. The agreement on grades is 30%, but 45% of the exams received an adjacent grade. On individual questions, ChatGPT is more inclined to avoid very high or very low scores. ChatGPT struggles to correctly score questions closely related to the course lectures but performs better on more general questions. The AI can generate plausible scores on university exams that, at first glance, look similar to a human grader. There are differences but it is not unlikely that two different human graders could result in similar discrepancies. During the interviews, teachers expressed their surprise at how well ChatGPT's grading matched their own. Increased use of AI can lead to ethical challenges as exams are entrusted to a machine whose decision-making criteria are not fully understood, especially concerning potential bias in training data.