Artificial Intelligence (AI) has been highlighted as a potentially disruptive force across several industries and in higher education. Research has suggested that education and upskilling of citizens should adopt a broad approach, not only focusing on experts, for better nationwide AI readiness. This study investigates the content of AI policies in higher education by analysing official documents from Swedish universities. It identifies key themes and patterns, comparing them with related research and international guidelines. Expanding on the results of the study, it develops a dynamic alignment model for higher education AI policy (DAMHEAP) which, grounded in institutional theory, highlights strategic, pedagogical, ethical and legal, operational and adaptive alignments. This model, together with 10 practical recommendations, provides a roadmap for higher education institutions to develop and maintain AI policies that are pedagogically relevant, ethically responsible and adaptive to technological change.