Objective: The article aims to identify factors that influence students’ behavioural intentions to use generative artificial intelligence (GenAI). Research Design & Methods: We proposed a research model based on the theory of planned behaviour, the technology acceptance model and a literature review. Findings: The results show that attitude, perceived usefulness, perceived quality, and perceived support from higher education institutions positively impact students’ behavioural intention to use GenAI. Implications & Recommendations: The findings allowed us to propose two practical implications for academic teachers and managers of higher education institutions. Firstly, we recommend supporting students in terms of their knowledge, skills and conscious use of GenAI. Comprehensive education and other forms of training may be of use here. Secondly, we recommend that educational establishments clearly define their expectations regarding students’ use of GenAI, particularly how and when they can safely use GenAI, not only during their studies. Contribution & Value Added: Our study offers a new multilevel model of students’ behavioural intentions to use generative GenAI. It enables the synthesis of our research results and the organisation of variables influencing students’ behavioural intention to use GenAI, as well as the relations between them. Furthermore, as far as we are aware, we are the first to encompass aspects of the perceived quality and ethics of students using GenAI in our research.