Generative artificial intelligence (GenAI) has revolutionised teaching and learning by making access to information easier, customising feedback, providing adaptive learning, and helping students with assessments despite the technology’s pitfalls. However, there is a dearth of literature on understanding university students’ behavioural intention to adopt GenAI, especially in resource-constrained settings like Lesotho. Thus, this study sought to model the behavioural intention of GenAI adoption in higher education institutions in Lesotho by applying structural equation modelling (SEM). Data were collected through a Google Form using a questionnaire designed following the Unified Theory of Acceptance and Use of Technology (UTAUT) model. The modified UTAUT model had five core constructs – effort expectancy, performance expectancy, social influence, hedonic motivation and facilitating conditions. 271 university students from a resource-constrained country, Lesotho, participated in this study. The participants, randomly selected, were drawn from the country’s three universities. The data were analysed using two software: IBM’s Social Statistical Package for Social Sciences for descriptive statistics on participants' demographics and SmartPLS for modelling the behavioural intention to use GenAI. The results revealed that only two of the five constructs significantly influenced students’ behavioural intention to use GenAI. These factors are effort expectancy and performance expectancy. The other constructs, social influence, facilitating conditions and hedonic motivation, were not significant in determining students’ behavioural intention to use GenAI. The findings of this study imply that universities in Lesotho do not need to invest in infrastructure to provide conditions that allow students to access and use GenAI. Moreover, the non-significance of social influence implies that the views of lecturers, classmates and important others are not important in determining Lesotho’s university students’ behavioural intention to use GenAI. While the study helps understand the factors affecting GenAI adoption in Lesotho, the generalizability of its findings is limited in that it was not cross-country.