While many papers have focused on socially unequal admissions in higher education, this paper looks at the persistence of class differentials after enrolment. I examine the social class gap in bachelor's programme dropout and in the transition from bachelor's to master's in Denmark from the formal introduction of the bachelor's degree in 1993 up to recent cohorts. Using administrative data, I find that the class gap in bachelor's departures has remained constant from 1993 to 2006, with disadvantaged students being around 15 percentage points more likely to leave a bachelor's programme than advantaged students, even after adjusting for other factors such as grades from upper secondary school. Importantly, the class gap reappears at the master's level, with privileged students being more likely to pursue a master's degree than less privileged students. The size of the class gap is remarkable, given that this gap is found among a selected group of university enrolees. As other studies have found that educational expansion in higher education is not necessarily a remedy for narrowing the class gap in educational attainment, scholars need to pay more attention to keeping disadvantaged students from leaving higher education.