The focus of this paper is on the relationships between social origin, participation in tertiary education (enrolment, drop-out, enrolment at second level and post-tertiary education) and occupational instability among university graduates in a recent period of university and labour market reforms (the differentiation of higher education due to the "Bologna process" and the flexibilization of employment contracts). In the first part of the paper we review these institutional reforms, discussing how they have changed the structure of opportunities and constraints for students and graduates. In the second part we analyse data from several cross-section waves of the Upper Secondary Graduates Survey and the University Graduates Survey which cover both pre- and post-reform cohorts. Results from logistic regression models show a slight decline in the association between parents' education and enrolment in tertiary education, whereas there is a reduction and a new increase of inequality in drop-outs. We also find remarkable effects of parents' education on enrolment in post-graduate courses, but smaller on the risks of having unstable jobs and both are mainly stable over time. Only a slight reduction of the role of social origin in university participation and in the transition to the labour market took place, but it seems not to be too closely connected to the specific reforms which occurred in the 1990s.