This article explores the determinants of the transition from higher education to work, analysing the time it takes college graduates to obtain their first job in Spain. To estimate the exit rate to employment of university graduates, we use parametric and nonparametric analysis of duration models. We have incorporated unobserved heterogeneity using frailty models to account for misspecification or omitted covariates. The results show that after graduation, men are more likely to obtain employment than women. Our results also show that graduates of private universities gain their first jobs sooner than graduates of public universities. Furthermore, we found that those graduates who have previous work experience and those who start looking for a job before the end of their degree programme are likely to obtain a job sooner. In addition, Arts and Humanities graduates have the greatest difficulty in finding work. Finally, the results suggest that graduates who have international experience and those with expert knowledge of communication are more likely to obtain employment.