We aim to investigate if men receive preferential treatment in promotions using the Italian system for the access to associate and full professor positions that is organized in two stages: first, candidates participate in a national wide competition to obtain the National Scientific Qualification (NSQ), then successful candidates compete to obtain a position in University Departments opening a vacancy. We investigate the probability of success in the two stages in relation to the candidate's gender, controlling for several measures of productivity and a number of individual, field and university characteristics. Whereas no gender differences emerge in the probability of obtaining the NSQ, females have a lower probability of promotion at the Department level. Gender gaps tend to be larger when the number of available positions shrink, consistent with a sort of social norm establishing that men are given priority over women when the number of positions is limited.