Purpose: The purpose of this paper is to measure students' satisfaction with the didactics in a large Italian university, that of Padua, giving special attention to its evolution over time in consecutive academic years. The overall level of the quality of the didactics is examined and its change over time is modeled. Moreover, the effect of courses' and teachers' variables on it is estimated. Design/methodology/approach: Latent cluster class models and mixture latent class Markov models are estimated in order to identify groups of courses that are homogeneous for the level of the quality of the didactics. Evolution over the three academic years of satisfaction is monitored. The effect on the clustering and its dynamics of potential covariates is also examined. Findings: Results of model estimation reveal some interesting evidences that are important indications for the university management to define targeted strategies to elevate teaching quality. Originality/value: The paper gives its original contribution both on the side of methods applied to analyze data collected with students evaluation of teaching and on the evidences obtained for a large university.