This paper presents an analysis of the efficiency of the University of Venice academic departments. The production of research and teaching is described by two interpretative models that impute in different ways the responsibility for the level of teaching activities. The empirical analysis is performed both with a Data Envelopment Analysis (DEA) and a Deterministic Frontier Analysis(DFA). The outputs used are indicators of the quantity and the quality of teaching and an indicator of fund raising for research, while the inputs are the budget and staff endowments. In the frontier production function approach the outputs are aggregated by means of a department utility function. The results obtained are quite different for the two interpretative models, both with respect to the level of efficiency and the ranking of departments.