The literature on quality management at higher education institutions has for some time been working on the basis of two issues: a) the diversity of ideas as to what "quality" means, which makes it harder to apply the principles of quality management in this context; and b) the idea that this diversity is in some way a response to the different positions occupied by stakeholders in regard to the processes and institutions of the sector. It has been suggested that students, employers, administrations in charge of funding and academics may hold different positions concerning the purposes of universities and, therefore, concerning the criteria on which their quality should be assessed. However, those stakeholders have rarely been asked directly what concept of quality they defend. This paper presents the results of a survey of deans of Spanish university faculties and schools in which this question was put to them. Their answers contrast with some of the commonplaces of current literature.