The responsibility of the university is analyzed in this empirical article, where the starting points are exposed, the conceptual transitions that have led, among others, to the incursion of university social responsibility (hereinafter RSU) in the management model and specifically of social projection. Studies of governmentality represent the methodological approach of this work, with which aspects related to political rationality, meaning and purposes of this type of discourse in the context of higher education are critically analyzed. The results of the work show that around the concept of responsibility, there are other categories that are important to analyze, such as the concept of university, university models and the dimension of a political and ethical responsibility of higher education. By way of conclusion, important epistemological references are exposed that allow expanding the analysis of this problem, which can serve as arguments that resist the incursion of neoliberal policies in the management of the university, which give, among others, a preponderant place to the market. and competition, an issue that should not be ignored or excluded, but that necessarily deserves constant reflection. Keywords: University; higher education; responsibility; government; university social responsibility.