Universities are trying to provide material, physical and human resources to enable them to meet the three functions established by national and international organizations in different national meetings: teaching; research, which involves the production, dissemination and socialization of knowledge; and outreach as a form of communication between universities and society, whether through the dissemination and development of culture or social programs that generate social projection. However, although there has been a preponderance of efforts to improve the conditions of higher education, the demands that the university community, and in particular the professors, must meet are such that it is difficult to do so completely. Therefore, the purpose of this qualitative study with narrative biographical method was to approach, through interviews, the tasks performed by graduate professors. From the analysis performed with Atlas.ti, it was found that the diversity of tasks performed by these professors is due to a characterization of teachers proposed in this work. It is concluded that the tasks performed by professors go beyond the depth of the three functions indicated at the beginning; there are other responsibilities that should be included in the professional identity of graduate professors.