The production of knowledge is an essential element in graduate schools and it is considered that this process is very advanced when the student completes and defends his research thesis. However, a number of students fails to develop research skills and complete their thesis. The objective of this proposal is to specify the roles and competencies required by the postgraduate tutor to achieve accompaniment and mediation in postgraduate students, promoting the organization of university tutorship and scientific research. A proposal that allows the strengthening of the research competencies in postgraduate students by means of the tutorship is raised. The proposal is based on the integrating model of the tutorship developed by Cruz, García and Abreu (2006), aimed at tutors and students who are developing their research theses at the graduate school.