This article is about the observation of a French institute of high education, the one of University of the French West Indies and Guiana. This institute is based in the American-Caribbean area and composed of three universities, based on three different French territories: Guiana, Guadeloupe and Martinique. The reflection concerns a discourses’ corpus within training in Master’s degree (MA, MS/MSc), that is also specific to the European higher education system. The discursive exploitation refers to the analysis of both the results of assessments that students obtained during the period 2009-2013 and the discourses of students and academics that intervene in the Master. The reflection enables to apprehend the uneasiness resulting of the gap between the ideal expected profile and the actual profile of the student in postgraduate training. Face this fact, we hypothesize that failures and even the lack of certain knowledge that appears at the necessary prerequisites to the two years of Master undertaken. The fact remains that in terms of results, various verbal reactions proceeding of the students’ language practice from one year to another, between 2009 and 2012, converge towards a same discourse namely that the operated investments, then the efforts realized have a low and even an absence of impact on the respective learning paths but also on the results obtained at the end of the assessments. Moreover, this discourse is not specific to the students that obtained the more disappointing results and therefore are referred. Actually, it is also the discourse of the students that are admitted. This can be explained by the fact that, indeed, notes given are beyond 10/20, the average note; however they are closed to it. This implies a success that appears very modest compared to the excellence expected.