This article analyzes problems relating to the effectiveness and the quality of the training of graduate students specializing in the area of the social sciences and the humanities. In order to ensure greater objectivity, account is taken of the opinions not only of humanities experts but also of representatives of the natural science disciplines. A total of 657 experts from 32 towns of Russia were surveyed; they included 412 representatives of the natural sciences and technical branches (63 percent), and 245 representatives of the bloc of the sociohumanities disciplines (37 percent), among which there were 36 doctors of science specializing in sociology. The respondents' place of employment was distributed as follows: 53 percent in classical universities; 19 percent in technical and technological universities; 20 percent in other institutions of higher learning; and 8 percent in institutes of the Russian Academy of Sciences. The data obtained from the study provide evidence that the scientific pedagogical community is not satisfied with the existing practice of evaluating the effectiveness of graduate programs. Basic conclusions from the study are also presented. (Contains 3 tables and 1 note.)