Based on the data obtained by the authors of the article in the framework of a analysis, held in the All-Russian Public Organization “Russian Professorial Assembly”, they define the problem of ensuring the quality of organizations’ activities, conducting professional and public accreditation in the higher education system. The authors describe typical mistakes in the activities of such organizations, as well as substantiate proposals for solving the problem of professional competence of such organizations.

The article raises the problem of ensuring the quality of evaluation tools for the procedures of independent assessment of the quality of university students’ training — first of all, in the aspect of the main scientific and methodological and, as a consequence, organizational reasons for the unresolved nature of this problem. The relevance of these procedures in connection with the introduction of a risk-based model of quality control of education in Russia is substantiated. It is shown that this uncertainty leads, on the one hand, to a reasonable distrust of the federal authorities in the field of education to the data of an independent assessment of the quality of training of university students and, on the other hand, to the unpopularity in the higher education system today of this procedure nationwide. The negative consequences of this situation are analyzed, in particular, the non-use of the state-public potential of the legislation that established this procedure, especially with regard to the objective assessment of the results of training in accordance with the requirements of federal state educational standards of higher education to the general cultural/universal and general professional competencies of students.