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The article clarifies the scientific basis of monitoring the quality of education on the basis of diagnostic and competence understanding of the possibilities of systematic research of this process in general secondary education institutions. The analysis of sources and publications made it possible to identify the importance of the problem of monitoring the quality of education for the theory of management of general secondary and higher education, considering this category as political, managerial, pedagogical. Clarification of the leading characteristics of the quality of education (multifaceted, multilevel end results, polychronicity, multi-subjectivity, multi-criteria, uncertainty in assessments, invariance and variability) in the works of Ukrainian and foreign authors led to the goal - outlining in research the scientific basis of quality monitoring on the basis of diagnostic-competence understanding of the possibilities of systematic research of this process in the institutions of general secondary school. The functions of monitoring the quality of education are characterized: activating, informational, corrective, formative, diagnostic and analytical, modeling and management, prognostic; the algorithm of their realization offered by T. Lukina and A. Belkin is chosen. The diagnostic and competence specifics of control methods in the system of quality monitoring of general secondary education are determined. One of the management tools and elements of the system is defined as quality monitoring, which is recommended to be understood as "supervision, tracking, observation; testing or measurement at specified time intervals to control and regulate processes" has the status of a study rather than an empirical collection of material, and is complex, systemic in nature. The conclusion on specificity of quality control of education which provides: check - revealing of a condition of formation of components of competence is carried out; assessment - measurement and conditional reflection of this condition in the form of a level of quantitative or qualitative assessment; accounting - recording results in the form of summary tables. It is recommended to reflect the process of education quality assessment in a certain scale, which systematically takes into account the data obtained during the current assessment, testing, performance of tests and practical tasks, exams, ranking, etc. [ABSTRACT FROM AUTHOR]