The restructuring of the quality assurance system of higher education in Kazakhstan is considered a condition for the formation of competitive human potential. The research interest of the authors of this article is aimed at the practice of organizing the internal quality assurance system as the first component of the three-dimensional model of the National Quality Assurance System, which also includes the external quality assurance system and mechanisms of management and regulation of the quality assurance system. The activity of Kazakhstani HEIs with orientation on the European Standards and Guidelines for Quality Assurance in Higher Education in the European Higher Education Area (ESG EHEA) is carried out through the activity of designing a system of measures, including planning, organization and implementation of the actual internal system of quality assurance, adequate to the features of the educational environment of the HEI. As a result of design activity, "author's" normative, organizational, personnel conditions of internal quality assurance systems are created. The purpose of our research was to analyze the practices of organization of internal quality assurance system by HEIs of Kazakhstan as a construct of the National Quality Assurance System. The study allowed us to identify the common and special in the organization of internal quality assurance systems in the context of the implementation of quality assurance methodology in higher education organizations, in the context of academic freedom.