The article analyses the system of institutional quality assessment at universities and lays foundation to its functional, morphological and processual parameters. It also presents the concept of the system and discusses the distribution of systems into groups, defines information, accountability, improvement and benchmarking functions of higher education quality assessment system at universities. The discussion of morphological parameters of this system presents the assessing sub-system and the assessed sub-system. It also presents the functional environment of the quality assessment system at universities. (Contains 5 figures.)