The article focuses on the problems of modern higher education in Ukraine and the EU. A special attention is paid to issues of the mechanisms for internal Quality Assurance of education and for increase of the role of the humanities inboth Ukraine and the EU. As such mechanisms are considered international cooperation and social partnership inhigher education. The paper describes the positive experience ofrealization of international cooperation and social partnership in Taras Shevchenko National University of Kyiv in the framework of the HESDeSPI project (2010-2013), the participants of which were European universities (Armenia, Georgia, Italy,Latvia, Moldova, Portugal, Ukraine), employers from Kyiv and Simferopol, government, public and administrative agents (especially Ministry of Education and Science of Ukraine and Ministries of partner countries), and students. Special attention is given to the tasks of the project, the stage of its implementation and the results, which had a significant impact on the formation of curricula for bachelors of cultural studies (2011) and masters of cultural studies (2015) at the Faculty of Philosophy of the Kyiv University. These mechanisms helped project-team first of all to determine the set of professional competences of bachelors of cultural studies and masters of cultural studies, and then to form these professional competencies of students in the educational process. Thus, it can be argued that the mechanisms of international cooperation and social partnership allow the exchange of experience in the modernization and reform of the higher education system with the EU universities, provide staff mobility in order to exchange teaching and scientific experience, provide information on the labor market in the cultural sector, help to introduce new academic disciplines and progressive teaching methods, organize training and practices. These actions allow graduates to be ready to the demands of the labor marketand allow our higher education to meet the high quality standards of the European Higher Education Area.