Abstract
This article discusses changes happening in higher education systems of the Russian Federation and the Republic of Kazakhstan namely diversification, democratization, globalization and regionalization of education, as well as the main directions of modernization of these systems according to the Bologna Declaration: increased access to the European education, improving the quality of higher education, introducing comprehensible, comparable qualifications in higher education, introducing assessment of study attainment and performance in terms of credit points, inclusion of the curriculum in the diploma supplement, the increased mobility of students, teachers and administrative staff.The article also deals with the problems of higher education in the Russian Federation and the Republic of Kazakhstan, and analyzes competency-based approach to the construction of the educational process in higher education, and comments on the shortcomings of the competency-based approach.It also covers the basics of active and interactive learning technologies and methods for the diagnosis and assessment of learning outcomes (NPS -technology of assessment of the quality of learning outcomes, the system of expert assessments and the method of calculating Spearman's rank correlation coefficient).