The article is devoted to the consideration of Master’s degree programmes as an institution of higher professional education. A brief historical overview of the 2nd level of tertiary education development in Russia made it possible to trace how the concept of master’s programme, its goals and objectives have changed, and what caused these changes. The purpose of our study is to determine the development trends in the modern programmes in Russian university; to track compliance with the stated goals and the results obtained; to determine, at the theoretical level, "gaps" in the organization and content of training drawing on surveys of students, teachers, heads of master's programmes and employers; to suggest possible ways for improvement of the current situation. The materials used to study the concept of the master's programme as the second stage of multilevel training and its current trends are as follows: the Federal State Educational Standards, statistical collections of the data "Education in Numbers". The empirical foundation of the study was formed on the basis of local reports of the heads of master's educational programmes, as well as a survey of students in undergraduate and graduate programmes in order to determine their motives for continuing their education in the magistracy after the bachelor's degree. In conclusion, there have been proposed some measures, which, according to the author, allow to customize the work on modernization of master's programmes and education in general. The major recommendations are: organization of preliminary diagnostic procedures for applicants to Master’s degree programmes; engagement of employers as experts that will strengthen the practical value of the educational process; multi-variability of organizational forms of education to improve the quality of the educational process and, as a result, to keep graduate students from withdrawal.