The political decision to convert to the system of multilevel professional training in the higher educational institutions of Russia has already been made and formalized in law. The system, a combination of the "bachelor's and master's" pattern and the "specialist" pattern is being adopted starting in 2009. However, in spite of the documents that have been adopted and the "voluntary" practice that has been in place for more than ten years, questions remain concerning the degree to which these changes are in demand and welcomed by society. On the conceptual plane, it is perfectly appropriate in this case to make use of the term "social demand." Social demand represents a heterogeneous phenomenon, and in order to determine what it is, a whole complex of measures are essential, which cannot, in any way, be reduced to nothing more than statistical methods of the study of the demand for cadres or for instruction in higher educational institutions of particular profile. In this article, the authors discuss the characteristics of the social demand for two-level professional training and present the views of potential consumers of educational services on the two-level system of training. The authors also present the opinions of master's degree candidates of higher educational institutions in Russia about the multilevel system in professional training. (Contains 5 tables and 3 figures.)