The study analyzes the post material values of the Y generation, which has developed in the conditions of the transversality of educational paradigms in Russia. The attention is drawn to the importance of social networks with horizontal communication. Another aspect is the growth of the digital technologies in the sphere of education. The post material values shared by teenagers make it difficult to motivate and stimulate them with a help of traditional means. The research is based on the modern theory of generations. The main provisions of the W. Strauss and N. Howe theory of generations, which are applied to the Russian problems of education, are described in the article. The authors agreed with the basic characteristics of generations "Y" and "Z". They are characterized in the article as the main actors of the modern educational process. The attention is paid to the basic difficulties encountered in teaching practice while working with these groups of young people. The researchers pay attention to the importance of the personal-oriented training in this situation, the need to use different models of education, the creation of a highly professional environment for the educational institutions, the significant increase of the humanitarian profile disciplines and the creation of individual educational routes, the applied baccalaureate system and etc. All these factors show the need of creating a fundamental theory that allows one to organize effective interaction with the young people.