The paper describes the view of Kazakhstan scholars on actual challenges of Higher Education. The authors investigate such vital aspect as students and faculty academic mobility. This action is known in the sphere of sociologists as “intellectual migration”. Particular attention is paid to double-diploma education and problems which are connected to the realization of the state education program in the Republic of Kazakhstan. In addition, the researchers deal with the discrepancy of legal norms of higher education and degree recognition in the post-soviet area. The authors adhere to the conception of intellectual migration viewed as Conception of knowledge and experience exchange, so called “brain exchange”. This conception explains migration as a need for searching the place for employment with taking into account the professional qualification. The next one is the conception of “brain waste” (brain drain). This conception is based on the intellectual migration as a loss of labor force of a exporter country. The reasons of intellectual migration are based on the possibilities of getting additional experience and having a good job which is not available in the home country. Nowadays, Kazakhstan has two forms of double-diploma education. The first one is Double Major when students have an opportunity to study two parallel educational programs and finally obtain two equally recognized diplomas. The second form is Major-Minor when a student gets one main diploma and an additional one. The paper also comprises problems of double-diploma program realization in post-soviet union area; for instance, master programs in Kazakhstan are referred to post graduate education; however, in Russia and Belarus it’s a level of higher education. In comparison with Kazakhstan the preparation of scientific staff in Russia is held in Aspirantura and Doctorantura. Moreover, the authors describe the problems of candidate and doctor degree recognition. They also suggest considering the use of distance learning technologies as a part of successful double-diploma programs realization. The usage of distance learning technologies is popular all over the world. However, Kazakhstani sphere of Higher Education does not implement these programs in educational process properly. Brief summary and suggestions are written in the conclusion.