According to forecasts, the competitive struggle on the worldwide scale to attract foreign students is going to get more intense, as many countries see students as the most desirable category of migrants. The world market of educational services has been estimated at $50-60 billion. The economically developed countries, such as the United States, Switzerland, Great Britain, Germany, France, and others, are actively attracting students. Considering the present demographic situation, Russia could be doing more to take advantage of the migration potential of young people in the Commonwealth of Independent States [CIS] and the developing countries of Asia, Africa, and Latin America. The number of foreign students has fallen compared to the Soviet era; foreigners account for not more than 2% of the students and graduate students in the higher educational institutions of Russia. Foreign students' and graduate students' migrating to Russia for an education has quite a long history. The collapse of the Soviet Union in 1991 put an end to the system of training of foreign students that had become established. Although Russia has a long history of attracting foreign students to its universities, it needs to do more to increase their number as well as to attract more students from the countries of the former Soviet Union. (Contains 2 tables.)