The higher education has been international for many years already. The focus now is on making the educational process more interesting, effective and resultative. The expected result largely depends on whether the purposes and the course content correlate with the educational demands of target audience. It is especially true for teaching foreign languages, in particular, Russian as a foreign language. Russia as well as the other countries accept many international students every year. The majority of them study in the Russian language, the language being the key component of their successful adaptation to the Russian educational environment. The article deals with the problem of teaching Russian as a foreign language to foreign post-graduates coming to study in Russia. The challenges they face in the Russian educational environment are caused by the specific characteristics of foreign post-graduates as the target audience. The 'specificity' is mostly caused by the professional experience they already have. A foreign post-graduate has to get accustomed to the new educational environment, which is often difficult due to the cultural and educational differences. For the short time, they have to grasp the basic grammar and vocabulary for everyday communication as well as professional vocabulary necessary for the communication with the colleagues in Russia. It influences the structure and the content of the language course making it both intensive and highly efficient, and the motivation to study in the Russian language. The purpose of the paper is to analyze these difficulties and to describe the ways of making the educational process for this target audience smooth and efficient. The authors study the teaching experience and the results of the survey conducted among the post-graduates during and after their pre-university language course at RUDN University. The authors of the article consider the research to be important as the number of post-graduates getting higher professional education in Russian universities is growing.