Teaching foreign students of non-philological specialties grammar is one of the most complex and urgent problems of modern methodology, firstly, due to its key role in Russian speech and the entire strategy of communicative teaching Russian as a foreign language; secondly, due to the fact that the process of mastering the gram- matical structure of Russian is time-demanding. This is revealed in the amount of study time for learning Russian grammar, the selection, organization and introduc- tion of language materials, the specific formation and development of grammatical (language and speech) skills in various types of speech activity. The humaniza- tion and humanitarization of education, achievements in the study of “language personality”, the developed personality-oriented approach to teaching Russian as a foreign language, the use of linguistic and cognitive approaches to analyzing foreign speech allow reconsidering the problem of teaching foreign students of non-philological specialties grammar in accordance with the gradual formation of a secondary language personality in the process of mastering the basic grammatical structure of Russian speech. This article aims to create and substantiate methods of teaching foreign students the grammatical structure of the Russian language based on the systematic-functional approach to the study of language units and succes- sive links among different stages of education in pre-university courses. The paper considers the dynamic and gradual formation of the basic grammatical system of Russian speech by foreign students of non-philological specialties in accordance with the linguistic and methodological model of learning developed by the authors of the article. The latter is compared with traditional methods of teaching Russian as a foreign language in pre-university courses of a non-linguistic institution of higher education.