For the efficient formation of grammar skills in the target language appears to be an important solution to the problem of selection and organization of grammatical material. The article describes a system of exercises for forming grammatical competence foreign students studying Russian language in non-linguistic environment. A system of exercises is based on linguistic, psycholinguistic, didactic and teaching factors that influence the effectiveness of teaching Russian grammar to foreign learners. The authors propose a classification of exercises built on multicode texts. Multicode texts serve as a means of communication, they reflect the worldview, values, ethical ideals of representatives of other culture, in connection with which such texts allow us to form not only grammatical, but also linguosociocultural competence.