The articles considers teaching writing in the Russian and foreign languages to undergraduate, graduate and postgraduate students using the strategies of teaching Russian as a foreign language. The authors focus on the culture of written scientific speech, which, performing accumulative and transmitting functions, is complex but especially important for the formation and development of learners' personality. In terms of linguodidactics, state-of-the-art studies on the scientific style as one of the functional-speech varieties of the contemporary Russian literary language, are described. In the context of the discursive approach to teaching foreign languages, in the article special attention is focused on the genre approach and a genre in terms of the modern sociolinguistics. The article gives classical and modern definitions of scientific genres, highlights the main classification characteristics of a genre and the factors that organize a speech genre as a holistic expression. The article considers scientific genres from the analytical, functional and linguodidactic points of view. The relevance of forming genre competence of students at the bachelor's, master's and doctoral levels in the academic, scientific and professional spheres of communication is emphasized. The genre competence enabling mastering scientific genres is considered as the most important component of the professional communicative competence. Teaching written scientific genres is described as the highest priority teacher's task as a learner's mastering written scientific genres, in particular, is supposed to bring a student's success in research activity and to ensure a graduate's social growth in the future. Also, there are defined and described typical learning difficulties that students of non-linguistic faculties encounter at different stages of the genre skills development. The article proposes a conceptual solution to the problem taking into account a student's degree level and a field of study. Moreover, the possibility to adapt the proposed methodology to teaching foreign languages and the native language is discussed in the article. Based on the studies of wellknown researchers, to achieve the teaching goal, the authors of the article propose to use the method of modeling. The article reveals the conceptual and structural characteristics of a teaching model used in teaching the Russian and foreign languages. The proposed model of teaching is based on Bakhtin's theory of speech genres and contemporary cognitive investigations. The article articulates a number of notions associated with text and genre competences and discusses their introduction into the list of methodological terms. The terms are as follows: socio-cultural cogniotype and individual cogniotype of foreign students, graduate and postgraduate students; enhancement of individual cogniotype of foreign students, graduate and postgraduate students. The content of the individual cogniotype of foreign students is described in detail. The authors' interpretation of the characteristics of the individual cogniotype is given, its gradual formation is presented. An invariant part of the teaching model containing information on linguistic and extra linguistic characteristics of the scientific style makes the proposed concept interdisciplinary. Furthermore, the targeted selection of teaching materials can ensure taking into consideration students' field of study and level of study. The proposed methodology involves forming genre competence of foreign students while realizing a stylistic genre-based approach and a learner-centered approach to course and syllabus design. The methodology implies using typological models of scientific genres as a source of information about new genres. The model introduces a genre fully and allows learners to predict its specific features at the text drafting stage. The heart of the methodology is an intergenre model of a scientific text that is a normative, integrated, abstract and contour algorithm with verbal representation in genres taught and learnt at undergraduate, graduate and postgraduate levels of study. The characteristic features and advantages of the intergenre model are defined to underline its universal nature. The results of the comparative analysis of the intergenre model of the Russian scientific text and the intergenre model of the English scientific text demonstrating common and invariant components within the structure of some secondary and primary scientific genres in Russian and English are presented in the article. The advantages of the intergenre model over IMRaD approach to structuring a scientific article are proven. A wider range of applications of the model in the context of teaching Russian and foreign languages is supported by long-term teaching experience of the authors.