The article considers the problem of forming and developing master’s students scientific communication skills in the Russian and foreign languages. The authors focus on the culture of written scientific speech, performing accumulative and transmitting functions, which is complex, but is especially important for cultivating and developing learners’ personality. The topicality of forming and enhancing genre competence as an important component of professional communicative competence is emphasized in the article. The authors propose courses for students in order to develop the competences at master level. The courses “Scientific Speech for postgraduate students” in Russian and “Foreign language (English)” are designed in accordance with learners’ communicative and activity needs and the requirements of the Federal State Educational Standard of Higher Education. The principles being methodological basis of the course are described. The content and topics to study in the framework of the courses are given in detail. The methodology used involves the use of typological models of scientific genres and Intergenre Model of Scientific Text that includes invariant and universal components corresponding to the stages of communicative and cognitive activity of a scientist: case - problem - idea - hypothesis - argument - conclusion. The results of an experimental course teaching are presented. The effectiveness of the proposed methodology is confirmed.