This paper addresses the issue of the development of learners’ writing skills in the sphere of writing scientific discourse. The author 1) gives the definition to the term discourse and 2) considers scientific discourse from many angles. Within the framework of teaching scientific discourse to post-graduate students the following writing skills should be developed: writing abstracts, reports, reviews, scientific reports, academic papers, monographs, dissertations, grant proposals, proposals for participation in academic conferences as well as making presentations and posters.