Academic writing is pertinent to postgraduate students because it is mandatory for them to write a research thesis as part of their degree programme. However, sometimes the theses that postgraduate students write do not communicate well or depict their professionalism. One of the problems these students face, as they write, is appropriate use of discourse markers. Discourse markers, when used appropriately, enhance coherence and signal the presence of particular relationships among text elements. They are also crucial tools for achieving communicative act in the text because they guide and influence the text-receivers’ interpretation of the text. To evaluate how postgraduate students in Kenya use discourse markers in their writing, as speakers of English as a second language, this paper analyzed the discourse markers in the literature review section of all the PhD theses deposited at JOOUST library. If postgraduate students use Discourse markers effectively, especially in the literature review section of their theses, this could help guard against plagiarism because their voices as writers will be forcefully brought out. Basing on Fraser’s taxonomy the study identified different hierarchies of discourse markers though elaborative and inferential markers were the most frequent types. The study also suggested how some of the discourse markers identified could be used to bring out the writer’s voice so as to guard against plagiarism.