Non-native speakers of English seeking to undertake university study frequently take English for Academic Purposes courses in order to prepare to meet the language requirements for such study. Of necessity, such courses usually include a strong focus on the development of the writing skill. This paper proposes two conceptual elements as necessary to the design of a general EAP writing syllabus and its subsequent realisation as a course. The first is Widdowson's [Widdowson, H. G. (1983). "Learning purpose and language use." Oxford: Oxford University Press.] idea of "capacity" in relation to the development of a discourse competence in written English. The second element is Widdowson's [Widdowson, H. G. (1990). "Aspects of language teaching." Oxford: Oxford University Press.] approach to Wilkins' [Wilkins, D. (1976). Notional syllabuses: A taxonomy and its relevance to foreign language curriculum development. London: Oxford University Press.] "analytic syllabus" as the pedagogic vehicle by means of which such capacity may be developed. The paper then presents the non-discipline specific discourse unit of the "cognitive genre" as the most suitable organisational unit for an analytic syllabus for a general EAP writing course. This is then illustrated by examining a unit of an analytic syllabus based around a cognitive genre. (Contains 4 tables.)