Argument construction is an important aspect of academic writing. Although literature presents a number of theoretical and pedagogical models of argument, research is lacking into authentic argument construction in expert writing. Moreover, it is not clear how disciplinary variation affects the construction of argument. Therefore, this paper analyses argument in four disciplines -philosophy, literature, chemistry, and computational science. The results show a degree of variation among disciplines. Three models of argument have been found, called here premise-based argument (found in philosophy and literature), hypothesis-based argument (found in computational science and to a lesser degree in literature) and exposition-based argument (in chemistry). These models differ from the theoretical and/or pedagogical models proposed in the literature, suggesting that EAP students might be asked to produce arguments very different from arguments encountered in the reading in their discipline. Given the disciplinary variation observed, the paper supports applying English for Specific Academic Purposes (ESAP) as well as English for General Academic Purposes (EGAP) approach to teaching argument construction.