The aim of this paper is to describe and analyse the disputational practices of science in medieval universities and studia during the thirteenth century, as well as to understand the connection of these practices to theories of scientific argumentation. It addresses the puzzle of the coexistence of a demonstrative, axiomatic theory of scientific knowledge and a disputational practice of science. The paper first sketches the two contradictory approaches one can find in Aristotle about the relationship to be established between scientific and disputational argumentations. Second, it offers a quick reminder of the important morphological and logical differences to be observed between Aristotelian disputations, be they dialectical or didactic, and medieval university disputations. This point leads to explaining the new categories we would like to introduce for a typology of medieval university disputations of science. Finally, it mainly presents Kilwardby’s views on Aristotelian disputations. I, then, consider the bridges one can try to build between epistemological theories and actual practices of science.