One of Guattari's most important conceptual contributions is his notion of transversality. This complex notion responds to the very concrete problem that, when we oppose certain power formations, we tend to reproduce these same power formations. This article proposes an examination of Guattari's concept of transversality through five of its aspects, which will be related to the various problematics they respond to. The aim is to show how power formations operate and how transversality responds to them, and also to highlight (...) the primordial importance of practical and political issues to Guattari's conceptual work. As we will see, Guattari conceived of transversality in relation to the Leninist cut; it thus is linked to democratic centralism and to the subject-group. Transversality is also linked to enunciation and autopoiesis; it is characterised by Guattari as transmonadic and transitive. The notion of transversality will also be put in relation to the war machine, on which it will thus shed light. (shrink)