This paper exposes firstly Deleuze’s reading of Bergson’s critique of the notion of possibility. In this reading Deleuze emphasizes and formulates a complex theory of virtuality, according to which what really happens is not previously given as only possible (and as such identical to the real), but, before becoming actual, is already real, virtual and different from the real that precedes it. Deleuze explains this process through the notions of repetition, Idea and Event. Secondly the paper deals with Badiou’s critique of this Deleuzian ontology because of its emphasizing the becoming as a continuous to the detriment of the strong specificity of the event. In fact, Badiou develops an original and powerful ontology that gives an account for such specificity. In their explanation of the event both Deleuze and Badiou refuse the notion of possibility. But while the former conceives the event as a result of the continuous becoming, the latter understands it as breakup of such becoming.