Abstract. Works on temporal relations between two eventualities e1 and e2 always suppose that e1 = e2. We will concentrate on cases where e1 = e2, i.e. on event coreference. Unlike object coreference, event coreference has rarely been studied in detail, except for (pro)nominal phrases referring to an event. We focus here on event coreference between two sentences. This study will put forward unusual linguistic phenomena, e.g. coreference between existentially quantified elements. These phenomena, which question well-established myths, have to be taken into account in text understanding and text generation. They will lead us to introduce and define new discourse relations which will be discussed in the framework of SDRT.