Except for some eliminativists, the notion of intentionality is considered to be one of the common goods of 20(th) century philosophy of mind. However, this rather general label may hide deeper differences. In his 'Husserl Memorial Lecture' Jocelyn Benoist investigates the different possible conceptions of intentionality and the problem of its nature. To examine this question he concurs with Wilfrid Sellars and John McDowell by positing an alternative between two conceptions of intentionality taken either as a relation or not. From this point of view he shows how Franz Brentano, who at the threshold of contemporary philosophy regained this notion, maintains a non-relational understanding of intentionality, whereas Husserl and McDowell up to a certain point adopt a relational conception - even though the formalism of relation might in fact not be the most appropriate to render the whole flavor of Husserl's position. The author wants to demonstrate that inside the conception, which rightly or wrongly is called relational, a new choice has to be made, depending on the moment actually assigned to this formalism of 'relations' and to the extent in which the 'relation' is taken for granted. Eventually, he intends to cone trast philosophies of two kinds: those which in the last resort rely on a concept of acquaintance, itself undiscussed, and those which convert intentionality into a means for describing the perpetual 'presence' while defining its problem.