The object of the invention is an aircraft nacelle that comprises at least one part, called a door (14), that moves relative to a stationary part (20) and a connecting device that makes it possible to limit the offset between said door and said stationary part in a direction that corresponds to the primary direction of the flow of air outside of the nacelle during flight, whereby said device comprises, on the one hand, an indexer (40) that is connected to the door (14) that comprises an attachment surface (63) and at least one attachment element (66), and, on the other hand, at least one stop (58) that is connected to the stationary part (20) against which said indexer (40) can rest in such a way as to limit its movement in said direction, characterized in that said at least one attachment element (66), oriented in the radial direction, is arranged upstream from the stop (58) in said direction, said at least one stop (58) comprising a surface relative to the door arranged essentially at the attachment surface (63) of the indexer (40).