To allow the attachment of an engine of the “Open Rotor Puller” type to the rigid structure of an attachment pylon, an attachment structure comprises a first attachment structure shifted forwards with respect to the center of gravity of the engine and connected to the rigid structure through a pyramid, a second attachment structure laid out at the rear with respect to the first attachment structure and extending in a plane of a first stringer of the rigid structure, and a third attachment structure laid out at the rear with respect to the second attachment structure. The second attachment structure comprises two engine attachments for recovering the moment along the axis of the engine, laid out on either side of a horizontal symmetry plane of the engine.