This invention relates to a mounting system (100) inserted between an aircraft engine (2) and a rigid structure (4) of an attachment strut (6) fixed under a wing (8) of this aircraft, the system including a forward mount (16), an aft mount (18) and a device (20, 120, 220) for resisting thrusts generated by the engine (2). The system also comprises additional means (23) for opposing the longitudinal bending of the engine (2), these additional means (23) being designed to resist loads only starting from a predetermined deformation of this engine (2). According to the invention, the additional means (23) comprise at least one connecting rod (32) capable of opposing longitudinal bending of the engine (2), each connecting rod (32) being connected firstly to the rigid structure (4) of the strut (6) and secondly to a fan casing (26) of the engine (2), so that it is only stressed starting from the predetermined deformation of this engine (2).