The aft stiffening frame of an air intake structure for an aircraft engine nacelle is made with an inflection area such that the part between the inflection area and one of its ends could be subjected to a large deformation when a constraint occurs in the direction of the frame part defined by the inflection area and its other end, usually normal to the casing. This particular shape of the aft stiffening frame makes it possible to improve its flexibility so that the air intake structure has better resistance to severe deformed shapes that could occur, for example, when a fan breaks on a wide body aircraft.