To increase a compactness of damping systems intended to operate in the event of a dynamic landing of an aircraft, a damping system comprises a primary damper device and a secondary damper device. The primary damper device comprises at least one beam, each beam extending along a direction of a longitudinal axis. The damping system is configured so that at rest, the primary damper device has a stiffness greater than a stiffness of the secondary damper device in the direction of the longitudinal axis. When a force is applied to the damping system along the direction of the longitudinal axis, with a value less than a limit value, each beam remains in a compression state. When the force applied has a value greater than or equal to the limit value, each beam undergoes buckling and the secondary damper device undergoes elastic deformation.