Damping device combined with a suspension comprising a damper assembly , the interior of which contains a piston connected to a rod , wherein the piston and its associated rod are mobile both in compression and expansion around a static position within the damper assembly in order to perform a Damping action, wherein the interior of the damper assembly is filled with a hydraulic fluid, said damper assembly interacting with means of variation of the damping so as to produce: - a compression phase consisting respectively of a sub-phase of compression directed from the static position towards the maximum compression position of the piston and of a sub-phase of expansion directed from said maximum compression position towards the static position, and - an expansion phase consisting respectively of a sub-phase of expansion directed from the static position towards the maximum expansion position of the piston and of a sub-phase of compression directed from said maximum expansion position towards the static position, wherein the means of variation of the damping act on the damper assembly such the damping value of at least one among the sub-phase of compression of the compression phase and the sub-phase of expansion of the expansion phase is different from the damping value of, respectively, the sub-phase of expansion of the compression phase and the sub-phase of compression of the expansion phase, characterised in that the Damping device furthermore comprises an expansion module acting on the damper assembly in order to modify both the value of the rigidity of the suspension and that of the damping for the travel sector of the suspension ranging from the fully expanded position corresponding to the expansion phase; in that the damper assembly comprises a floating piston arranged on said rod between the piston and a first end of the assembly , wherein said floating piston is mobile along said rod and delimits a first internal chamber (c3) directed towards said first end in the damper assembly , and in that the damper assembly comprises a sealed separation arranged between the piston and the floating piston creating a second internal chamber (c2) between the floating piston and the separation , wherein the position of the floating piston influences the pressure of the hydraulic liquid in said second internal chamber (c2); in that a twin-tube architecture is implemented for the first and second internal chambers (c2, c3) in order to create a duct emerging via an orifice towards the expansion module , wherein driving of the floating piston by the through-rod between the static position and the fully expanded position expels from the second internal chamber (c2) a volume of oil operating the expansion module ; and in that the expansion module features an inlet port for passage of the hydraulic fluid expelled from the second internal chamber (c2) of the damper assembly, wherein inflow of said hydraulic fluid inside the expansion module activates a receiving piston, compressing via a connecting stop , a counteracting spring , wherein the expansion rate of the counteracting spring is controlled by a throttle damper controlling the expansion module . - a compression phase consisting respectively of a sub-phase of compression directed from the static position towards the maximum compression position of the piston and of a sub-phase of expansion directed from said maximum compression position towards the static position, and - an expansion phase consisting respectively of a sub-phase of expansion directed from the static position towards the maximum expansion position of the piston and of a sub-phase of compression directed from said maximum expansion position towards the static position, <EOS>