Damping system for closets with sliding doors comprising: - a damping device and an actuating element , wherein said damping device is to be fitted in an upper guide of a frame of a door and said actuating element is coupled to the door and comprises at least one projection configured for coming into contact with the damping device and reducing the closing speed thereof; and wherein the damping device comprises: - an oblong body in turn having a damping element, defining a longitudinal direction of the oblong body parallel to the upper guide of the frame of the door of the closet; and - a pair of respective supporting parts coupled to the ends of said oblong body , such that each supporting part has a rectangular base on which one of the ends of the oblong body is coupled and two pairs of flanges being located on the sides of the rectangular base of the supporting part itself, such that each pair of flanges is located respectively on the sides of the rectangular base of each supporting part , and in the direction parallel to the longitudinal direction of the oblong body , and said flanges being configured to allow the damping device to be secured in the upper guide of the closet itself as a result of the pressure of said flanges on side walls of the guide and to allow said damping device to be slid driven by the actuating element during the relative movement between both. - a damping device and an actuating element , wherein said damping device is to be fitted in an upper guide of a frame of a door and said actuating element is coupled to the door and comprises at least one projection configured for coming into contact with the damping device and reducing the closing speed thereof; and wherein the damping device comprises: - an oblong body in turn having a damping element, defining a longitudinal direction of the oblong body parallel to the upper guide of the frame of the door of the closet; and - a pair of respective supporting parts coupled to the ends of said oblong body , such that each supporting part has a rectangular base on which one of the ends of the oblong body is coupled and two pairs of flanges being located on the sides of the rectangular base of the supporting part itself, such that each pair of flanges is located respectively on the sides of the rectangular base of each supporting part , and in the direction parallel to the longitudinal direction of the oblong body , and said flanges being configured to allow the damping device to be secured in the upper guide of the closet itself as a result of the pressure of said flanges on side walls of the guide and to allow said damping device to be slid driven by the actuating element during the relative movement between both. - an oblong body in turn having a damping element, defining a longitudinal direction of the oblong body parallel to the upper guide of the frame of the door of the closet; and - a pair of respective supporting parts coupled to the ends of said oblong body , such that each supporting part has a rectangular base on which one of the ends of the oblong body is coupled and two pairs of flanges being located on the sides of the rectangular base of the supporting part itself, such that each pair of flanges is located respectively on the sides of the rectangular base of each supporting part , and in the direction parallel to the longitudinal direction of the oblong body , and said flanges being configured to allow the damping device to be secured in the upper guide of the closet itself as a result of the pressure of said flanges on side walls of the guide and to allow said damping device to be slid driven by the actuating element during the relative movement between both. <EOS>