A closing system for a compartment, in particular for a storage compartment or glove box of a motor vehicle; said system comprising: - a support structure in which a passage is defined; - an oscillating assembly co-operating with said support structure to define a container compartment; said oscillating assembly being hinged at said passage, so that it can be rotated between a pair of stable positions including: a closed position, in which said oscillating assembly closes said passage and is releasably coupled to said support structure, and a fully open position, in which said oscillating assembly opens said passage and allows full access to said compartment; and - a damping device configured for damping or slowing down the movement of said oscillating assembly in at least one predetermined tract of the travel from said closed position to said fully open position; wherein said damping device comprises: - a cam carried by said oscillating assembly and having an outer surface with an eccentric portion; and - a buffer made of elastically deformable material, mounted to said support structure and co-operating with said outer surface, wherein said buffer is housed in a seat located on the support structure; and in said predetermined tract, said eccentric portion pushes said buffer that exerts friction against said cam, thereby damping or slowing down the movement of said oscillating assembly; characterized in that said buffer is housed in said seat at an adjustable distance from an axis of rotation (X-X) of said cam; wherein said buffer comprises a head portion and a leg portion, wherein the head portion is wider than leg portion and is configured for coming in contact with the outer surface of the cam; the leg portion is configured for constraining the buffer to the seat for adjusting the position of the buffer relative to the axis of rotation (X-X) of the cam; wherein said seat has a through aperture through which the leg portion is inserted in an adjustable manner; wherein the leg portion has a plurality of locking portions spaced apart along its longitudinal or axial extension, by means of which it can be coupled to the through aperture by interference. - a support structure in which a passage is defined; - an oscillating assembly co-operating with said support structure to define a container compartment; said oscillating assembly being hinged at said passage, so that it can be rotated between a pair of stable positions including: a closed position, in which said oscillating assembly closes said passage and is releasably coupled to said support structure, and a fully open position, in which said oscillating assembly opens said passage and allows full access to said compartment; and a closed position, in which said oscillating assembly closes said passage and is releasably coupled to said support structure, and a fully open position, in which said oscillating assembly opens said passage and allows full access to said compartment; and - a damping device configured for damping or slowing down the movement of said oscillating assembly in at least one predetermined tract of the travel from said closed position to said fully open position; - a cam carried by said oscillating assembly and having an outer surface with an eccentric portion; and - a buffer made of elastically deformable material, mounted to said support structure and co-operating with said outer surface, wherein said buffer is housed in a seat located on the support structure; and