An oscillating damping system for a backrest of an item of seating furniture, wherein the item of furniture includes a seat and the backrest; wherein the oscillating damping system allows an independent movement of the backrest with respect to the seat and wherein the oscillating damping system comprises - a spring element, a base structure attachable to the seat and a support structure attachable to the backrest; wherein the support structure is coupled to the base structure by means of an articulated connection; - the support structure comprises a transverse shaft and an intermediate body; wherein said transverse shaft articulates in the base structure; wherein end parts of the transverse shaft are configured to be attached to armrests that form part of the backrest; and wherein the intermediate body extends in a direction perpendicular to the transverse shaft; wherein the spring element is inserted between the intermediate body and the base structure; - the mechanical tension of which spring element is configured to push the intermediate body with the tendency to tilt the backrest towards a resting position; wherein the opposite ends of the spring element are in contact with the intermediate body and the base structure; and - the oscillating damping system is configured such that, in a first direction of rotation, the backrest tilts against the resistance of the spring element, and in a second direction of rotation, opposite to the first direction of rotation, the backrest tilts driven by the mechanical stress accumulated in the spring element towards the resting position; wherein the oscillating damping system comprises a securing device that is configured to secure the intermediate body of the support structure to the base structure; and wherein the securing device comprises a threaded extension attached to the base structure and a nut that threads onto an end section of said threaded extension; wherein the intermediate body includes a groove in which the threaded extension is fitted; and wherein the intermediate body includes two opposite faces: a first face that is in contact with one of the ends of the spring element and a second face that is in contact with the nut when the backrest is in the resting position. wherein the item of furniture includes a seat and the backrest; wherein the oscillating damping system allows an independent movement of the backrest with respect to the seat and wherein the oscillating damping system comprises - a spring element, a base structure attachable to the seat and a support structure attachable to the backrest; wherein the support structure is coupled to the base structure by means of an articulated connection; - the support structure comprises a transverse shaft and an intermediate body; wherein said transverse shaft articulates in the base structure; - a spring element, a base structure attachable to the seat and a support structure attachable to the backrest; wherein the support structure is coupled to the base structure by means of an articulated connection; - the support structure comprises a transverse shaft and an intermediate body; wherein said transverse shaft articulates in the base structure; wherein end parts of the transverse shaft are configured to be attached to armrests that form part of the backrest; and wherein the intermediate body extends in a direction perpendicular to the transverse shaft; wherein the spring element is inserted between the intermediate body and the base structure; - the mechanical tension of which spring element is configured to push the intermediate body with the tendency to tilt the backrest towards a resting position; wherein the opposite ends of the spring element are in contact with the intermediate body and the base structure; and - the oscillating damping system is configured such that, in a first direction of rotation, the backrest tilts against the resistance of the spring element, and in a second direction of rotation, opposite to the first direction of rotation, the backrest tilts driven by the mechanical stress accumulated in the spring element towards the resting position; - the mechanical tension of which spring element is configured to push the intermediate body with the tendency to tilt the backrest towards a resting position; wherein the opposite ends of the spring element are in contact with the intermediate body and the base structure; and - the oscillating damping system is configured such that, in a first direction of rotation, the backrest tilts against the resistance of the spring element, and in a second direction of rotation, opposite to the first direction of rotation, the backrest tilts driven by the mechanical stress accumulated in the spring element towards the resting position; wherein the oscillating damping system comprises a securing device that is configured to secure the intermediate body of the support structure to the base structure; and wherein the securing device comprises a threaded extension attached to the base structure and a nut that threads onto an end section of said threaded extension; wherein the intermediate body includes a groove in which the threaded extension is fitted; and wherein the intermediate body includes two opposite faces: a first face that is in contact with one of the ends of the spring element and a second face that is in contact with the nut when the backrest is in the resting position.