The invention relates to a damping device of a mechanical tensioning system (1, 1') for a traction mechanism drive, for example of a motor vehicle, for damping pivoting movements of a tensioning arm (2) which is supported at one end via a tensioning roller on a traction mechanism and which is rotatably mounted at the other end on a positionally fixed housing part (3), having an annular friction element (8, 8'), the periphery of which is formed as a friction lining (9, 9') which, to generate a friction torque, interacts with a friction surface (15) of the housing part (3) which surrounds the friction element (8, 8'), wherein a torsional spring (11, 11') which connects the housing part (3) and the tensioning arm (2) in terms of rotational force, which is embodied as a coil spring and by means of which the tensioning arm (2) can be acted on with a torsional moment so as to generate a continuous preload of the traction mechanism is supported on the friction element (8, 8') and exerts a radially outwardly acting force on the friction lining (9, 9'). In order that the damping device has a high level of operational reliability and load capacity and a long service life and is neverthelessof structurally simple and cost-effective design, surface contact means (14, 24) which act on the friction lining (9, 9') are provided for the transmission of the radial force between the torsional spring (11, 11') and the friction lining (9, 9').