Pulley device for a rotating machine comprising a pulley containing a plurality of axial ribs, a torque transmission means containing an axial sleeve intended to be installed on a rotating shaft of the rotating machine and a radial plate extending radially from the axial sleeve and comprising a plurality of regularly distributed radial teeth extending towards the outside, two adjacent teeth being separated in the circumferential direction by an indentation, and a damping element arranged between the said pulley and the torque transmission means.The damping element includes at least one damping portion arranged in each of the indentations of the radial plate, being situated circumferentially between a radial tooth of the torque transmission means and an axial rib of the pulley.