A pulley device for a tensioner roller or winding roller for a transmission element, providing a bearing and a pulley. The pulley including two pulley elements that are C-shaped in axial section. At least one of the pulley elements has an axial through-opening, the other pulley element providing an axially protruding portion housed in the opening, a collar being formed by deformation of the protruding portion in order to provide axial retention with the opening. The at least one through-opening is provided at its periphery with at least one recessed zone formed in a substantially radially set-back manner with respect to the protrusion, which passes through the opening.