A damping device for damping speed irregularities of a rotating shaft includes an armature having at least one armature part made of a non-ferromagnetic, electrically conductive material. An exciter configured to permeate the armature part in at least some regions with a magnetic flux. The armature, together with the at least one armature part, is movably supported relative to the exciter, transversely to the direction of the magnetic flux. In one region permeated by the magnetic flux in a position of normal use, the armature part has at least one opening in which a ferromagnetic flux-guide member is located.