A damping device for damping flexural vibration of a shaft rotating about a first axis, the device having: a supporting body; and a member, which defines an annular opening fitted through with the shaft, and is movable, with respect to the supporting body and radially with respect to the first axis, between a first and a second position when the shaft flexes radially with respect to the first axis. The member is set to the first position, and the opening is traversed loosely by the shaft when the rotation speed of the shaft is within a first range; the member is set to the second position, and the opening cooperates with the shaft, when the rotation speed of the shaft is within a second range differing from the first range and including at least one critical speed of the shaft; and the damping device has elastic means interposed between the supporting body and the member.