Torsion damping device intended to be connected to an internal combustion engine, this device comprising at least one first pendulum flyweight with periodic oscillation mounted movably on a support which can rotate about an axis, and at least two rolling elements (12, 14), each of them being in rolling contact with a path (31, 131, 32, 132) on an edge integral with the first flyweight on the one hand and with a path (41, 141, 42, 142) on an edge of the support on the other hand, each of these paths comprising at least two contiguous sub-paths (31, 131, 41, 141, 32, 132, 42, 142) on either side of a junction point (A1, D1, A2, D2), respectively to the left and to the right of this junction point, the two sub-paths of one and the same path being non-symmetrical; characterized in that: - the two left sub-paths (131, 132) on the edges integral with the first flyweight are superposable in pairs by translation and/or rotation about the axis; - the two right sub-paths (31, 32) on the edges integral with the first flyweight are superposable in pairs by translation and/or rotation about the axis; - the two left sub-paths (41, 42) on the edges of the support are superposable in pairs by translation and/or rotation about the axis; - the two right sub-paths (141, 142) on the edges of the support are superposable in pairs by translation and/or rotation about the axis; - the two left sub-paths (131, 132) on the edges integral with the first flyweight and the two right sub-paths (141, 142) on the edges of the support are configured to damp the torsion vibrations corresponding, for a given speed of rotation of the support, to a first periodic excitation function in torsion generated by the engine during a first sub-period of each engine period, - the two right sub-paths (31, 32) on the edges integral with the first flyweight and the two left sub-paths (41, 42) on the edges of the support are configured to damp the torsion vibrations corresponding, for the same speed of rotation of the support, to a second periodic excitation function in torsion generated by the engine during a second sub-period of each engine period, adjacent to the first sub-period, the first and the second periodic function having different periods for the same speed of rotation of the support. - the two left sub-paths (131, 132) on the edges integral with the first flyweight are superposable in pairs by translation and/or rotation about the axis; - the two right sub-paths (31, 32) on the edges integral with the first flyweight are superposable in pairs by translation and/or rotation about the axis; - the two left sub-paths (41, 42) on the edges of the support are superposable in pairs by translation and/or rotation about the axis; - the two right sub-paths (141, 142) on the edges of the support are superposable in pairs by translation and/or rotation about the axis; - the two left sub-paths (131, 132) on the edges integral with the first flyweight and the two right sub-paths (141, 142) on the edges of the support are configured to damp the torsion vibrations corresponding, for a given speed of rotation of the support, to a first periodic excitation function in torsion generated by the engine during a first sub-period of each engine period, - the two right sub-paths (31, 32) on the edges integral with the first flyweight and the two left sub-paths (41, 42) on the edges of the support are configured to damp the torsion vibrations corresponding, for the same speed of rotation of the support, to a second periodic excitation function in torsion generated by the engine during a second sub-period of each engine period, adjacent to the first sub-period, the first and the second periodic function having different periods for the same speed of rotation of the support.