A torsional vibration attenuation apparatus, comprising: a drive rotation member (12, 13), a driven rotation member provided in coaxial relationship with the drive rotation member (12, 13) and relatively rotatable with respect to the drive rotation member, and a first resilient member and a second resilient member respectively having the drive rotation member and the driven rotation member relatively rotatably connected with each other, the first resilient member and the second resilient member being deformable in parallel when the driven rotation member is twisted in a positive side opposite to the rotational direction of the drive rotation member with respect to the drive rotation member (12, 13), the first resilient member and the second resilient member being deformable in series in an order of the first resilient member and the second resilient member when the driven rotation member is twisted in a negative side the same in direction to the rotational direction of the drive rotation member (12, 13) with respect to the drive rotation member (12, 13), an intermediate rotation member relatively rotatably provided on the driven rotation member in a predetermined torsion angular range, a third resilient member having a spring constant lower than the spring constant of each of the first resilient member and the second resilient member to have the intermediate rotation member and the driven rotation member relatively rotatably connected with each other, and an urging member provided on the drive rotation member (12, 13), the intermediate rotation member being constructed to be relatively rotatable with respect to the driven rotation member in the states in which the first resilient member and the second resilient member are not resiliently deformed and in which the driven rotation member is twisted in the negative side, the torsional vibration attenuation apparatus characterized in that the urging member being adapted to urge the intermediate rotation member from the negative side to the positive side to have the torsion angle between the intermediate rotation member and the driven rotation member increased in the state in which the driven rotation member is twisted in the negative side. a drive rotation member (12, 13), a driven rotation member provided in coaxial relationship with the drive rotation member (12, 13) and relatively rotatable with respect to the drive rotation member, and a first resilient member and a second resilient member respectively having the drive rotation member and the driven rotation member relatively rotatably connected with each other, the first resilient member and the second resilient member being deformable in parallel when the driven rotation member is twisted in a positive side opposite to the rotational direction of the drive rotation member with respect to the drive rotation member (12, 13), the first resilient member and the second resilient member being deformable in series in an order of the first resilient member and the second resilient member when the driven rotation member is twisted in a negative side the same in direction to the rotational direction of the drive rotation member (12, 13) with respect to the drive rotation member (12, 13), an intermediate rotation member relatively rotatably provided on the driven rotation member in a predetermined torsion angular range, a third resilient member having a spring constant lower than the spring constant of each of the first resilient member and the second resilient member to have the intermediate rotation member and the driven rotation member relatively rotatably connected with each other, and an urging member provided on the drive rotation member (12, 13), the intermediate rotation member being constructed to be relatively rotatable with respect to the driven rotation member in the states in which the first resilient member and the second resilient member are not resiliently deformed and in which the driven rotation member is twisted in the negative side, the torsional vibration attenuation apparatus characterized in that the urging member being adapted to urge the intermediate rotation member from the negative side to the positive side to have the torsion angle between the intermediate rotation member and the driven rotation member increased in the state in which the driven rotation member is twisted in the negative side.