A torque transmission device for a motor vehicle includes a torque input element for coupling to a driving shaft, a torque output element for coupling to an input shaft of a gearbox, the torque output element and the torque input element pivotable with respect to one another, and first and second elastic damping stages installed in series between the torque input element and torque output element. The first damping stage has an elastic member installed between the torque input element and a guidance device so as to act against the rotation of the guidance device with respect to the torque input element. The second damping stage has at least one elastic member installed between the guidance device and the torque output element so as to act against the rotation of the torque output element with respect to the guidance device. The guidance device has first and second stop means.