A torque transmission device for a motor vehicle, having a torque input element, a torque output element, and at least one pair of elastic members mounted between the torque input and output elements and counteracting rotation of input and output elements with respect to one another. The elastic members are arranged serially by means of a phasing member so that the elastic members deform in phase with one another. The stiffness K1 of the elastic member mounted between the torque input element and the phasing member is less than the stiffness K2 of the elastic member mounted between the phasing member and the torque output element, the ratio K2/K1 being equal to at least 2. One elastic member of the at least one pair of elastic members includes two coaxial helical springs mounted one inside the other.