A double damping flywheel comprises primary and secondary coaxial members. The members are rotatable relative to one another and coupled by first and second damping elements arranged in series by a connecting web. The first damping element includes at least one curved elastic member running circumferentially between two first seatings. The second damping element includes at least two groups of elastic members, each including at least two straight elastic members arranged in series by an intermediate bearing element. Each of the groups of straight elastic members runs circumferentially between two second seatings. An annular member for phasing the straight elastic members, separate from the connecting web, carries the intermediate bearing element of each group. The difference between the maximum angular displacement between the primary member and the connecting web, and the maximum angular displacement between the secondary member and the connecting web, is less than 30°.