This set of roller bearings, which is a grounding bearing for a rotary machine, comprises a first-angular contact rolling bearing having a first outer race, a first inner race and first rolling elements, a second angular-contact rolling bearing having a second outer race, a second inner race and second rolling elements, a mount in which the first angular-contact rolling bearing and the second angular-contact rolling bearing are mounted. The first outer race and the second outer race are arranged in the mount either directly one beside the other or via the interposition of an intermediate member, the axial stiffness of which is greater than that of the mount and than those of the first and second outer races. Application for example to asynchronous motors.