A device for centering and guiding a shaft of an aircraft turbine engines. The device includes an outer ring of a rolling bearing, the ring extending about a main axis and having orifices arranged around the axis axis; an annular bearing support extending about the main axis and at least partially about the ring, the support having orifices and openings arranged about the axis; and a series of studs for linking the ring to the support, the studs being distributed about the main axis and having elongation axes substantially parallel to the main axis, the body of each of the studs passing through one of the openings. Some of the studs, have bodies that pass with a first positive clearance and a second virtually zero clearance through the first openings, the first and second clearances being configured so that the device has different displacement amplitudes.