Abstract: A method is described for enabling operation of an aircraft turbo-engine to be continued in spite of the accidental occurrence of an unbalance in a tor of the engine, such as may be caused by the breakage of a fan blade. The method involves constructing the bearing support of at least one of the bearings of the rotor so that the support has at least two levels of stiffness, arranging for the support to change from a normal stiffness level to a lower stiffness level in response to the occurrence of an unbalance in excess of a pre-determined minimum value, and setting the clearance between the tips of the rotor blades and the inner wall of the surrounding casing so that it is at least equal to the radial displacement of the rotor under the action of a pre-determined maximum unbalance when the rotor is rotating at the flight idling speed of the engine and the bearing support is at the lower stiffness level. A bearing support construction for implementing the method is also described.