In a disengageable axial abutment for a rotary machine fitted with fluid bearings, an outer ring (103) comprises first and second outer half-rings (103A, 103B) centered in the casing (111) by a flexible suspension system, with the outer half-rings (103A, 103B) being held in the axial direction between a static abutment member (113) and a pre-loading system (104) exerting a predetermined axial force such that, so long as the axial load exerted on the axial abutment via a synchronization cone (108) is greater than a given threshold, each rolling element (101) presents a single line (121) of two points of contact (121A, 121B) with an inner ring (102) and with the first outer half-ring (103A) respectively, and the inner ring (102) is driven in rotation by the synchronization cone (108), whereas, when the axial load exerted on the axial bearing becomes smaller, a gap (115) is created between the outer half-rings (103A, 103B) and a second line (123) of two additional points of contact (123A, 123B) is created between each rolling element (101) and the inner ring (102) and the second outer half-ring (103B) respectively, such that the axial abutment is disengaged.