Axial floating bearing assembly, with: - a first bearing outer ring, - a second bearing outer ring, - a first bearing inner ring, - a second bearing inner ring, and - rolling bodies (5, 6) of crown-conoidal form, which, to form a first rolling-body running row and to form a second rolling-body running row, are accommodated in an annular space defined between the respective bearing outer ring (1, 2) and the assigned bearing inner ring (3, 4), - the first bearing inner ring and the second bearing inner ring being coupled axially to one another, - the rolling-body axes of the rolling bodies of the first rolling-body running row and the rolling-body axes of the rolling bodies of the second rolling-body running row revolving respectively on a first and on a second cone envelope (K1, K2), - the apices (S1, S2) of the respective cone envelopes (K1, K2) lying in an intermediate region between the outer axial end faces (FA3, FA4) of the bearing inner rings (3, 4), - the bearing outer rings (1, 2) forming in each case raceways (1a, 2a) which are concavely curved uniformly in an axial section containing the bearing axis, the centres of curvature (RZ1, RZ2) lying on the bearing axis, - a tension device being provided for the axial tensioning of the bearing outer rings (1, 2) against the rolling bodies (5, 6) of the first and of the second rolling-body running row, - the tension device being designed for this purpose as an annular cylinder which comprises an annular chamber which can be widened in the axial direction according to the fluid pressure prevailing therein, and - the tension device being arranged in an axially floating manner between the bearing outer rings (1, 2) and, sealed off over its outer circumferential surface, being seated in an annular step of a bearing housing, and - the bearing outer rings (1, 2) being supported axially in the housing on the annular step. - a first bearing outer ring, - a second bearing outer ring, - a first bearing inner ring, - a second bearing inner ring, and - rolling bodies (5, 6) of crown-conoidal form, which, to form a first rolling-body running row and to form a second rolling-body running row, are accommodated in an annular space defined between the respective bearing outer ring (1, 2) and the assigned bearing inner ring (3, 4), - the first bearing inner ring and the second bearing inner ring being coupled axially to one another, - the rolling-body axes of the rolling bodies of the first rolling-body running row and the rolling-body axes of the rolling bodies of the second rolling-body running row revolving respectively on a first and on a second cone envelope (K1, K2), - the apices (S1, S2) of the respective cone envelopes (K1, K2) lying in an intermediate region between the outer axial end faces (FA3, FA4) of the bearing inner rings (3, 4), - the bearing outer rings (1, 2) forming in each case raceways (1a, 2a) which are concavely curved uniformly in an axial section containing the bearing axis, the centres of curvature (RZ1, RZ2) lying on the bearing axis, - a tension device being provided for the axial tensioning of the bearing outer rings (1, 2) against the rolling bodies (5, 6) of the first and of the second rolling-body running row, - the tension device being designed for this purpose as an annular cylinder which comprises an annular chamber which can be widened in the axial direction according to the fluid pressure prevailing therein, and - the tension device being arranged in an axially floating manner between the bearing outer rings (1, 2) and, sealed off over its outer circumferential surface, being seated in an annular step of a bearing housing, and - the bearing outer rings (1, 2) being supported axially in the housing on the annular step.