Tapered roller bearing for mounting a first machine part rotatably relative to a second machine part, having conical rolling bodies and cage segments with in each case - two circumferential webs which lie opposite one another and extend in each case between a first circumferential end and a second circumferential end of the cage segment, and - at least two connecting webs which lie opposite one another, connect the two circumferential webs to one another and, together with the circumferential webs, configure at least one pocket which receives one of the conical rolling bodies, - the circumferential webs and the connecting webs having pocket sides which delimit the pocket, - the circumferential webs and the connecting webs which are arranged in the region of the first circumferential end and the second circumferential end having opposed surrounding sides with respect to the pocket sides, characterized in that, - in each case on their pocket side, the connecting webs have a concavely shaped first guide face and a concavely shaped second guide face, and in each case on their circumferential side, the connecting webs which are arranged in the region of the first circumferential end or the second circumferential end additionally have a concavely shaped first guide face for partially engaging around a rolling body in its circumferential direction, - the first guide faces and the second guide faces on the pocket sides of the connecting webs which adjoin the same pocket secure a rolling body which is arranged in the said pocket against falling out in a first direction and in a second direction which is opposed to the first direction in a positively locking manner and, as a result, fix the rolling body captively in the pocket, the first guide faces engaging around a greater circumferential region of a rolling body than the second guide faces, and - the cage segments are guided by rolling bodies. - two circumferential webs which lie opposite one another and extend in each case between a first circumferential end and a second circumferential end of the cage segment, and - at least two connecting webs which lie opposite one another, connect the two circumferential webs to one another and, together with the circumferential webs, configure at least one pocket which receives one of the conical rolling bodies, - the circumferential webs and the connecting webs having pocket sides which delimit the pocket, - the circumferential webs and the connecting webs which are arranged in the region of the first circumferential end and the second circumferential end having opposed surrounding sides with respect to the pocket sides, - in each case on their pocket side, the connecting webs have a concavely shaped first guide face and a concavely shaped second guide face, and in each case on their circumferential side, the connecting webs which are arranged in the region of the first circumferential end or the second circumferential end additionally have a concavely shaped first guide face for partially engaging around a rolling body in its circumferential direction, - the first guide faces and the second guide faces on the pocket sides of the connecting webs which adjoin the same pocket secure a rolling body which is arranged in the said pocket against falling out in a first direction and in a second direction which is opposed to the first direction in a positively locking manner and, as a result, fix the rolling body captively in the pocket, the first guide faces engaging around a greater circumferential region of a rolling body than the second guide faces, and - the cage segments are guided by rolling bodies.