A differential (110, 210, 310, 410, 510, 610) for transmitting power from an input shaft to a first output shaft and a second output shaft in a vehicle, the differential comprising: a differential housing comprising a bearing seat (146A, 480A); an input gear rotatably carried by the differential housing and rotatably driven by the input shaft; a ring gear rotatably carried by the differential housing and rotatably driven by the input gear; a first bearing carried by the differential housing in the bearing seat (146A, 480A); a second bearing carried by the differential housing; a bi-directional overrunning clutch comprising: a clutch housing formed on or coupled to the ring gear and rotatable in combination with the ring gear, the clutch housing comprising an inner surface; a roll cage assembly disposed inwardly of the inner surface of the clutch housing, the roll cage assembly comprising a roll cage and a plurality of rollers carried by the roll cage; two output hubs, comprising: a first output hub disposed within the clutch housing and carried by the first bearing for rotation relative to the differential housing, the first output hub driving the first output shaft; a second output hub disposed within the clutch housing and carried by the second bearing for rotation relative to the differential housing, the second output hub driving the second output shaft; wherein when the plurality of rollers wedge between the inner surface of the clutch housing and the output hubs, the output hubs and the clutch housing thereby rotate in combination; and an electromagnet assembly being energized to cause engagement of the bi-directional overrunning clutch; characterized by: a retaining ring (152A, 482A) carried by the differential housing, the retaining ring compressing the first bearing against the differential housing and securing the first bearing in the bearing seat. a differential housing comprising a bearing seat (146A, 480A); an input gear rotatably carried by the differential housing and rotatably driven by the input shaft; a ring gear rotatably carried by the differential housing and rotatably driven by the input gear; a first bearing carried by the differential housing in the bearing seat (146A, 480A); a second bearing carried by the differential housing; a bi-directional overrunning clutch comprising: a clutch housing formed on or coupled to the ring gear and rotatable in combination with the ring gear, the clutch housing comprising an inner surface; a roll cage assembly disposed inwardly of the inner surface of the clutch housing, the roll cage assembly comprising a roll cage and a plurality of rollers carried by the roll cage; a clutch housing formed on or coupled to the ring gear and rotatable in combination with the ring gear, the clutch housing comprising an inner surface; a roll cage assembly disposed inwardly of the inner surface of the clutch housing, the roll cage assembly comprising a roll cage and a plurality of rollers carried by the roll cage; two output hubs, comprising: a first output hub disposed within the clutch housing and carried by the first bearing for rotation relative to the differential housing, the first output hub driving the first output shaft; a second output hub disposed within the clutch housing and carried by the second bearing for rotation relative to the differential housing, the second output hub driving the second output shaft; a first output hub disposed within the clutch housing and carried by the first bearing for rotation relative to the differential housing, the first output hub driving the first output shaft; a second output hub disposed within the clutch housing and carried by the second bearing for rotation relative to the differential housing, the second output hub driving the second output shaft; wherein when the plurality of rollers wedge between the inner surface of the clutch housing and the output hubs, the output hubs and the clutch housing thereby rotate in combination; and an electromagnet assembly being energized to cause engagement of the bi-directional overrunning clutch;