A transfer case for a vehicle having two output shafts, a gear reduction assembly, a coupling mechanism and an overrunning roller clutch for selectively producing driving of one shaft only or both shafts concurrently. The coupling mechanism selectively couples one output shaft to either (1) an input shaft, (2) the gear reduction assembly, or (3) a neutral position. The overrunning clutch has an inner race, an outer race, and rollers located between the races. Drag shoes are positioned to frictionally slide on a drag surface of a selectively grounded member to retard the rollers. A resilient band urges the drag shoes against the drag surface. When the drag shoes rotate at a sufficient speed they disengage from the drag surface so as to provide no force to retard the rollers. When the ground member is grounded it provides the drag surface for the drag shoes. When the ground member is ungrounded it is free to rotate and the drag shoes do not provide a drag force to bias the rollers. A latch may be coupled to the inner race to engage a roller cage to prevent high speed lock-up. A drag ring is located inside the outer race and provides a drag force on the rollers to advance the rollers when it is desired, e.g., when front wheel compression braking is advantageous. An actuator assembly is provided with a variable speed drive for shifting the transfer case between modes of operation.