A drive system drives a pulley along a curved track to open and close a sliding vehicle door. The pulley is pivotally mounted to the sliding door to permit the pulley to pivot when the pulley traverses the curved portion of the track. An electric motor drives the pulley through a drive belt. In operation, as the pulley pivots when it traverses the curved portion of the track, the drive belt twists. Torque transfer between the pulleys and the motor is maintained during twisting of the drive belt which thereby permits an uncomplicated yet effective system for driving the sliding door along the curved portion of track. Another drive system transmits torque through a drive shaft arrangement which rotates as the drive system traverses the curved portion of track.