A transmission system for an adjusting device, of a waste gate of an exhaust gas turbocharger, including a four bar coupling mechanism, a driver arm operatively connected to a drive via a transmission, an output arm and a coupler, operatively connecting the driver and output arms, the transmission having a driving gear, assigned to the drive, and a driven gear, assigned to the driver arm and interacting with the driving gear having a rolling curve radius, which changes over the circumference, the driven gear having a rolling curve radius running complementary to the former. The rolling curve radii is selected in an angle of rotation range about the extended position of the coupling to form at least in regions a first transmission ratio and outside the angle of rotation range to form at least a second transmission ratio larger than the first ratio. Also described is an exhaust gas turbocharger.