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Maintaining stability in the variator control system after quick torque changes is an important factor in achieving smooth mode changes in a power-split CVT system. In this paper, the ratio-changing characteristics of a half-toroidal CVT variator with hydraulic and mechanical loading devices are analyzed using a newly developed analytical model under dynamic load transmission. The ratio-changing characteristics of a variator with a mechanical loading device show a large overshoot after quick torque changes. In the case of a hydraulic loading device under constant application of axial pressure, it has been demonstrated that the ratio-changing characteristics are stable both theoretically and experimentally.