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The torque controlled full toroidal IVT (Infinitely Variable Transmission) provides significant fuel economy benefit over conventional stepped ratio transmissions. This is achieved, in part, by using high overdrive ratios. This benefit must be provided alongside good driveability, which requires the system to have a fast response while being well damped. This paper gives a theoretical overview of the dynamic response of the IVT focusing on different interactions between the full toroidal variator and hydraulic control circuits. The concept of system stability is applied to sub-systems and their interactions to indicate design requirements of this torque controlled transmission.