The torque-induced transverse vibration of rotor systems driven by Cardan joints with with initial intersecting angles is analyzed. Three systems, MR2, MR4, SR4 models are analyzed. MR2 and MR4 are models for working machines such as the compressor and SR4 is for transmission shafts. The analysis proves that the initial intersecting angle induces parametric terms of frequency 4ν(νis frequency of shaft rotation) in addition to 2ν, which is induced when there is no initial intersecting angle. The 4νterms make the system unstable especially in the low-speed range. MR2 and MR4 models are shown to have quite different instability boundaries, depending on the sign of torque. The parametric tems of SR4 have no principal parametric instability region. SR4 is more stable than MR4.