Abstract—Utilizing the U-joint is the most usual and familiar way to connect rotating shafts, which are at an angle with each other. Although, this mechanical coupling has various advantages, converts a constant input velocity to a fluctuating output one. Consequently, this produces resonance conditions in the power transmission system of vehicles. In this study, the vibrations of drivetrains are considered to examine the system torsional behaviors. Here, the derived mathematical model is investigated by means of Floquet theory. Furthermore, the acquired results are validated analytically by applying the frequency analysis. In order to examine the influence of different parameters on the vibrations, the unstable zones are identified and analyzed. In addition, the effects of joint angle and shaft length are investigated. The obtained model is useful to simulate the torsional behaviors of various two-axis power transmission systems and identify the resonance conditions.