The dynamic stability of overhung flexible rotors subjected to load torques has been studied analytically. Other factors, such as external damping, distributed shaft mass, and gyroscopic moments, are considered. For the analyses, the transfer matrix is developed to include the effect of the applied torque and then integrated into a computer program to investigate the stability of overhung rotor systems under both tangential and axial load torques. Two overhung rotor systems are considered: the cantilevered rotor and the overhung rotor with an intermediate support. The ratio of the load torque to the damping for the stability is presented for the various locations of the intermediate supports. It was found that stability depends strongly on both the mode shape and the dimensionless torque to damping ratio.