This paper is concerned with the theoretical investigations of the practical problem of the response of plane hydrodynamic journal bearing systems during acceleration and deceleration periods. The nature of the theoretically predicted journal response during starting and stopping is found to be similar to the experimental behavior reported by other authors. The motion of an accelerating or a decelerating journal shows concurrence with the linearized stability chart. An interesting finding is that, beginning from an equilibrium state, a journal can be accelerated only to a limiting value so that it may return to its original state on being decelerated from the accelerated speed.