- In  and  the authors have proposed a new class of Fluctuation Smoothing scheduling policies for re-entrant lines. Through extensive simulations, they have demonstrated that these scheduling policies substantially reduce the mean and variance of the cycle time in several models of semiconductor manufacturing plants. In this paper we establish that all the policies in this class of Fluctuation Smoothing Policies for Mean Cycle Time (FSMCT) are stable, in the sense of positive Harris recurrence, for all stochastic re-entrant lines. These constitute the first analytical results on this promising class of scheduling policies for stochastic systems. This is done by showing that the fluid limits corresponding to the FSMCT policies empty in finite time from all suitable initial conditions. A special case of FSMCT policies is the Last Buffer First Serve policy, and its stability is also thus established.