In this paper we establish that all the policies in the class of Fluctuation Smoothing Policies for Mean Cycle Time (FSMCT), proposed in (Lu et al. 1992) and (Lu and Kumar 1993), 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 which have been shown to substantially reduce the mean and variance of cycle times in stochastic re-entrant lines. Stability is established 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.