The MWD moments are derived for a "living" polymerization process which proceeds via active and "dormant" species and where the activity is directly exchanged between these chain ends. Such a mechanism is believed to be applicable to many "living" polymerizations (e.g, anionic, group transfer, cationic, radical). It is shown that for low ratios of rate constants of exchange to propagation, beta = k(ex)/k(p) < 1, the polydispersity index, M(w)/M(n), increases with monomer conversion whereas for beta > 1 it decreases (after a marked increase at low conversions). The latter case coincides with a common observation in group transfer polymerization (GTP). For a given conversion, polydispersity has its maximum for 0.1 < beta < 1. In a limiting case, at full conversion, a very simple relation is valid : M(w)/M(n), approximate to 1 + 1/beta. The dependence of polydispersity on initiator and monomer concentrations is not very pronounced. The results are compared to experimental data of the GTP of methyl methacrylate using nucleophilic catalysts.