The MWD function and 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 in a bimolecular reaction ("degenerative transfer"). Such a mechanism is believed to be applicable to many "living" polymerizations (e.g., anionic, group transfer, cationic, and radical). For constant monomer concentration (slow addition of monomer or low conversion), the polydispersity index, <(P)over bar (w)>/<(P)over bar (n)>, depends on the ratio of molar concentrations of monomer and initiator, gamma = M/I-o, the degree of polymerization, <(P)over bar (n)>, and the ratio of rate constants of exchange and propagation, beta = k(ex)/k(p). In a limiting case (beta > 1, and <(P)over bar (n)> much greater than 1), <(P)over bar (w)>/<(P)over bar (n)> approximate to 1 + 2 gamma/(beta(P)over bar (n)>). The molecular weight distributions are always narrower than those obtained for a batch process, where monomer concentration decreases during polymerization.