In quasiliving polymerizations with reversible chain transfer (QL0Rsystems), polymers with narrow molecular weight distribution can be obtained, It has been shown that while in true living systems (L00) R = 1, and in quasiliving systems with irreversible chain transfer (QL01) R = 2 is the limiting value of polydispersity, in QL0Rsystems r = 4/3 is the polydispersity to which the distribution of the polymer tends with increasing polymerization time. This limit is independent of the rate of reinitiation; the course of the R vs t curves is, however, determined by the various rate constants.