A novel class of living radical polymerizations with germanium, tin, and phosphorus catalysts were developed. The polymerizations are based on a new reversible activation mechanism, Reversible chain Transfer(PT) catalysis. Low-polyclispersity (M-w/M-n approximate to 1.1-1.3) polystyrene, poly(methyl methacrylate), poly(glycidyl methacrylate), and poly(2-hydroxyethyl methacrylate) with predicted molecular weight were obtained with fairly high conversion in a fairly short time. The pseudo-first-order activation rate constant k(act) for the styrene/Gel(4) (catalyst) system was large enough, even with a small amount of Gel(4), explaining why the system provides low-polydispersity polymers from an early stage of polymerization. The retardation in the polymerization rate observed for the styrene/Gel(4) system was kinetically proven to be mainly due to the cross-termination between the propagating radical with Gel(3)*. Attractive features of the germanium, tin, and phosphorus catalysts include their high reactivity hence small amounts (1-10 mM) being required under relatively mild conditions (at 60-100 degrees C), high solubilityin organic media without ligands, insensitivity to air hence sample preparation being allowed in the air, and minor color and smell. The germanium and phosphorus catalysts may also be attractive for their low toxicity. The phosphorus catalysts may also be attractive for their low cost.