A principle conception for quasiliving TEMPO-mediated radical copolymerization was advanced. It was concluded that TEMPO-mediated copolymerizafion of styrene with other monomers (which are not able to polymerize via quasiliving mechanism) may proceed via quasiliving mechanism in two regimes-"azeotropic" and "gradient" according to the reactivity ratio of comonomers. The "azeotropic" regime gives an almost linear increase in molecular weight with conversion and provides controlled synthesis of copolymers with a low polydispersity index. "Gradient" copolymerization proceeds via a dead-end mechanism with formation of gradient copolymers. A simple kinetic scheme was proposed for "azeotropic" copolymerization. Experimental kinetic data correlating with the advanced concept were obtained for quasiliving copolymerization of styrene with methyl and butyl acrylates, methyl methacrylate, and acrylonitrile ("azeotropic" regime); and for styrene copolymerization with N-vinyl pyrrolidone and vinyl acetate ("gradient＇＇ regime).