It was found that sulfanylethanoic and 3-sulfanylpropanoic acids are effective regulators of molecular weight with chain transfer constants of 0.441 and 0.317, respectively, and show an unexpected acceleration effect on the radical polymerization of N-vinyl-2-pyrrolidone, initiated by 2,2’-azobisisobutyronitrile. It was determined for the first time that the thiolate anions of mercapto acids form a high-temperature redox initiating system with 2,2’-azobisisobutyronitrile during the radical polymerization of N-vinyl-2-pyrrolidone in 1,4-dioxane. Considering the peculiarities of initiation, a kinetic model of the polymerization of N-vinyl-2-pyrrolidone is proposed, and it is shown that the theoretical orders of the reaction rate, with respect to the monomer, initiator, and chain transfer agent, are 1, 0.75, 0.25, and are close to their experimentally determined values. Carboxyl-containing techelics of N-vinyl-2-pyrrolidone were synthesized so that it can slow down the release of the anticancer drug, doxorubicin, from aqueous solutions, which can find its application in the pharmacological field.