A mathematical model is developed for the polymerization of isobutylene initiated with Et//2AlCl plus Cl//2. Previous experiments have shown that this polymerization is 'kinetically living'. A computer analysis based on a mathematical model permits the calculation of the theoretical conversion-time curves, the molecular weight averages, and polydispersity. The good agreement between experimental and theoretical results suggests that the reaction mechanism proposed and the mathematical model derived are quite correct