Hyperbranched polymers (HBPs) formed by the self-condensing vinyl polymerization (SCVP) or self-condensing ring-opening polymerization (SCROP) of monomer AB activated by stimuli with various reactivities were investigated by the generating function method. Two different cases were discussed: in case I, the concentration of the stimulus decayed during the activating reaction, and in case II, the stimulus acted as a catalyst to activate the monomer AB, and the change in stimulus concentration was neglected. The reduced number- and weight-average degree of polymerization ((DP) over bar*(n) and (DP) over bar*(w)) and degree of branching (DB) of the HBPs were found to depend not only on the mole ratio of stimulus to monomer AB (A) but also on the reactivity ratio of the stimulus (beta). The (DP) over bar*(n), (DP) over bar*(w), and polydispersity index of the reduced degree of polymerization increased with decreasing reactivity of the stimulus, In case II, when lambda beta > 1, there were only a few influences on the average degree of polymerization by lambda beta, and the results were similar to those of case I. However, when lambda beta<1, the degree of polymerization differed significantly between the two cases. The maximum degree of branching of about 0.5 was obtained with near full conversion of A, and the deuce of branching depended on the amount and reactivity ratio of the stimulus.