In order to synthesize a variety of block polymers having poly(1,4-divinylbenzene) (PDVB) segments, the living anionic block polymerizations of DVB with styrene, 2-vinylpyridine (2VP), tert-butyl methacrylate ((t)BMA), methyl methacrylate (MMA), N-(4-vinylbenzylidene)cyclohexylamine (1), 2-(4'-vinylpheny1)-4,4-dimethyl-2-oxazoline (2), or 2,6-ditert-butyl-4-methylphenyl 4-vinylbenzoate (3) were conducted in THF at -78 degrees C with the anionic initiator bearing K+ in the presence of a 10-fold excess of potassium tert-butoxide. With the sequential addition of DVB and each of these monomers, the following block polymers having PDVB segments were successfully synthesized: PS-b-PDVB, P2VP-b-PDVB, PDVB-b-P2VP, PDVB-b-P(t)BMA, PDVB-b-P(1), PDVB-b-P(2), PDVB-b-P(3), PS-b-PDVB-b-PBMA, PS-b-P2VP-b-PDVB-b-P(t)BMA, and PS-b-PDVB-b-P2VP-b-P(t)BMA. The resulting polymers are all novel block polymers with well-defined structures (predictable molecular weights and compositions and narrow molecular weight distributions) and possess reactive PDVB segments capable of undergoing several postreactions. Based on the results of such sequential block polymerizations, the anionic random copolymerization of DVB and 2VP, the polymerizability with (C4H9)(2)Mg, and some other addition reactions, it was found that the comparable reactivity of the chain-end anions follows the sequence of PS- > PDVB- > P2VP(-) > P(t)BMA(-). Accordingly, the reactivity of the corresponding monomers increases as follows: styrene < DVB < 2VP < (t)BMA.