Block copolymers of p-tert-butoxystyrene (tBOS) with isobutyl vinyl ether (IBVE), p-methoxystyrene (pMOS), and p-methylstyrene (pMS) were synthesized by sequential living cationic polymerizations with the hydrogen iodide/zinc halide (HI/ZnX2; X = I, Cl) initiating systems in toluene at -15-degrees-C. tBOS-IBVE and tBOS-pMS block copolymers were obtained only by initiating sequential polymerization from a more reactive monomer (IBVE for tBOS; tBOS for pMS), followed by further addition of ZnX2 in order to accelerate the subsequent polymerization of the second monomer from the resultant living polymer. In contrast, the tBOS-pMOS block copolymerization could be started from either of the monomers, because of their similar reactivities. These tBOS-based AB block copolymers possessed controlled molecular weights and narrow molecular weight distributions (MBAR(w)/MBAR(n) = 1.04-1.22), being free from homopolymers. The poly-(tBOS) segments in the block copolymers could be converted into poly(p-vinylphenol) segments by acidolysis with hydrobromic acid. The deprotected block polymers were insoluble in benzene and dichloromethane, which are good solvents for the starting block copolymers of tBOS.