Block copolymers of alkoxyallenes were obtained in high yield by the two-stage living coordination polymerization of two kinds of alkoxyallenes using an allylnickel catalyst. The resulting copolymers had narrow molecular weight distributions (similar to 1.1), regardless of the order of the monomer additions. When an alkoxyallene-bearing hydrophilic substituent was used as a comonomer for the block copolymerization with that bearing a hydrophobic one, the resulting copolymer showed amphiphilic properties. For example, a block copolymer obtained by the copolymerization of n-hexyloxyallene with diethylene glycol allenyl methyl ether was soluble in water as well as n-hexane.