A novel star block copolymer represented by the general formula as shown below and a process for the production thereof are described. The copolymer has superior physical properties, particularly impact strength and, furthermore, is reduced in coloration. Thus the copolymer can find numerous uses; for example, it can be used in preparation of fibers, foams, automotive parts, and electrical components. The copolymer is produced by copolymerizing a star-shaped polyether prepolymer and a lactam, said prepolymer being prepared by reacting a star-shaped polyoxyalkylene having at least 3 terminal hydroxy groups and an N-chlorocarbonyl lactam, in the presence of an anionic polymerization catalyst. ##STR1## In this formula, all the symbols are as defined hereinbefore.