PURPOSE: To obtain a vinylic block copolymer in the form of particles of excellent powder processability and having excellent transparency, by polymerizing a vinyl monomer by adding a radical initiator in portions and polymerizing the mixture after adding another vinyl monomer.

CONSTITUTION: In the production of a vinylic block copolymer by a 1st-stage polymerization wherein a vinyl monomer is polymerized in the presence of a radical initiator in an organic solvent which does not dissolve a vinyl monomer and a 2nd-stage polymerization wherein another vinyl monomer is added and polymerized; the same or different radical initiators are added to the 1st-stage polymerization system in portions to obtain the 1st-stage polymer, and another vinyl monomer is added to this polymerization system and polymerized in a vapor phase or a liquid phase to obtain the 2nd-stage polymer. The degree of blocking tends toward increasing when the polymerization temperature in the 2nd stage is higher than that in the 1st stage, and this different in temperature is generally preferred to be at least 5°C.