A process for interpolymerizing a vinyl aromatic hydrocarbon polymer and a block polymer is disclosed. The process includes the following steps: (a) forming a block polymer precursor of at least one polymeric block containing conjugated diene monomer contributed units in the presence of an anionic initiator and in an inert diluent, the block polymer precursor having living ends; and (b) thereafter adding to the block polymer precursor a charge of a vinyl aromatic hydrocarbon monomer and an additional charge of an anionic initiator to simultaneously form (1) a block polymer having a terminal block formed from the charge of vinyl aromatic hydrocarbon monomer attached to the block polymer precursor and (2) a poly(vinyl aromatic hydrocarbon) polymer interpolymerized with the block polymer. The practice of this process produces a vinyl aromatic hydrocarbon block terminated block polymer, such as SBS, interpolymerized with a polymer formed from vinyl aromatic hydrocarbon monomer, such as polystyrene. The resultant interpolymer has a high Gardner Impact Strength and good processability.