Abstract: Thermoplastic, elastomeric, conjugated diene (e.g., butadiene)/methyl methacrylate block copolymers having elevated Tg and improved impact strength, well suited as polymer impact strength-modifiers and for conversion into pressure-sensitive adhesives, are prepared by (a) anionically polymerizing a conjugated diene monomer in an apolar solvent medium to provide a living polydiene, (b) next adding an alkali metal alkoxyalcoholate ligand to the medium comprising the living polydiene thus formed, (c) block copolymerizing the step (b) living polydiene with methyl methacrylate comonomer to provide a living copolymer, and (d) reacting the step (c) living copolymer with at least one protonic compound, e.g., water, alcohol and/or acid, and completing the polymerization thereof, with the proviso that polymerization of the conjugated diene and the methyl methacrylate comonomers is strictly carried out in the apolar solvent medium, in particular in toluene, benzene or ethylbenzene.