A process for the preparation of a thermoplastic, elastomeric, conjugated diene/methyl methacrylate block copolymer having improved heat resistance, which comprises (a) anionically polymerizing a conjugated diene monomer in an apolar solvent medium to provide a living polydiene, (b) next adding a ligand of formula ROM to the medium comprising said living polydiene, in which M is an alkali metal and R is a radical R.sup.1 (OR.sup.2).sub.m wherein R.sup.1 is a linear or branched alkyl, arylalkyl or alkylaryl radical, the alkyl moiety of which having from 1 to 6 carbon atoms, R.sup.2 is a linear or branched alkylene radical having from 2 to 4 carbon atoms and m is an integer 1, 2 or 3, (c) reacting the step (b) living polydiene with methyl methacrylate comonomer, also in said apolar solvent medium, to provide a living copolymer, and then (d) reacting the step (c) living copolymer with at least one protonic compound and completing the polymerization thereof, with the proviso that polymerization of said conjugated diene and said methyl methacrylate comonomers is carried out essentially exclusively in said apolar solvent medium.