A novel process for preparation of block copolymers containing, for example, alpha-methyl-styrene/styrene glassy blocks is claimed, where the glassy blocks contain 25-50 mol % alpha-methyl-styrene and have Tg values in the range of 120 to 140° C. The copolymerization process, which is conducted at 35 to 60° C. and relatively high solids contents and with continuous addition of styrene, results in very high conversions of the alpha-methyl-styrene. Selectively hydrogenated block copolymers having high glassy block Tg values are also disclosed and claimed as well as high service temperature elastomeric compositions comprising the block copolymer and an olefin polymer or copolymer.