A nitrile group-containing highly saturated copolymer rubber which is a hydrogenated product of an unsaturated nitrile-conjugated diene copolymer. The highly saturated copolymer rubber has an alkylthio group having 12 to 16 carbon atoms, which include at least three tertiary carbon atoms, and having a sulfur atom which is directly bound to at least one of the tertiary carbon atoms, and the highly saturated copolymer rubber further has a Mooney viscosity of 15 to 200 and an iodine value not larger than 80. The highly saturated copolymer rubber is produced by copolymerizing an unsaturated nitrile and a conjugated diene by using as a specific alkylthiol molecular weight modifier. The highly saturated copolymer rubber exhibits a high-rate vulcanizability with a sulfur-containing vulcanizer.
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