The present invention provides a nitrile group-containing highly saturated copolymer rubber comprising an α,β-ethylenically unsaturated nitrile monomer unit (a1) in a content of 10 to 40 wt %, an α,β-ethylenically unsaturated monocarboxylic acid ester monomer unit (a2) in a content of 10 to 60 wt %, and a conjugated diene monomer unit (a3) in a content of 20 to 70 wt %, and having an iodine value of 35 to 85.