NOVELTY - A highly-saturated nitrile rubber composition comprises carboxyl group-containing highly-saturated nitrile rubber (A1) comprising 15-60 wt.% ( alpha ),( beta )-ethylenically-unsaturated nitrile monomer units and 1-60 wt.% ( alpha ),( beta )-ethylenically-unsaturated dicarboxylic acid monoester monomer units, highly-saturated nitrile rubber (A2) comprising 15-60 wt.% ( alpha ),( beta )-ethylenically-unsaturated nitrile monomer units and 0.9 wt.% or less ( alpha ),( beta )-ethylenically-unsaturated dicarboxylic acid monoester monomer unit, and polyamide resin (B).    USE - Highly-saturated nitrile rubber composition is used for forming crosslinkable nitrile rubber composition for forming rubber crosslinked material (all claimed) and sealing material. Uses include but are not limited to oil seal, shaft seal, bearing seal, seal for pneumatic pressure machine, rolling bearing, hub unit for motor vehicle, motor vehicle water pump, linear guide apparatus, ball screw, gasket for fuel cell separator, etc.    ADVANTAGE - The rubber crosslinked material obtained using highly-saturated nitrile rubber composition has excellent cold resistance and compression set-proof property.    DETAILED DESCRIPTION - A highly-saturated nitrile rubber composition comprises carboxyl group-containing highly-saturated nitrile rubber (A1) comprising 15-60 wt.% ( alpha ),( beta )-ethylenically-unsaturated nitrile monomer units and 1-60 wt.% ( alpha ),( beta )-ethylenically-unsaturated dicarboxylic acid monoester monomer units, highly-saturated nitrile rubber (A2) comprising 15-60 wt.% ( alpha ),( beta )-ethylenically-unsaturated nitrile monomer units and 0.9 wt.% or less ( alpha ),( beta )-ethylenically-unsaturated dicarboxylic acid monoester monomer unit, and polyamide resin (B). The carboxyl group-containing highly-saturated nitrile rubber (A1) and highly-saturated nitrile rubber (A2) has iodine number of 120 or less, each. INDEPENDENT CLAIMS are included for the following:    (1) crosslinkable nitrile rubber composition, which is obtained by mixing crosslinking agent (C) with highly-saturated nitrile rubber composition; and    (2) rubber crosslinked material, which is formed by crosslinking crosslinkable nitrile rubber composition.