There is provided an ethylene--olefin-non-conjugated diene copolymer rubber satisfying the following requirements (1) to (4):

    • (1) a ratio of a Z-average molecular chain length (Az) measured according to a gel permeation chromatography to a number average molecular chain length (An), Az/An, of the ethylene--olefin-non-conjugated diene copolymer rubber is from 20 to 30,
    • (2) a ratio of a weight average molecular chain length (Aw), which is an index of a molecular weight distribution, to the number average molecular chain length (An), Aw/An, of the ethylene--olefin-non-conjugated diene copolymer rubber is more than 5,
    • (3) a unimodal or bimodal molecular weight distribution structure having a molecular chain length component, which component is present in a maximum amount in a range of 3.8Log Aw4.5, exists in the ethylene--olefin-non-conjugated diene copolymer rubber, and
    • (4) a viscosity (ML1+4, 121 C.) of the ethylene--olefin-non-conjugated diene copolymer rubber measured with a ML viscometer is more than 60 and less than 160.
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