An ethylene/.alpha.-olefin/7-methyl-1,6-octadiene copolymer rubber, said copolymer rubber being a random copolymer rubber of ethylene, .alpha.-olefin and 7-methyl-1,6-octadiene copolymer and obtained by copolymerizing ethylene, .alpha.-olefin and 7-methyl-1,6-octadiene in the presence of a Group IVB transition metal catalyst comprising (a) a Group IVB transition metal compound containing a ligand having cyclopentadienyl skeleton and (b) an organoaluminum oxycompound, wherein the ethylene/.alpha.olefin/7-methyl-1,6-octadiene copolymer rubber comprises
- (i) a molar ratio of ethylene to .alpha.-olefin (ethylene/.alpha.-olefin) in the range of 40/60 to 90/10;
- (ii) a content of 7-methyl-1,6-octadiene copolymer in the range of 0.4 to 25% by mol;
- (iii) an intrnsic viscosity (.eta.) as measured in decahydronaphthalene at 135.degree. C., from 0.1 dl/g to 8 dl/g;
- (iv) an intensity ratio D of T.alpha..beta. to T.alpha..alpha.(T.alpha..beta./T.alpha..alpha.) in a .sup.13 C-NMR spectrum of said copolymer rubber not more than 0.5;
- (v) a B value determined by a .sup.13 C-NMR spectrum of said copolymer rubber and the following formula in the range of 1.00 to 1.5
- B=P.sub.OE /(2P.sub.E .multidot.P.sub.O)
- wherein P.sub.E is a molar fraction of the ethylene units derived from ethylene;
- P.sub.O is a molar fraction of the .alpha.-olefin units derived from .alpha.-olefin;
- and P.sub.OE is a ratio of the number of .alpha.-olefin/ethylene chains to the number of all dyad chains in the random copolymer rubber;
- and
- (vi) a glass transition temperature Tg measured by DSC not higher than -53.degree. C.