To obtain a polyolefin elastomer which is useful for producing rubber articles such as hoses, belts, and molded articles, a polymer blend containing at least one other hydrocarbon polymer, and various lubricating-oil-containing articles where an elastomer functions as a viscosity modifier.

A polyolefin elastomer having specifically combined characteristics, i.e. a high mol.wt. (MW), a high Mooney viscosity (ML1+4 at 125°C), a low polydispersity index (MW/Mn), a low glass transition temperature (Tg), and a low hysteresis (tan δ), is obtained by a polymerization method using a metallocene catalyst of a specific type.