To provide an oily composition of moderate viscosity maintaining a sufficiently high coefficient of traction over a wide range from a low temperature to an elevated temperature.

This oily composition is produced by dissolving a hydrogenated ring-opened polymer comprising tricyclo[4.3.0.12,5]deca-3,7-diene, bicyclo[2.2.1]hept-2-ene, and tetracyclo[4.4.0.12,5.17,10]dodec-3-ene into an -methylstyrene dimeric hydride as a synthetic oil, that is, 2-methyl-2,4-dicyclohexylpentane. The resultant oily composition can be suitably used as oil for a traction drive.