A lubricating oil composition which comprises (I) a base oil selected from mineral oils having an aromatic content of not higher than 30 wt%, synthetic oils which are free of aromatic rings in the structural units, and mixtures thereof, and (II) 0.01 to 5.0 wt%, based on the total composition, of N-p-branched alkylphenyl-alphanaphthylamine which has an alkyl moiety having 12 or 15 carbon atoms and which is derived from a propylene oligomer.