A compounding oil for polymers which can be used as a plasticizer, process oil, thinner, softening agent, extender or the like. The compounding oil of the invention comprises a fraction mainly containing triaryldialkanes and having boiling points in the range of 350.degree. to 450.degree. C., which fraction is prepared by disproportionating a by-product oil fraction at temperatures in the range of 20.degree. to 500.degree. C. in the presence of a disproportionation catalyst, said by-product oil fraction mainly containing diarylalkanes, having boiling points in the range of 260.degree. to 320.degree. C., and being obtained from the process to prepare alkylated monocyclic aromatic hydrocarbons by alkylating monocyclic aromatic hydrocarbons with olefins in the presence of an alkylation catalyst.