Heavy fractions (boiling point 450°C or higher) derived from alkylation products, alkyl benzenes and styrenes, (Fig. 1, Table 1), were cracked by the following two methods: Case 1: thermally hydrocracked in the presence of tetralin Case 2: catalytically hydrocracked on N-diatomaceous earth catalyst The cracked products were, then, nuclear-hydrogenated by Rh-C catalyst at same reaction conditions (Figs. 2, 3). Gas chromatograms of the cracked products show that the compounds produced by the two methods, respectively, remarkably different (Fig. 5). Structural parameters of the products from the two methods show that side chains are cleft but aromatic rings remain unchained during the cracking stage of Case 1 (Table 2, Fig. 6). Ring-hydrogenations of the cracked products differ greatly between the two cases as follows; (1) Hydrogen consumption during the nuclear-hydrogenation of the cracked products Case 1:5.62wt%/feed Case 2:2.06wt%/feed (2) H/C (atomic ratio) of the nuclear-hydrogenated products Case 1:1.56 Case 2:1.42 (Table 3) To go into more in details, saturates and aromatics were separated from the nuclear-hydrogenated products and analyzed. Significant results follows; (1) Yields of saturates and aromatics Case 1: saturates 85.5wt% aromatics 14.5% Case 2: saturates 18.3wt% aromatics 81.7% (2) Fraction of aromatic carbons in aromatics Case 1:0.35 Case 2:0.43 (3) Ha/H in aromatics (Table 4) Case 1:0.051 Case 2:0.148 Results of gas chromatograms of saturates and aromatics from the two cases follow Case 1: Compounds containing two aromatic rings are entirely converted to saturates and greater parts of the compounds containing three aromatic rings are also converted to saturates. Case 2: Compounds containing two aromatic rings remained and compound containing three aromatic rings were not converted to saturates. (Fig. 7) From these facts, the conclusions arrived are as follows; (1) Thermally cracked products can be easily nuclear hydrogenated. (2) The differences between the cases are remarkable in heavier fractions. The nuclear-hydrogenated products derived in Case 1 were evaluated as a traction fluid, as follows; (1) Traction coefficient of the fractions are fairly good (0.080-0.087) (2) The extent of nuclear-hydrogenation is over 90% (350°C lower fractions) (Tables 5, 6) It was confirmed that a Ru-C catalyst exhibited performances which were as good as those of Rh-C catalyst (Table 7) These data suggest that naphthenic oils can be produced from other heavy alkyl-aromatics.