A synthetic lubricating oil which is an α-olefin (co)polymer, which i) contains (a) 90-100 mol-% of constituent units derived from at least one C 8-20 -α-olefins monomer and (b) 0-10 mol-% of constituent units derived from ethylene; ii) has a kinematic viscosity at 100°C of 8-500 mm 2 /s; iii) has a number-average molecular weight (Mn), measured by gel permeation chromatography, of 1,500-15,000; iv) satisfies the following formulae and: A ≤ 24.0 × Exp − 0.0239 × K B ≤ 0.0775 × K wherein A is the (co)polymer content (%) having a molecular weight of < 1,000, and B is the (co)polymer content (%) having a molecular weight of ≥ 20,000, each measured by GPC; and K is the kinematic viscosity (mm 2 /s) at 100°C; v) has a molecular weight distribution (Mw/Mn) of 1.1-1.8; vi) has a content of unsaturated groups at the molecular one ends of 0.05-10 %; calculated according to the formula N × M × 2 / 14 wherein N is the number of unsaturated groups per hydrogen atom, calculated as N = S B / 2 + S C + S D / 3 + S E S A + S B + S C + S D + S E + S F with S A to S F representing signal peak areas in the 1 H-NMR spectrum of the α-olefin (co)polymer as follows: S A = peak of terminal methyl at 0.65-0.85 ppm, S B = peak of vinylidene at 4.70-4.80 ppm, S C = peak of vinyl at 4.85-5.0 ppm, S D = peak of vinyl at 5.7-5.9 ppm, S E = peak of inner olefin at 5.10-5.30 ppm, S F = peak of methylene at 0.90-2.0 ppm; and M is the average absolute molecular weight of the α-olefin (co)polymer measured from VPO (Vapor Pressure Osmometry); and vii) satisfies the formula: C ≥ 0.3178 × K + 140 wherein C is the viscosity index measured according to JIS K2283, and K is the kinematic viscosity (mm 2 /s) at 100°C. i) contains (a) 90-100 mol-% of constituent units derived from at least one C 8-20 -α-olefins monomer and (b) 0-10 mol-% of constituent units derived from ethylene; ii) has a kinematic viscosity at 100°C of 8-500 mm 2 /s; iii) has a number-average molecular weight (Mn), measured by gel permeation chromatography, of 1,500-15,000; iv) satisfies the following formulae and: A ≤ 24.0 × Exp − 0.0239 × K B ≤ 0.0775 × K wherein A is the (co)polymer content (%) having a molecular weight of < 1,000, and B is the (co)polymer content (%) having a molecular weight of ≥ 20,000, each measured by GPC; and K is the kinematic viscosity (mm 2 /s) at 100°C; v) has a molecular weight distribution (Mw/Mn) of 1.1-1.8; vi) has a content of unsaturated groups at the molecular one ends of 0.05-10 %; calculated according to the formula N × M × 2 / 14 wherein N is the number of unsaturated groups per hydrogen atom, calculated as N = S B / 2 + S C + S D / 3 + S E S A + S B + S C + S D + S E + S F with S A to S F representing signal peak areas in the 1 H-NMR spectrum of the α-olefin (co)polymer as follows: S A = peak of terminal methyl at 0.65-0.85 ppm, S B = peak of vinylidene at 4.70-4.80 ppm, S C = peak of vinyl at 4.85-5.0 ppm, S D = peak of vinyl at 5.7-5.9 ppm, S E = peak of inner olefin at 5.10-5.30 ppm, S F = peak of methylene at 0.90-2.0 ppm; and M is the average absolute molecular weight of the α-olefin (co)polymer measured from VPO (Vapor Pressure Osmometry); and S A = peak of terminal methyl at 0.65-0.85 ppm, S B = peak of vinylidene at 4.70-4.80 ppm, S C = peak of vinyl at 4.85-5.0 ppm, S D = peak of vinyl at 5.7-5.9 ppm, S E = peak of inner olefin at 5.10-5.30 ppm, S F = peak of methylene at 0.90-2.0 ppm; and M is the average absolute molecular weight of the α-olefin (co)polymer measured from VPO (Vapor Pressure Osmometry); and vii) satisfies the formula: C ≥ 0.3178 × K + 140 wherein C is the viscosity index measured according to JIS K2283, and K is the kinematic viscosity (mm 2 /s) at 100°C.