To provide a lubricating oil compsn. for internal combustion engines which is excellent in oxidation stability to NOx and evaporation character and controls poisoning to a NOx absorbing and reducing three-way catalyst and formation of deposit on an intake valve system.

This compsn. is prepared by compounding 0.04-0.10 wt.% as phosphorus (to the total of the compsn.) of zinc dithiophosphate (A), 1-10 wt.% calcium phenate and/or calcium sulfonate (B) having a total base number of 100-400 mgKOH/g, and 0.01-0.20 wt.% as nitrogen of polyalkenyl succinic acid imide (C) having a boron to nitrogen wt. ratio of 0-1.2 and an alkenyl group of 1,000-3,500 mol.wt. to a base oil contg. not more than 1 wt.% aromatics, not more than 10 ppm sulfur, not less than 50 wt.% total of paraffin and one ring naphthene, and having a kinematic viscosity at 100°C of 2-50 mm2/s and a NOACK vaporization of not greater than 16 wt.%.