To obtain an automatic transmission oil compsn. which meets all the requirements on transmission torque capacity, oxidation stability, capability for preventing shudder vibration, and long-term persistence of the capability by incorporating a specified amt. of a specific alkaline earth metal sulfonate into a base oil.

This compsn. is prepd. by incorporating 30-1,200ppm (in terms of metal and based on the compsn.) alkaline earth metal sulfonate having at least one 12-30C linear or branched hydrocarbon group and a total base number of 120mgKOH/g or lower into a base oil. Examples of the sulfonate are a compd. represented by formula I (wherein R3 is a 12-30C linear or branched hydrocarbon group; R4 is H or a 1-30C linear or branched hydrocarbon group; and M is an alkaline earth metal) and a compd. represented by formula II (wherein at least one of R5 to R8 is the same as R3, the rest being the same as R4; and M is the same as described above). The compsn., as one used for an automatic transmission with a slip control mechanism, is excellent in oxidation stability and in capability of preventing shudder vibration and persistence of the capability during long-term use.