A diester represented by the formula ##STR00001## wherein A represents a cyclohexane ring, cyclohexene ring or benzene ring, X is H or methyl group, R.sup.X and R.sup.Y are the same or different and each is C3-C18 branched-chain alkyl group, C1-C18 straight-chain alkyl group, C2-C18 straight-chain alkenyl or C3-C10 cycloalkyl, provided that when A is a benzene ring, R.sup.X and R.sup.Y are different from each other and --COOR.sup.X and --COOR.sup.Y are attached to two adjacent carbon atoms of the benzene ring, and having the following properties: 1) a total acid number of 0.05 mgKOH/g or less, 2) a sulfated ash content of 10 ppm or less, 3) a sulfur content of 20 ppm or less, 4) a phosphorus content of 20 ppm or less, 5) a peroxide value of 1.0 meq/kg or less, 6) a carbonyl value of 10 or less; 7) a volume resistivity of 1.times.10.sup.11.OMEGA.cm or more, 8) a hydroxyl value of 3 mgKOH/g or less, and 9) a water content of 100 ppm or less, a process for preparing the same and a refrigerator lubricating oil comprising the diester.