The present invention provides lubricant oil compositions comprising a polyalkylene glycol polycarbonate. The lubricant oil compositions are useful for industrial gear oil, automotive gear oil, and lubricant oil for refrigerators, rolling installations and fibers, which are excellent in lubricating properties and detergency. The present invention also relates to lubricant oil compositions which comprise a polyalkylene glycol polycarbonate having mutual solubility with an ozone layer-nondestructive Freon such as Freon R-134a, and which are accordingly especially suited for refrigerators using hydrogenated fluorocarbon as a refrigerant. A polyalkylene glycol polycarbonate according to the invention comprises a polyoxypropylene group in the molecular chain and an alkyl group and an alkyloxyalkylene group at the molecular terminals.; This invention provides a process for preparing said polyalkylene glycol polycarbonate wherein a polypropylene glycol and a carbonate are allowed to react, said reaction including condensation polymerization. The invention also provides a process without condensation polymerization for preparing a polyalkylene glycol polyol wherein a polyol and a carbonate is allowed to react in the presence of a basic catalyst while a produced alcohol is being distilled off, the catalyst is removed then, and the unreacted carbonate is eliminated.