Abstract: A lubricant composition for a wet clutch or a wet brake is disclosed, which comprises a base oil having added thereto an inorganic phosphorus compound which may contain sulfur atoms and/or oxygen atoms as its constituent elements, or an amine salt thereof, or having added thereto said inorganic phosphoric compound or an amine salt thereof, and an organic polyol compound having at least two hydroxyl groups in one molecule. The composition which exhibits excellent frictional properties in a wet clutch or a wet brake, in particular, provides a high .mu.d (dynamic friction coefficient) and a high .mu.s (static friction coefficient), shows good prevention of vibration in a lock-up clutch (which is imparted with good durability for preventing such vibration, has friction coefficients free from the temperature dependence, and is effective as a shock absorber oil, a power steering oil, a hydraulic suspension oil, etc.