A torque fluctuation absorbing apparatus provided between a driving source and a transmission and transmitting torque from the driving source to the transmission, the apparatus absorbing fluctuations in the torque and limiting a maximum value of the torque, the apparatus includes a flywheel, a supporting member, a first plate having a sliding surface, a second plate having a sliding surface, a disc spring supported by the supporting member and biasing one of the first and second plates towards the other one thereof, a friction material sandwiched tightly between the sliding surface of the first plate and the sliding surface of the second plate, a damper mechanism connected to the friction material and transmitting the torque from the driving source to an input shaft of the transmission, and a cover member demarcating the sliding surfaces of the first and second plates from an exterior of the torque fluctuation absorbing apparatus.