A fluid pump having a housing, a pair of rotors, a pair of rotor shafts for supporting the rotors in the housing, identical mating gears provided on the rotor shafts, and rotary drive for rotating the rotor shafts to rotate the rotors, and comprising a one-way clutch operatively connecting the rotary drive to the rotor shaft, a multiple-disc clutch operatively connecting the rotary drive to the other rotor shaft, and coils for generating a magnetic force by which the multiple-disc clutch is activated. When the multiple-disc clutch is not activated, rotation of the rotary drive is transmitted to the rotor shaft through the one-way clutch, and when the multiple-disc clutch is activated by the coils, rotation of the rotary drive is transmitted to the other rotory shaft through the multiple-disc clutch. By activating or inactivating of the multiple-disc clutch, it is possible to change the drive-driven relationship between the rotor shafts, so that a nonuniform wear of the mating gears is eliminated.