A power transmitting apparatus on a four-wheel-drive motor vehicle can distribute and transmit drive power from a power unit to front and rear drive road wheels such that the rotational speeds of the front and rear drive road wheels can differ from each other. The power transmitting apparatus includes a casing rotatable by the drive power from the power unit, an output shaft disposed in the casing, first and second planetary gear mechanisms disposed between the casing and the output shaft, the first and second planetary gear mechanisms comprising first and second ring gears fixed to an inner periphery of the casing, first and second sun gears aligned with the first and second ring gears, respectively, first and second planet gears meshing with the first ring and sun gears and the second ring and sun gears, respectively, and rotatable about their own axes and the ring gears, and a planet carrier coupled to the output shaft, the first and second planet gears being rotatably supported on the planet carrier, the first and second planetary gear mechanisms having different speed-changing ratios, one of the speed-changing ratios being selected such that the rear drive road wheels rotate faster than the front drive road wheels, first and second clutches coupled respectively to the first and second sun gears, respectively, for selectively holding the first and second sun gears nonrotatable thereby to enable the first and second planetary gear mechanisms to transmit the drive power, and a pair of variable-torque-transmitting clutches coupled to respective ends of the output shaft.