A power transmitting apparatus for transmitting power from a driving source of a vehicle to its wheels can be adapted to properly select transmitting or cutting-off of the driving force of the driving source to or from the wheels. The apparatus can comprise a torque converter having a torque amplifying function; a clutch mechanism including a first clutch device operable on advancement of the vehicle and adapted to transmit the driving force of the driving source to the wheels through a power transmitting system of the torque converter and a second clutch device adapted to transmit the driving force of the driving source to the wheels without the power transmitting system of the torque converter. A selecting device can be configured to operate the first clutch device and/or the second clutch device in accordance with operation modes of the vehicle, including starting.