A power transmitting apparatus can be configured to restart an engine when the acceleration pedal is actuated in an assist-start engine speed range and can improve responsiveness of engine restart. Such a power transmitting apparatus of a vehicle can provided with a clutch for selectively transmitting or cutting off a driving power of an engine to wheels. The power transmitting apparatus can comprise an assist-controller configured to increase an engine rotational speed above an self-start rotational speed by actuating the clutch when the vehicle is decelerated and fuel supply to the engine is stopped, in response to operation of an acceleration pedal of the vehicle, when the engine rotational speed is in an assist-start range which is an engine rotational speed range lower than the self-start rotational speed and higher than a starter-start rotational speed in which the engine cannot be started by a starter.