An in-vehicle power transmission apparatus is equipped with a plurality of power split rotors and a power transmission control mechanism. The power split rotors work to split power among a rotary electric machine such as a motor-generator, an internal combustion engine, and a driven wheel of the vehicle. If rotational energy, as outputted from the power split rotors, is defined as being positive in sign, the power split rotors are so assembled that when the power transmission control mechanism establishes transmission of the rotational energy that is positive in sign as the power from a first rotor that is one of the power split rotors to the internal combustion engine, the other power split rotors are so linked as to provide output rotational energies which are opposite in sign to each other. This enables the speed of the first rotor to be placed at substantially zero.