A cooling apparatus of vehicle driving apparatuses of the invention controls flow of cooling water so as to cool engine cooling water by at least two radiators when a requested ability of cooling an internal combustion engine, is equal to or larger than a requested ability of cooling a hybrid device. The number of the radiators used for cooling the engine cooling water is larger than the number of the remaining radiator(s). The cooling apparatus controls the flow of the cooling water so as to cool device cooling water at least two radiators when the requested ability of cooling the hybrid device, is larger than the requested ability of cooling the internal combustion engine. The number of the radiators used for cooling the device cooling water is larger than the number of the remaining radiator(s).