The invention discloses a synchronous motor and a power system for extended-range electric vehicles. The synchronous motor comprises a housing, a first stator, a second stator, a permanent-magnet outer rotor, an electro-magnetic inner rotor, a motor input shaft, a motor output shaft, and a Hall sensor. The first stator and the second stator are located in an inner cavity and fixed to the housing. The first stator surrounds the second stator. A gap is left between the first stator and the second stator, and a cooling water channel is arranged in the gap. The motor input shaft is directly connected with an output shaft of an internal combustion engine. The motor output shaft is connected with a decelerator. The motor input shaft, the inner rotor and the second stator form an electro-magnetic synchronous motor, and the electro-magnetic synchronous motor is a generator. The first stator, the outer rotor and the motor output shaft form a built-in permanent-magnet synchronous motor, and the built-in permanent-magnet synchronous motor is a drive motor. Integrated manufacture of a generator and a drive motor in an extended-range electric vehicle is realized, so that the size is decreased greatly, and the space in an engine cabin is saved. The synchronous motor has the advantages of no interference between the electric generator and the drive motor, high vibration resistance, good heat radiation performance, low cost and the like.