The invention relates to a synchronous machine (1) including a stator (2) and a rotor (3). Said machine is provided with at least one sensor (1a) of the angular position of the rotor (3) and is characterized in that the stator (2) includes a winding provided such as to be supplied with polyphase current by an electronic power device. The rotor (3), which includes permanent magnets (4), is provided such as to rotate about the stator (2). The angular position sensor (1a) extends away from the rotor (3) and is in alignment with the latter at the permanent magnets (4). The angular position sensor (1a) includes at least two sensors (6) for measuring magnetic induction and are provided for detecting variation in the axial magnetic field of the rotor (3) in the form of voltage, and the angular position sensor (1a) moreover includes at least one electronic unit provided for receiving the voltages of the magnetic induction measurement sensors (6) such as to absolutely deduce therefrom the angular position of the rotor (3) and send corresponding information, in real time, to the electronic power device.