An axial-gap rotary-electric machine which can rotate at a very high speed and can generate a large output and in which a gap is formed extending in the axial direction of the shaft. The rotary-electric machine comprises a rotor (12) and a stator (11). The rotor comprises a plurality of discs members (24-1, 24-2) made of fiber-reinforced plastic or nonmagnetic metal, and a plurality of groups (25) of permanent magnets embedded in said disc members (24-1, 24-2), forming a plurality of magnetic poles on said disc members (24-1, 24-2). Each of the groups (25) consists of a plurality of permanent magnets (25a). The stator (11) includes a casing (11A) and a first stator winding (16B). The casing (11A) comprises a frame (13), brackets (14-1, 14-2), back yokes (15-1, 15-2), and at least one second stator winding (16A-1, 16A-2) divided into a plurality of units in a radial direction.