A brushless rotary electric machine includes a stator having an annular armature core with first radial teeth at the outer periphery thereof and second radial teeth at the inner periphery thereof and an armature winding wound between the teeth, a rotor having a pair of first and second rotary cores disposed tandem in the axial direction thereof, and a field coil. Each of the first and second rotary cores has a pair of coaxial outer and inner cylindrical pole members respectively facing the first and second radial teeth, a center core and a disk member magnetically connecting the pair of coaxial cylindrical pole members and the center core. The stator is accommodated by a first space defined by the outer and inner cylindrical members of the pair of first and second rotary cores. The field coil is accommodated by a second space defined by the inner cylindrical pole member and the center core of the first and second rotary cores.