The latest developments in carbon nanotube (CNT) wires and yarns attract great interest for potential application to electromagnetic devices, such as electrical machines and transformers. The CNT material properties are largely different from copper and aluminum in terms of electrical conductivity, mass density, and thermal transfer, creating a new design paradigm for which the traditional rules and device topologies no longer apply. This paper proposes a brushless permanent magnet multidisc axial flux construction with coreless stator and special windings and minimal rotor back iron, as a suitable topology for CNT winding application. Specific analytical closed-form sizing equations, as a function of winding electric conductivity, machine dimensions, and operating speed/frequency, are derived and employed in a systematic comparative study over a range of kW power ratings and speeds between 1,000 and 10,000 rpm. The numerical study is complemented by 3D and 2D electromagnetic FEA. The results show that the designs with CNT windings may have substantially higher specific power per mass, particularly at high rotational speeds and/or supply frequency, where the combined effect of DC and AC conduction losses in the windings is significant. Index Terms-axial flux machine, coreless motor, sizing equations, carbon nanotube conductors, CNT wire, CNT yarn.