The brushless doubly fed reluctance machine (BDFRM) is related to the better known brushless doubly fed induction machine (BDFIM). Research into doubly fed machines is motivated by the fact that they allow the use of a partially rated inverter in many variable-speed applications. Research into the BDFRM has been largely ignored in comparison to the BDFIM, despite the fact that it has the potential for greater efficiency as compared to the BDFIM, and the rotor is simpler to manufacture. This paper compares the BDFRM and its singly fed cousin, the synchronous reluctance machine. This is a natural comparison since both machines use the same reluctance rotor. The first part of the paper establishes relationships between the inductances of the two machines. This is then used to facilitate a comparison using the constraints that both machines have the same amount of active material, i.e., the same amount of copper and iron, and that the copper losses for both machines are the same. This analysis also allows an approximate comparison with the conventional squirrel-cage induction machine. The analysis is carried out using machine-independent normalizations.