The brushless doubly fed induction machine (BDFIM) has been extensively researched for approximately 30 years, but a related machine [the brushless doubly fed reluctance machine (BDFRM)], has not. This was mainly due to the fact that reluctance rotor designs were not capable of generating saliency ratios large enough to make the BDFRM competitive with other machines. However, recent developments in reluctance rotors, spurred on by research into synchronous reluctance machines, has resulted in high saliency ratio rotors that are economic to build. This, together with the promise of higher efficiency and simpler control compared to the BDFIM, means that further investigation of the BDFRM is warranted. A relatively limited amount of work to date has been published on the BDFRM. This paper attempts to fill this void by presenting a theoretical analysis of some of the important control properties of the ideal BDFRM.