The Brushless Doubly Fed Reluctance Machine (BDFRM) is a form of slip recovery machine that allows a smaller inverter to be used if the speed range required is limited. Therefore in many applications it may lead to a significant reduction of the drive cost. Owing to its brushless property and the use of a cageless rotor, the BDFRM is more mechanically robust and more reliable than an induction machine and offers a prospect of higher efficiency and simpler control with respect to its competing and closely related doubly fed brushless induction machine. This paper will present a comprehensive theoretical study of the BDFRM performance limitations when fed by an inverter. In order to justify the consideration of this machine, a comparison with a more traditional synchronous reluctance machine (SYNCREL) will be made.