In the paper it is shown that a reluctance-machine rotor of the conventional salient-pole type can be successfully operated, not only with a stator winding developing the same number of magnetic poles as the rotor has salient poles, but also with a winding developing twice this number. The mode of operation at the lower speed is explained in the light of a recently described machine,¹ in which salient poles are replaced by peripheral segments. The theory of low-speed operation is developed, and calculated results of performance are shown to be in good agreement with experimentally obtained values for a number of different machines. It is concluded that, for a single-winding two-speed machine, it is possible to design for either equal torques or, with mesh connection, equal powers at both speeds. Good efficiencies and approximately equal power factors are possible at both speeds.