It is shown that a single reluctance-machine rotor can be made to operate in magnetic fields with differing numbers of poles. A general theory of performance for machines withppairs of segments andMpmagnetic pole pairs is developed. This theory is fully supported by the results of measured performances (a) for a range of rotors at one pole number and (b) for a single rotor operated in stator fields havingM= 1, 2, 3 and 4. Performance figures are predicted for machines with pole numbers in the ratio 2:4:6:8, and it is shown that, at each pole number, rotor proportions can be chosen so as to give power outputs equal to those that would be achieved with normal single-speed reluctance machines. The associated power factors and efficiencies are also good. Further, for the great majority of all the possible speedcombinations, substantially the same levels of performance can be maintained. It is concluded that individual studies of designs for particular speed combinations and load duties are justified and would result in industrially acceptable multispeed reluctance machines.