This paper shows how asynchronous operation of a reluctance motor may be obtained by taking advantage of one of the properties of a series LCRcircuit, in which the inductance is a function of current. Parametric variation of the machine inductance is accomplished by variation of the rotor iron-circuit reluctance, instead of the more conventional change in air gap. These changes in reluctance are utilised in such a way that the circuit alternates between resonant and nonresonant states, with consequent variation in current amplitude. When the resonant state coincides with a positive rate of change of air-gap inductance with rotor position, and hence the nonresonant state with a negative rate of change, the net average torque developed is positive. The speed/torque characteristics are dependent upon applied voltage, series resistance and series capacitance, as well as the rotor geometry. Thus a simple variable-speed a.c. motor having no windings on the rotor is possible. Maximum average torque obtainable from such a machine at very low speeds is of the same order as that obtainable from the same machine running synchronously. A mathematical model is proposed for the machine, from which expressions for torque in terms of the machine and circuit parameters can be obtained. These lead to an equivalent circuit and the differential equations of motion, which are nonlinear with time-dependent coefficients, so requiring solution by numerical or analogue methods. Assumptions made when setting up the model and in subsequent simplifications have been tested experimentally and the results presented. These suggest that the proposed model will provide at least a qualitative indication of dynamic behaviour. All discussion and analysis applies equally well to linear motion provided the appropriate change is made in the `rotor' geometry. The problems of self starting and line-current fluctuation are briefly discussed, and possible solutions are suggested.