Of the two main groups of electrical machines, those with alternating, mostly rotating, and those with pulsating, mostly swinging, fields, the second has advanced more rapidly in recent years. A variety of new inductor-type machines have been developed for telecommunication and industrial purposes. The paper suggests that, instead of attempting to adapt the rotating-field theory to pulsating-field machines, it is more satisfactory to employ an independent theory developed by finding an expression for the pulsating permeance of the magnetic path and considering the total m.m.f. acting upon that permeance, both on open-circuit and on load. A new method for determining rapidly the air-path permeance as a function of time leads to the “belt characteristics,” thence to the e.m.f. and its waveform on open-circuit, to the armature reaction including its effect on the waveform, and to the necessary excitation for a given load. The analytical results are supplemented by simple vector diagrams. The means for controlling the waveform are then discussed, among them a new device for eliminating undesirable odd harmonics in addition to the even harmonics. Finally, suggestions are made for simplifying the work in design offices by standardizing the most favourable slotting and the corresponding characteristics.