To reduce the problems involved in the design of magnetrons of low voltage and power for operation at frequencies of the order of 10000Mc/s and higher, a system is proposed in which the anode has only a few gaps, e.g. two or four. Operation at low anode voltage and magnetic field is achieved by electron interaction with the Fourier space components of the field.A convenient and simple embodiment is described, and factors likely to result in operation different from the conventional multiple-circuit magnetrons are analysed briefly. In particular, the modes of oscillation and the magnitudes of the components of the different possible spatial harmonics are discussed for two types of anode circuit.Details of operation of valves using both types of anode with two and four gaps are given, and comparisons are made where appropriate with the earlier analysis. The simple electrical structure of the two-gap anode enables a useful tuning range to be obtained by external-circuit adjustment, and some details of tuning performance are given.The paper concludes with comments on noise performance and speed of build-up of oscillations.