The electromagnetic response of a sphere and of a two-layer conducting earth placed in a rotating electromagnetic field is considered. A rotating electromagnetic field is generated by passing alternating currents of equal strength and frequency that are out of phase by 90 degrees through two identical, orthogonal coils, one horizontal and the other vertical. The resultant elliptically polarized primary field, whose ellipticity is a function of the spatial location, seems to have several advantages over the linearly polarized field ordinarily employed in the slingram method of airborne electromagnetic prospecting.The responses of the two models have been obtained under certain simplifying assumptions which hold in some cases of airborne electromagnetic prospecting. Based on the theoretical results, several master-charts have been plotted which may be used for the determination of parameters such as the shape, size, depth, and conductivity of the inhomogeneities from the field data. The principal advantages of the rotary field method over the conventional electromagnetic methods, such as its insensitivity to small variations in the separation between the transmitters and the receivers, and to small rotations along the direction of the flight path, and automatic cancellation of the primary fields at the receivers, make it possible to measure the 'pure anomaly,' and to use much greater transmitter-receiver separation than in the conventional methods. The main disadvantages of this system are noise and the inability to map closely spaced anomalous bodies.