An analysis and numerical estimates of induction effects in the metal of a flat circular solenoid located between the branches of an external bifilar coil in a flat inductor system excited by unidirectional currents in the bifilar windings are presented. Such a device, the design of which was first proposed earlier by the authors of this work, is of practical interest for circuits of equipment for magnetic-pulse processing of metals. The use of the considered inductor system makes it possible to minimize the influence of induction effects on electromagnetic processes in the metal of the internal inductor. Numerical estimates are obtained for the induced currents excited in the metal of the inner circular inductor placed between the outer windings of the bifilar coil. It is shown that in the low-frequency mode of acting fields, the time dependence of the excited current is a derivative of the time dependence of the exciting current and the transverse distribution of the current in the metal of the internal inductor is a linear dependence passing through the central axis of the inductor. In the high-frequency regime of acting fields, the time dependence and the radial distribution of the excited current coincide with the corresponding analogs for the exciting current, and the transverse distribution of the induced current is characteristic of a sharp surface effect, when the induced current is displaced to the boundary surfaces of the metal. It is proved that the minimum influence of the fields of the external bifilar on the electromagnetic processes in the internal inductor should be observed in the low-frequency mode, when the spatial superposition of multidirectional induced currents adds up to the zero value of the excited electromotive force of induction. The results of the analysis based on the specific calculations performed are aimed at finding the conditions for the successful technical implementation of the proposed inductor system. The creation of workable models of the proposed inductor systems and experiments to determine the real conditions for their maximum efficiency are seen as very promising in the direction of subsequent research.