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In solid ferromagnetic parts of magnetic circuits, eddy currents occur during changes of the magnetic flux. Magnetic circuits of real devices may often be decomposed into parts having approximately rectangular or circler cross sections. As the solutions for phenomena in infinite configurations of such cross sections are known, we can use these for solving phenomena in more complicated arrangements. The method described in this paper is based on the use of Duhamel's integral. This method enables one to solve phenomena in such magnetic circuits, which are composed of both parts made of solid ferromagnetic materials and parts made of materials in which no eddy currents may occur. The method is convenient for transient phenomena but may also be used for cases with periodic non-sinusoidal exciting currents. Some examples are given.