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The modeling of an induction machine using a nonlinear magnetodynamic complex method coupled with the circuit equations is presented. The squirrel cage rotor is a polyphase circuit with connection between bars and end-rings. Eddy currents induced in the bars are important, and the end-ring resistances have a considerable influence on the reaction of the rotor. Normally, the effect of the end-ring is taken into account by calculating an equivalent conductivity on the bar, but in using this method an error is made on the distribution of induced current density in the bar of the rotor and the effect of the end-ring inductance is forgotten. An induction squirrel cage machine can be modeled using a formulation which combines the analysis of magnetic fields with electrical circuit equations taking the squirrel cage as a polyphase cycling circuit.