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The partial element equivalent circuit (PEEC) method is a widespread numerical method for creating full-wave models of interconnection structures in the frequency and time domains for use in modeling EMC problems. The possible instabilities of time domain solutions-so-called late time instabilities-can complicate the use of the method. Several attempts to improve the stability of time domain solutions have been made in the literature. A new mathematically correct approach for analyzing the stability of PEEC circuits is presented in this paper. The reason for instabilities is discovered, and a method for stability improvement is developed and tested.