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This paper suggests a general method for analysis of a reciprocating self-excited induction generator based on the coupled finite-element/boundary-element method in a harmonic domain. The finite-element method is used for iron and copper parts in order to deal with nonlinearity and eddy currents, while the boundary-element method is utilized for the air-gap region between the moving parts using a free-space Green function that facilitates the application of a linear time periodic movement. The proposed method leads to a static global matrix that is symmetrical for particular boundary conditions. The results agree well with those obtained by the time-stepping methods.