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A time-domain method is presented to treat transient quasistatic electric problems if the permittivity depends on frequency. The inverse Fourier transform of the complex permittivity spectrum is used in a time-stepping procedure. The method is numerically realized using finite-element techniques. The approach is validated by assuming a frequency dependence having an analytical inverse transform. Thus, the frequency dependence of the permittivity of a real electroceramic material is determined from measurement results by curve fitting. An example using this curve illustrates the effect of the frequency dependence of permittivity on the time-domain solution.