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A model that describes the magnetic behavior of nanocrystalline ring cores is useful for simulations of electronic circuits that contain inductors or transformers using these cores. A general but computationally demanding model combines a macroscopic model of the ribbon with a dynamic Preisach hysteresis model. In this paper, we present two models that-taking into account the principle of loss separation-make it possible to avoid the use of the CPU time consuming dynamic Preisach model. Both models compute the waveform of the magnetic flux density for an arbitrary waveform of the magnetic field, or vice versa. The first model uses a macroscopic model based on the plane wave theory and the classical rate-independent Preisach formalism. The macroscopic model operates in the frequency domain and applies the harmonic balance principle. Because of nonlinearity, the model is solved iteratively by a Newton-Raphson scheme. The second model starts from a single evaluation of the classical Preisach model. Additionally, it uses a lookup table that is a function of the flux density and its time derivative to evaluate the classical and excess field to be added. The models are validated by measurements between 2 and 100 kHz on Vitroperm nanocrystalline ring cores.