In recent studies it has been shown how the effects of classical eddy current losses can be used to extend the quasi-static hysteresis model to account for the frequency dependence of hysteresis in electrically conducting media. This paper deals with the extension of the hysteresis model to include anomalous or excess losses. The instantaneous power loss due to eddy currents then consists of two terms, one of which depends on (dB/dt)/sup 2/ and the other one on (dB/dt)/sup 1.5/. The first term is the classical power loss and the second term, due to Bertotti, is the excess power loss. It is shown how these terms are incorporated into a time dependent hysteresis model. The main achievement is that a self-consistent model of hysteresis has been developed in which the quasi-static hysteresis curves are shown to be a limiting case of the more general frequency dependent model. >