This technical report reviews methods for measurement of the magnetic loss of soft magnetic materials under the condition of magnetic polarization which includes higher harmonic components. Nowadays, by computer aided testing (CAT), a.c. magnetic properties of electrical steel sheets can be measured under various measuring conditions automatically. For example, the magnetic loss in the presence of higher harmonic frequency components of magnetic polarization can be measured using the arbitrary waveform synthesizer, digitiser and computer. The present standard methods (IEC 60404-2, IEC 60404-3 and IEC 60404-10) for the determination of specific total loss are restricted to the sinusoidal waveform of magnetic polarization, and these standards are still important for the characterization of core materials. However, actual waveforms of magnetic polarization in the electrical machines and transformers always include higher harmonic polarizations, and nowadays electrical machines can be designed using numerical methods including higher harmonics. But for these conditions, there is still no standard testing method.