Measurements of the complex initial permeability of several specimens of Mumetal (77% Ni, 14% Fe, 5% Cu, 4% Mo) have been made from 0-30 MHz. The samples were polycrystalline rings 50 μm in thickness; the mean grain size ranged from 9 μm to 140 μm. The results were analysed in terms of the domain model previously employed by the authors in 1969 and 1970, yielding the following main conclusions.Despite the low anisotropy (of order 100 erg cm−3), there exists a well-defined domain structure. Except near the surface, where the domain size is independent of grain size, the scale of the domain structure is found to be nearly proportional to crystallite size to the power 0·4.Some of this domain structure persists in polarizing fields as great as 20 times the coercive field. There is no evidence for an independent contribution to the permeability from rotational processes which, it is suggested, are instead strongly coupled to wall motion. There is evidence that the behaviour is beginning to be influenced by intrinsic spin phenomena at frequencies greater than about 30 MHz.