The theory, measurement and interpretation of frequency-dependent susceptibility (Xfd) are examined. A new model is proposed which explains Xfd in terms of the behaviour of all superparamagnetic grains (SP) with diameters between 0 and ~0.03 um. The model predicts maximum Xfd percentage values of 14-17 per cent for spherical SP ferrimagnetic grains in the grain size range 0.01-0.025 um, and a maximum value of 10-12 per cent for grain assemblages spanning a wider range of grain sizes (0-0.03 um). Synthetic and experimental data support the model predictions in terms of both maximum Xfd percentage values and the relationship between Xfd percentage and mass specific Xfd, which exhibits an envelope of data points partly related to grain size distributions within the SP range. When the Xfd percentage is at a maximum, the mass specific Xfd term can be used to estimate the concentration of SP grains in a sample. Lower values of Xfd percentage in soils are caused by the presence of narrow distributions of ultrafine SP grains, frequency-independent stable single and multi-domain ferrimagnetic grains. Some soils with low susceptibilities may have low Xfd percentages because of an appreciable content of paramagnetic and canted antiferromagnetic minerals. A simple mixing model predicts proportions of SP grains in mixed grain assemblages, but model validation requiring further characterization of grain interaction and grain size distributions is needed before it can be applied to environmental data.