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The theory, measurement and interpretation of frequency-dependent susceptibility (χ_FD) are examined. A new model is proposed which explains χ_FD in terms of the behaviour of all superparamagnetic grains (SP) with diameters between 0 and ≈0.03 μm. The model predicts maximum χ_FD percentage values of 14–17 per cent for spherical SP ferrimagnetic grains in the grain-size range 0.01–0.025 μm, and a maximum value of 10–12 per cent for grain assemblages spanning a wider range of grain sizes (0–0.03 μm). Synthetic and experimental data support the model predictions in terms of both maximum χ_FD percentage values and the relationship between χ_FD percentage and mass specific χ_FD, which exhibits an envelope of data points partly related to grain-size distributions within the SP range. When the χ_FD percentage is at a maximum, the mass specific χ_FD term can be used to estimate the …