A theory of the longitudinal susceptibility (response to an rf field applied parallel to the dc field) of magnetic materials with a nonuniform saturation magnetization is described. According to this theory the imaginary part of the longitudinal susceptibility, χ″, considered as a function of dc magnetic field, should show a maximum when the internal magnetic field is approximately equal to (ω/γ)‐π〈M0〉, where ω is the frequency, γ the gyromagnetic ratio, and 〈M0〉 the average saturation magnetization. The height of the absorption peak is calculated to be proportional to the degree of inhomogeneity (mean square deviation of the local saturation magnetization from its average) and approximately inversely proportional to the square of the frequency. The width of the absorption peak is approximately 2π〈M0〉. If the nonuniformity of the saturation magnetization is due to the presence of pores or nonmagnetic inclusions, the absorption at low dc fields (near remanence) is found to be proportional to the total cross‐sectional area of the inclusions (rather than their volume). Thus many small inclusions have a stronger effect than few large ones of the same total volume. The real part of the susceptibility is negative on the low‐field side, positive on the highfield side of the absorption peak. In most of the calculations, the effect of the inhomogeneity‐induced scattering of spin waves has been neglected. This scattering is shown to be substantially equivalent to an additional damping of the spin waves, which is strongly frequency and field dependent.