Anhysteretic magnetization is the magnetization that results if a constant bias field and an alternating field with decreasing amplitude are applied simultaneously to a ferromagnetic sample. Both anhysteretic magnetization and magnetization curves were measured on strips of iron shielding material in two cases where the product of the demagnetization factor and magnetization is much smaller than or comparable with the external field. The influence of demagnetizing fields on the measured effective anhysteretic permeability can be described neither by “normal’’ shearing of the magnetization curve nor by a dependence predicted by Ne´el for anhysteretic permeability. A crucial role in Ne´el’s theory is played by so-called “frozen magnetization.’’ During anhysteretic magnetization an increasing fraction of the magnetization ceases to follow the applied alternating field and remains fixed. Comparison with Preisach models suggests that deviation from normal behavior is connected with a gradual rather than an instantaneous buildup of frozen magnetization. It is concluded that Ne´el’s theory gives a qualitative but not a quantitative explanation of the dependence of anhysteretic permeability on demagnetizing fields in the material investigated. ©1997 American Institute of Physics.