The induced in‐plane and local magnetic anisotropies of rf sputtered (Co93Zr7)100−xRExthin films were investigated as a function of RE content for RE=Pr, Nd, and Tb by transverse biased initial susceptibility measurements at both film/air and glass/film interfaces. The deposition was performed in a magnetic field. The films exhibit a very well defined in‐plane anisotropy with negligible long‐range fluctuations and a small coercive fieldHc, in accordance with the experimental data. The overall variations of the transverse susceptibility are related to the ripple. The variations of the local anisotropy with composition were measured. Both the induced anisotropyKuand the local anisotropyKlocincrease with the increasing amount of RE in the layers. A clear relationship betweenKuandKloccould be established. The results are discussed in terms of the single‐ion anisotropy of the rare earth. While the value ofKuis the same at both interfaces, the ripple constants were found to be slightly different. This last result is believed to be related to some local defects, the origin of which is also suggested. Also the coercive force is discussed and explained in terms of a theoretical model. ©1996 American Institute of Physics.