This article reports on a magnetometric study of the effects of diluted local random anisotropy in a ferromagnetic Fe80B20 amorphous matrix. In the low‐temperature and low‐field regime the samples, Fe74RE6B20 (RE=Nd, Ce), show a very rich behavior as a consequence of the competition between, and different dependence on T, of the correlation length associated with local random anisotropy and exchange interactions. In the high‐field regime (Happlied≥1.5 kOe) we observe ferromagnetic behavior with the saturation magnetization varying with temperature according to Bloch’s law. The spin wave stiffness constant D could be determined and lies close to 100 meVÅ2.