The magnetic behavior of some amorphous ferromagnets of composition Fe 80 − x R x B 20 (R being a rare-earth element) is investigated as a function of the external applied magnetic field and temperature using dc magnetic measurements. Random magnetic anisotropy is generated by dilution of rare-earth atoms in the Fe 80 B 20 ferromagnetic matrix. Hysteresis curves show a quasireversible behavior with very small coercivity and remanence, suggesting a weak random magnetic anisotropy. In the high-applied-field regime the samples show ferromagnetic saturation, and from the M values it is possible to conclude that the light rare-earth atoms (Ce, Nd) are ferromagnetically coupled with the iron atoms, whereas the heavy atoms (Gd, Dy) couple ferrimagnetically to the Fe moments. The temperature dependence of the magnetization has also been studied in the conventional spin-wave framework, and the values obtained for the spin-wave stiffness constant D are close to 100 meV A ˚ 2 , which is typical for this kind of material. In the low-applied-field and low-temperature regime a much more complex behavior is observed as a consequence of the competition between local random anisotropy and exchange interactions. The different dependence on T of the correlation length associated to the local random anisotropy and to the exchange interactions makes possible the existence of different magnetic orderings, but no phase transition is observed between them.