The coherent anisotropy and the magnetostriction constants A, were studied in amorphous r.f. sputtered (Co,Zr,) , , ( R E ) ? (RE = rare earth) thin films for a large variety of magnetic rare earth, and the concentration range 0 I x 13. During the deposition magnetic field of 700 Oe was applied in the film plane. For RE = Nd, Pr, Jly and Tb substitutions, a well defined in-plane uniaxial anisotropy is formed. K,, and A, both increase linearly with increasing RE content, the absolute values being related to the substitutional RE element. The magnitude of K,, correlates nicely with that of A,, in agreement with a theoretical computation based on asingle-ion anisotropy model for rare-earth atoms. When RE=Sm a more heterogeneous local magnetic structure forms as revealed by a biaxial anisotropy and the correlation between K,, and X, is no more observed.