The coherent anisotropy and the magnetostriction constants /spl lambda//sub s/ were studied in amorphous RF sputtered (Co/sub 93/Zr/sub 7/)/sub 100-x/(RE)/sub x/ (RE=rare earth) thin films for a large variety of magnetic rare earth, and the concentration range 0/spl les/x/spl les/3. During the deposition magnetic field of 700 Oe was applied in the film plane. For RE=Nd, Pr, Dy and Tb substitutions, a well defined in-plane uniaxial anisotropy is formed. K/sub u/ and /spl lambda//sub s/ both increase linearly with increasing RE content, the absolute values being related to the substitutional RE element. The magnitude of K/sub u/ correlates nicely with that of /spl lambda//sub s/, in agreement with a theoretical computation based on a single-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/sub u/ and /spl lambda//sub s/ is no more observed. >