The properties of the coherent anisotropy, formed by applying a magnetic field in the film plane during deposition, were studied in amorphous (Co1-yZry)(100-x) (RE)(x) thin films, for various RE and deposition parameters. When RE = Pr,Nd,Dy and Tb an in-plane uniaxial anisotropy K-u is developed. The variations of K-u versus x, RE and measuring temperature are well explained by a single-ion anisotropy mechanism. The change of K-u with P-Ar and deposition temperature T-d was studied on Co95-xZr5DYx films and far 5<x<30. The variations of K-u with the P-Ar are due to an evolution of the local structure. K-u is maximum for the lowest T-d used (-100degrees>C) and its value decreases continuously when T increase. When x> 22 films with isotropic magnetic properties are obtained at T-d higher than T-crit = f(x). Structural investigations show that K-u is related to sites containing CoDy pairs. The data are explained by a model based on the bond orientational mechanism: In samples prepared at low T-d, K-u is related to the individual deformations of sites, while when thermal fluctuations are important, directional correlations of the sites are formed. The peculiar results obserled for RE = Sm and Gd are due to the inirinsic properties of these RE.