The temperature dependence of the elastic moduli and the Mössbauer effect in Hox,Er1-x, Fe2 cubic Laves compounds (x, between 0.3 and 0.9) has been investigated in the temperature region where spin rotation occurs. The composition-dependence minima in the elastic moduli, and the Mössbauer effect measurements, were used to determine the boundaries between the various directions of easy magnetization in these compounds. The experimental spin orientation diagram was found to deviate from the predictions of a one-ion model based on the rare-earth ions alone. From the Mössbauer effect measurement it was deduced that in compounds for which a spin reorientation was observed, the spin rotates continuously with temperature between the major axes of the cubic symmetry. This was attributed to the contribution of higher-order magnetocrystalline anisotropy constants. The ΔE effect, measured in external magnetic fields up to 25 kOe, was found to be constant, and relatively small, in the holmium composition range of x = 0.45-1.00 in the HoxEr1-xFe2; compounds.