The variation of the fall-back angle ergo of evaporated Permalloy films due to the magnetic anneal was measured on restricted small areas of films in the composition range from 50 percent Ni to 95 percent Ni. The magnitude of the random anisotropy of crystallites was indirectly evaluated by using the dispersion theory of Hoffmann. For films deposited in a conventional vacuum (

torr), the compositional dependence of the random anisotropy agrees satisfactorily with that of modified Doyle-Finnegan\´s model so far as the Ni concentration exceeds 70 percent. Here the modification is made, taking into consideration that the uniaxial anisotropy of each crystallite fluctuates spatially, depending upon its crystallographic orientation. The deviation of the experiments from the theory in the case of Ni concentration less than 70 percent may be partly due to the magnetostrictive contribution through the anisotropic planar stress in crystallites. For films prepared in an ultra-high vacuum ( <10
-7tort), on the other hand, any stress effect does not seem to play an important role to the random anisotropy.