The peculiarities of induced magnetic anisotropy and magnetization reversal processes of single-layer and 10 to 200-nm-thick multilayer Fe20Ni80 films, which were prepared by oblique angle deposition, have been studied. In-plane uniaxial magnetic anisotropy has been found for all single-layer films. Upon deposition of multilayer films, the substrate holder was rotated by 90° before the deposition of each of the subsequent layers. The axis of the resulting magnetic anisotropy was found to make an angle of 45° with the magnetic anisotropy axes of individual layers. The magnetization reversal processes in the samples are considered taking into account both the coherent magnetic moment rotation and the nucleation of reverse magnetization domains and domain wall motion.