The magnetic and optical anisotropies observed in oblique-incidence Permalloy films show anomalousbehavior for incidence angles greater than 60° (grazing incidence). In particular, the easy axis and thedirection of greatest optical absorption are parallel to the vapor beam for incidence angles greater thanabout 70°, while they are perpendicular to this direction for smaller angles. The anomalies for grazing-incidencefilms are caused by a shape anisotropy differing from that previously found in lower angle oblique-incidencefilms. This new shape anisotropy is attributed to the elongation in the beam direction of theparticles composing the crystallite chains which are found in all oblique-incidence films; such shape anisotropyhas been directly observed by electron microscopy.