Ferromagnetic resonance measurements between 4 and 300°K, of 81% Ni-19% Fe evaporated uncoated and Al-overcoated 50-1000-Å-thick films, at frequencies from 1 to 8 GHz, with the static magnetic field parallel and perpendicular to the film have been performed. The unprotected films exhibit the following anomalous low-temperature resonance characteristics: the onset of a resonance field shift below 80°K, unsymmetric resonance field hysteresis below 20°K, and a linewidth maximum near 80°K. The amplitude of all these effects varies with temperature and is inversely proportional to the film thickness. The resonance field shift of a 100-Å-thick film is as large as 200 Oe at 4°K. The Al-protected films, overcoated immediately after the evaporation of Permalloy, do not exhibit these anomalies, suggesting that these are caused by an oxide layer on the unprotected films. These results are in part explained by partial pinning of the bulk magnetization at the film-oxide interface. The characteristic temperatures are ascribed to critical transitions within the oxide. The extent of pinning at 4°K is consistent with an additional effective surface anisotropy energy of 0.07 erg/cm2. The resonance behavior is in part consistent with previous low-temperature hysteresis loop investigations. The complex nature of the oxide is described in the following paper.