Polycrystalline nickel films between 26 and 296 Å in thickness were obtained by evaporation at normal incidence from tungsten filaments onto microscope‐slide glass substrates maintained at 75°C, at pressures between 6×10−10and 12×10−10Torr. In the same vacuum the substrates with their films were arranged to be parts of an automated torsion magnetometer in which the sample rotated about an axis in its own plane perpendicular to the magnetic field. Measurements were made of the torque as a function of the magnetic field required to maintain the plane of the sample at various fixed angles &thgr;0ranging from 3° to 84° with respect to the magnetic field, at sample temperatures of about 300°, 77°, and 4.2°K. The torque data were analyzed by a new method which permits detailed investigation of models for the magnetization. It is shown that for a single‐domain model with an out‐of‐plane uniaxial anisotropy, the saturation magnetizationMSand the total anisotropy fieldScan be calculated from the magnitude and slope of the torque/field curve at any field strengthH′and any angle &thgr;0. The single‐domain model was verified for four samples with thicknesses of 87, 109, 182, and 296 Å. For these samples, bothMSandSwere independent ofH′and &thgr;0. This shows that for films thicker than 87 Å,MSis independent of thickness within the experimental error of ±2&percent;, and has the temperature dependence of bulk material, decreasing by 6.2±1.0&percent; between 4.2° and 300°K. The anisotropy field was completely accounted for by the shape demagnetizing field, and by magnetostriction and strain in nickel film. The torque data from the thinnest film, which was 26‐ Å thick and electrically discontinuous, did not fit the single‐domain model. The characteristic torque behavior of such very thin films probably indicates that they contain islands small enough to be superparamagnetic, This conclusion was supported by a theoretical analysis which showed that a film model consisting of identical, noninteracting, superparamagnetic particles does indeed give rise to torque curves like those of the 26‐ Å film. If such a superparamagnetic film is erroneously assumed to be a single domain, itsMSvalues appear to be less than the bulk values. Therefore, a detailed analysis of torque curve shapes is required to obtain reliable values forMS.