Experiments are reported in which (1) the resistivity has been measured as a function of the angle between the magnetic field direction and the current direction and as a function of the thickness in 82% Ni‐18% Fe thin films, (2) the ferromagnetic resistance anisotropy in these films has been measured as a function of thickness, (3) the anisotropy in the fractional magnetoresistance has been measured as a function of thickness in these films, and (4) the anisotropy in the fractional magnetoresistance of films ranging in composition from 65% Ni‐35% Fe to 92% Ni‐8% Fe has been measured. The angular dependence of the resistivity agreed with theoretical predictions, provided suitable values are assumed for the mean free path and bulk resistivity of the films. The ferromagnetic resistance anisotropy appears to be independent of film thickness in the range from 75 to 2500 Å. The anisotropy in fractional magnetoresistance is lower than in bulk due to an abnormally high value for the resistivity of the zero magnetostrictive films studied. Nonzero magnetostrictive films also exhibit anomalies when the anisotropy in fractional magnetoresistance is compared with that in bulk material. A simple analytic expression relating these resistance anomalies to the magnetostriction parameter for the films is explained in terms of the magnetostriction of the films and the fact that they are attached to the substrate.