We have derived general equations to calculate intermodulation distortion in resonators with high temperature superconducting (HTS) films which are not restricted to a specific resonator shape and may be used whenever the fields in a resonator generate currents on the surface of one or more HTS films. These equations are applied to rutile-loaded cavities with one or two 10 × 10 mm² Y-Ba₂-Cu₃-O^7– endplates and are used to extract parameters characterizing the nonlinearities of these films from intermodulation measurements. Even though the films have similar small-signal performance, we have found large variation in the strength of their nonlinearities.