A thin-film resonator structure has been used for quantitative measurements of ferromagnetic resonance foldover and the associated bistable power response for yttrium iron garnet (YIG) thin films. The resonator consisted of a 1-mm by 1-mm-square, 4.9-m-thick epitaxial YIG film on top of a 50m-wide, 3-mm-long microstrip transducer. A static magnetic field of 3200 Oe was applied perpendicular to the film. Loworder magnetostatic forward volume wave standing modes were excited at low power levels in the 020-dBm range and detected as resonance dips in reflected power versus frequency spectra over the range 4-5 GHz. At powers in the 0-to +15-dBm range, these dips showed foldover and bistable response characteristics for increasing and decreasing frequency or power sweeps. The use of 1-10-s-wide pulses instead of continuous-wave (CW) excitation resulted in the consistent disappearance of the foldover and bistability characteristics. The frequency sweep pulse data at fixed power reproduced the down-sweep CW results, and the pulse data for both increasing and decreasing power at fixed frequency reproduced the increasing-power CW results. A quantitative theoretical analysis demonstrates that observed foldover and bistable response characteristics are much weaker than predicted from the classical precession foldover mechanism proposed by Anderson and Suhl, in which the decrease in the static component of the magnetization drives the response. The up-sweep and down-sweep foldover frequency jumps both occur sooner than predicted by this classical mechanism and the calculated foldover profiles are much more severe than the data show.