The paper reports a theoretical and experimental study of the nonlinear spin-wave resonance (SWR) modes in normally magnetized ferrite films. Particular attention is focused on the principal, lowest frequency, SWR mode. It is shown theoretically that, as the precession amplitude increases, the profile of the principal mode changes to make the excitation distribution across the film thickness more uniform. The nonlinear shift of the resonance field depends on the surface-spin pinning parameters. An experimental study has been made of YIG films with a strong uniaxial anisotropy field gradient over the film thickness, as well as of YIG films of submicron thickness. As the microwave power was increased, the principal-mode resonance field was observed undergoing a sublinear shift accompanied by a superlinear growth of absorbed power. This behavior is attributed to a change in the profile of the spatial distribution of ac magnetization.