We report experimental evidence of nonlinear gyrotropic vortex core motion. Using soft x-ray transmission microscopy we observed the time-averaged dynamic response of a magnetic vortex core in a 2 mu m diameter, 100 nm thick permalloy (Ni80Fe20) disk as a function of the amplitude and frequency of an applied RF magnetic field. At lower amplitude fields a single resonance was observed, but two distinct resonances, above and below the low amplitude resonance frequency, were observed when higher amplitude fields were applied. The results are discussed in the context of a nonlinear vortex energy potential. (C) 2012 American Institute of Physics. [doi:10.1063/1.3678448]