In the spectral range of the extreme ultraviolet at a wavelength of 13.3 nm, we have studied the photoionization of xenon at ultrahigh intensities. For our ion mass-to-charge spectroscopy experiments, irradiance levels from 10(12) to 10(16) W cm(-2) were achieved at the new free-electron laser in Hamburg FLASH by strong beam focusing with the aid of a spherical multilayer mirror. Ion charges up to Xe21+ were observed and investigated as a function of irradiance. Our surprising results are discussed in terms of a perturbative and nonperturbative description.