The interaction of intense vacuum-ultraviolet radiation from a free-electron laser with rare gas atoms is investigated. The ionization products of xenon and argon atomic beams are analyzed with time-of-flight mass spectroscopy. At 98 nm wavelength and approximately 10(13) W/cm(2) multiple charged ions up to Xe6+ (Ar4+) are detected. From the intensity dependence of multiple charged ion yields the mechanisms of multiphoton processes were derived. In the range of approximately 10(12)-10(13) W/cm(2) the ionization is attributed to sequential multiphoton processes. The production of multiple charged ions saturates at 5-30 times lower power densities than at 193 and 564 nm wavelength, respectively.