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Abstract
The combination of short wavelengths and ultrahigh intensities as provided by the new soft and hard X-ray free electron laser sources opens the doorway to totally new experiments on photon-matter interaction. It concerns, in particular, new classes of nonlinear inner-atomic processes. In the present contribution, recent results on sequential and nonsequential multi-photon ionization of gas phase targets are presented and discussed; including processes where also inner shells are affected. Moreover, examples are given how linear and nonlinear photoionization may be used for online photon diagnostics at these new radiation sources.